Full course modules on the lives and work of mathematicians and physicists, each a biography and a technical course with exercises. 337 modules so far; names in each module link to the others.
Before the chart: Archytas of Tarentum (428 BC–350 BC), Plato (428 BC–347 BC), Eudoxus of Cnidus (390 BC–338 BC), Aristotle (384 BC–322 BC), Euclid (325 BC–265 BC), Aristarchus of Samos (310 BC–230 BC), Archimedes (287 BC–212 BC), Eratosthenes (276 BC–194 BC), Apollonius of Perga (240 BC–190 BC), Hipparchus (190 BC–120 BC), Claudius Ptolemy (100–170), Diophantus of Alexandria (200–284), Pappus of Alexandria (290–350), Hypatia of Alexandria (360–415), Proclus (412–485), Aryabhata (476–?), John Philoponus (490–570), Brahmagupta (598–?), Muhammad ibn Musa al-Khwarizmi (780–850), Ibn al-Haytham (965–1040), al-Biruni (973–1048), Ibn Sina (980–1037), Omar Khayyam (1048–1131), Fibonacci (1170–1240), Nasir al-Din al-Tusi (1201–1274), Jean Buridan (1300–1360), Madhava of Sangamagrama (1340–1425).
Pythagorean mathematician and general of Tarentum who defined the three musical means, proved that superparticular ratios have no mean proportional, and gave the first solution of the doubling of the cube.
geometry, theory of proportion, music theory
Athenian philosopher who founded the Academy, the centre of Greek mathematics in the fourth century BC, and whose Timaeus built a cosmos from ratios and the five regular solids.
philosophy, philosophy of mathematics, cosmology
Greek mathematician and astronomer who created the theory of proportion and the method of exhaustion preserved in Euclid's Elements, and the first geometrical model of planetary motion.
geometry, theory of proportion, astronomy
Greek philosopher and student of Plato who founded the Lyceum and wrote the first systematic treatises on motion, the cosmos, formal logic, zoology and meteorology, which framed natural science until the Scientific Revolution.
natural philosophy, physics, cosmology
Greek mathematician of Alexandria whose Elements organized the geometry and arithmetic of his predecessors into the model of an axiomatic deductive science.
geometry, number theory, optics
Greek astronomer of the third century BC who proposed that the Earth rotates and orbits a motionless Sun, and whose surviving treatise measured the sizes and distances of the Sun and Moon by geometry.
astronomy, geometry
Greek geometer of Syracuse who measured areas and volumes of curved figures by exhaustion and founded statics and hydrostatics.
geometry, mechanics, hydrostatics
Hellenistic scholar and head of the Library of Alexandria who measured the circumference of the Earth, drew a gridded world map, founded scientific chronology and gave his name to the prime-number sieve.
geography, geodesy, number theory
Hellenistic geometer, called the Great Geometer in antiquity, whose eight-book Conics named and systematized the ellipse, parabola and hyperbola and who proved the theorem on planetary stationary points.
geometry, conic sections, astronomy
Greek astronomer of the second century BC who built the first known chord table, fitted geometric models of the Sun and Moon to observations, bounded the Moon's distance, compiled a star catalogue and discovered the precession of the equinoxes.
astronomy, trigonometry, geography
Alexandrian astronomer of the second century AD whose Almagest set out the geocentric models, chord table and star catalogue that governed astronomy until Copernicus and Kepler.
astronomy, trigonometry, geography
Alexandrian author of the Arithmetica, whose rational solutions of indeterminate equations founded algebraic notation and Diophantine analysis.
arithmetic, algebra, number theory
Alexandrian geometer whose Mathematical Collection preserved much of Greek geometry and contains the hexagon theorem, the cross-ratio lemma and the centroid rule for solids of revolution.
geometry, projective geometry, mechanics
Alexandrian mathematician, astronomer and Platonist teacher who revised the text of Ptolemy's Almagest and was killed by a Christian mob in 415.
astronomy, mathematics, Neoplatonic philosophy
Neoplatonist head of the Athenian school whose Commentary on the First Book of Euclid's Elements is the main source for early Greek geometry and contains an influential attempted proof of the parallel postulate.
philosophy, history and philosophy of mathematics, geometry
Author of the Aryabhatiya (499), the earliest surviving Indian mathematical-astronomical treatise by a named author, with a sine table, the kuttaka method, pi as 3.1416 and a rotating Earth.
astronomy, mathematics, trigonometry
Alexandrian Christian commentator on Aristotle who proposed an impressed force for projectiles, argued that falling times barely depend on weight, defined place as extension, denied the aether, and argued from the infinite that the world had a beginning.
natural philosophy, mechanics, cosmology
Author of the Brāhmasphuṭasiddhānta (628), which gave the first systematic rules for zero and negative numbers, a general quadratic rule, the composition law for x² − Ny² = k, and formulas for cyclic quadrilaterals.
astronomy, mathematics, algebra
Baghdad scholar whose book on al-jabr founded algebra as the systematic solution of equations, whose arithmetic carried Indian decimal numerals and his name (algorithm) to Europe, and who compiled the Zij al-Sindhind and a coordinate geography of the world.
algebra, arithmetic, astronomy
Scholar of Basra and Cairo whose Book of Optics founded the intromission theory of vision on experiment and geometry, and whose Doubts concerning Ptolemy demanded physically realizable planetary models.
optics, astronomy, mathematics
Khwarazmian polymath who measured the Earth's radius from a hilltop, determined longitudes from eclipse timings, systematized trigonometry for astronomy in the Mas'udic Canon, and wrote the classic medieval study of India.
astronomy, trigonometry, geodesy
Persian physician and philosopher whose Book of the Cure recast Aristotelian physics, including a theory of imparted inclination (mayl) for projectiles, and whose Canon of Medicine organized medicine as a science and was taught in Europe for five centuries.
natural philosophy, medicine, logic
Persian mathematician and astronomer who classified and solved cubic equations by intersecting conics, helped design the Jalali calendar, and analysed Euclid's parallel postulate.
algebra, geometry, astronomy
Pisan merchant mathematician whose Liber abaci taught Europe the Hindu-Arabic numerals and Arabic algebra, and whose Book of Squares is the outstanding medieval European work of number theory.
arithmetic, algebra, number theory
Persian scholar who devised the Tusi couple and equant-free planetary models, made trigonometry an independent discipline, and directed the Maragha observatory.
astronomy, trigonometry, geometry
Paris arts master who named and developed the theory of impetus, a motive power growing with quantity of matter and speed, weighed the daily rotation of the Earth, and wrote the most widely taught nominalist logic of the late Middle Ages.
natural philosophy, mechanics, logic
Founder of the Kerala school, credited by his successors with the infinite series for π, the arctangent, the sine and the cosine, with end-correction terms, two and a half centuries before their European rediscovery.
astronomy, mathematics, infinite series
Fifteenth-century German astronomer who completed the Epitome of the Almagest, wrote the first European textbook of trigonometry and founded one of the first scientific printing presses.
astronomy, trigonometry, mathematical tables
Canon of Warmia whose De revolutionibus (1543) set the Earth in motion around the Sun and fixed the order and relative distances of the planets.
astronomy, mathematics, medicine
Self-taught Venetian abacus master who independently found the solution of the cubic in 1535, founded mathematical ballistics, and made the first translation of Euclid's Elements into a modern European language.
algebra, ballistics, mechanics
Renaissance physician and polymath whose Ars Magna published the solutions of the cubic and quartic and the first computations with square roots of negative numbers, and who wrote the first book on the mathematics of chance.
algebra, probability, medicine
Bolognese engineer whose L'Algebra (1572) gave the first rules for calculating with complex numbers, resolved the irreducible case of the cubic, and introduced Diophantus's problems to Western readers.
algebra, complex numbers, number theory
French lawyer and royal councillor who introduced letters for known quantities, founding symbolic algebra and the theory of equations.
algebra, theory of equations, trigonometry
Elizabethan physician whose De Magnete (1600) showed that the Earth is a great magnet and first distinguished electrical from magnetic attraction.
magnetism, electricity, geomagnetism
Danish nobleman whose observatory on Hven produced the most accurate naked-eye observations ever made, who showed the new star of 1572 and the comet of 1577 lay beyond the Moon, and whose data made Kepler's laws possible.
astronomy, astronomical instrumentation, alchemy
Flemish engineer who popularized decimal fractions and founded modern statics and hydrostatics.
arithmetic, algebra, statics
Scottish laird and theologian who invented logarithms, published in 1614, and the calculating rods known as Napier's bones.
logarithms, spherical trigonometry, calculating devices
Founder of the mathematical science of motion and of telescopic astronomy, condemned by the Roman Inquisition in 1633 for defending the Copernican system.
mechanics, astronomy, strength of materials
Discoverer of the three laws of planetary motion and founder of modern optics, who made astronomy a physical science.
astronomy, optics, mathematics
Minim friar who established the laws of the vibrating string, gave his name to the primes 2^p − 1, and ran the correspondence network at the centre of European science in the 1630s and 1640s.
acoustics, music theory, number theory
Lyon engineer and architect whose 1639 Brouillon project on conics founded projective geometry and whose theorem on perspective triangles underlies the foundations of geometry.
projective geometry, perspective, architecture
Philosopher and mathematician who joined algebra to geometry, published the sine law of refraction and the theory of the rainbow, and built a mechanical physics of inertia and vortices.
analytic geometry, algebra, optics
Jesuate friar and Bologna professor whose method of indivisibles, with Cavalieri's principle and the quadrature of the higher parabolas, prepared the integral calculus.
geometry, method of indivisibles, logarithms and trigonometry
Holder of the Ramus chair at the Collège Royal who squared the cycloid, drew tangents by composing motions, integrated powers and the sine, and invented the Roberval balance.
geometry, method of indivisibles, kinematic geometry
Magdeburg engineer and burgomaster who invented the air pump and demonstrated atmospheric pressure with the Magdeburg hemispheres.
pneumatics, vacuum physics, electrostatics
Toulouse magistrate whose letters founded modern number theory, co-founded analytic geometry and probability, anticipated differential calculus and introduced the principle of least time.
number theory, analytic geometry, calculus
Galileo's successor at the Medici court who invented the mercury barometer, found the law of efflux, and showed that an infinitely long solid can have finite volume.
geometry, mechanics, hydrodynamics
Savilian Professor of Geometry at Oxford whose Arithmetica infinitorum extended quadrature to fractional powers, gave the infinite product for π and led Newton to the binomial series.
analysis, infinitesimal methods, number theory
Mathematician, physicist and writer who proved the hexagram theorem, built the Pascaline, established atmospheric pressure, co-founded probability theory with Fermat, and wrote the Provincial Letters and Pensées.
projective geometry, probability, combinatorics
Observational astronomer who discovered four moons of Saturn and the Cassini division, measured planetary rotation and the solar parallax, and founded a dynasty that directed the Paris Observatory.
astronomy, planetary science, geodesy
Anglo-Irish experimental philosopher who, with Robert Hooke's air pump, established the law of pressure and volume and argued for a corpuscular, experimental chemistry.
pneumatics, chemistry, natural philosophy
Dutch mathematician and physicist who invented the pendulum clock, discovered Titan and the ring of Saturn, founded probability theory in print and proposed the wave theory of light.
mechanics, optics, astronomy
First Lucasian Professor of Mathematics at Cambridge, whose geometric lectures proved that tangent and area problems are inverse to each other.
geometry, calculus, optics
English mathematician and astronomer who rectified the cycloid, stated the law of elastic collision and proved the hyperboloid ruled, then became the architect of St Paul's Cathedral and of London rebuilt after the Great Fire.
geometry, astronomy, mechanics
English experimental philosopher, the Royal Society's first Curator of Experiments, author of Micrographia and of the law of elasticity, and an architect of London's rebuilding after the Great Fire.
experimental physics, elasticity, microscopy
Author of the laws of motion and universal gravitation in the Principia, co-inventor of the calculus, and founder of the modern theory of colours.
mechanics, gravitation, calculus
Danish astronomer who showed from the eclipses of Io that light travels at a finite speed, invented the transit instrument and meridian circle, and standardized Danish weights, measures and the calendar.
astronomy, optics, instrument making
Co-inventor of the calculus and author of its notation, discoverer of vis viva, advocate of binary arithmetic and of a relational theory of space and time.
calculus, combinatorics, logic
First Astronomer Royal, founder of the Royal Observatory at Greenwich and compiler of the British Catalogue of 2,935 stars.
astronomy, positional astronomy, lunar theory
Basel mathematician who helped develop Leibniz's calculus, introduced the Bernoulli numbers and proved the first law of large numbers in Ars Conjectandi.
probability, calculus, infinite series
Astronomer who predicted the return of the comet that bears his name, financed and published Newton's Principia, and founded the life table and the magnetic chart.
astronomy, celestial mechanics, geophysics
Huguenot exile in London who found the normal approximation to the binomial distribution, the formula (cos x + i sin x)^n = cos nx + i sin nx, and the first practical mathematics of life annuities.
probability theory, analysis, actuarial science
Jesuit mathematician and logician whose Euclides ab omni naevo vindicatus (1733), meant to prove the parallel postulate, derived the first systematic theorems of hyperbolic geometry.
geometry, foundations of geometry, logic
Basel mathematician who developed and taught Leibniz's calculus, posed the brachistochrone problem and taught Leonhard Euler.
calculus, differential equations, calculus of variations
English mathematician of Newton's circle who published the Taylor series and the calculus of finite differences in 1715, the first mathematical theory of the vibrating string, and a geometric theory of perspective.
calculus, finite differences, mathematical physics
Third Astronomer Royal, who discovered the aberration of light and the nutation of the Earth's axis.
astronomy, astrometry, optics
Scottish Newtonian whose Treatise of Fluxions gave a rigorous calculus, the integral test and the Euler–Maclaurin formula, and who found the equilibrium figures of rotating fluid bodies.
calculus, analysis, geometry
French mathematician and philosopher who led the Lapland expedition that showed the Earth is oblate, proposed the principle of least action, and presided over the Berlin Academy.
geodesy, mechanics, variational principles
Basel physician and mathematical physicist who wrote Hydrodynamica, founded the kinetic theory of gases, introduced expected utility and built the first epidemic model.
fluid mechanics, kinetic theory, vibrations and acoustics
Presbyterian minister whose posthumous essay of 1763 gave the first solution of the problem of inverse probability, the origin of Bayesian inference.
probability theory, statistics, calculus
Printer and statesman whose one-fluid theory of electricity introduced conservation of charge and positive and negative, and who proved lightning electrical and invented the lightning rod.
electricity, atmospheric physics, oceanography
Natural philosopher who defended Leibniz's vis viva, wrote the Institutions de physique and produced the only complete French translation of Newton's Principia.
natural philosophy, mechanics, mathematics
The most prolific mathematician in history, who shaped modern analysis and notation, founded graph theory, and wrote the equations of rigid bodies and ideal fluids.
analysis, number theory, graph theory
Leading French Newtonian who derived the figure of the Earth from hydrostatics, resolved the motion of the lunar apogee and predicted the 1759 return of Halley's comet.
geodesy, celestial mechanics, differential geometry
French mathematician and philosopher who founded dynamics on d'Alembert's principle, solved the wave equation, and co-edited the Encyclopédie.
mechanics, partial differential equations, fluid dynamics
Self-taught polymath of the Berlin Academy who proved π irrational, founded photometry, introduced the Lambert map projections and developed the acute-angle hypothesis of the parallel problem.
number theory, geometry, cartography
Scottish physician and chemist who identified carbon dioxide (fixed air) by quantitative weighing and discovered specific heat and latent heat.
chemistry, physics of heat, calorimetry
Comet hunter who recovered Halley's comet in 1759, discovered Lexell's comet and compiled the catalogue of nebulae and star clusters whose M numbers are still in use.
astronomy, comets, nebulae and star clusters
English natural philosopher who isolated hydrogen, showed the composition of water, tested the inverse-square law of electricity, and weighed the Earth with a torsion balance.
experimental physics, electrostatics, gravitation
Dissenting minister and experimenter who isolated oxygen and many other gases, discovered that plants restore air, and inferred the inverse-square law of electric force.
chemistry, electricity, natural philosophy
French military engineer and physicist who measured the inverse-square law of electric force with his torsion balance and founded the classical laws of friction and earth pressure.
electrostatics, magnetism, applied mechanics
Scottish instrument maker and engineer whose separate condenser, rotative double-acting engine, parallel motion, governor and indicator transformed the steam engine and supplied the problems from which thermodynamics grew.
mechanical engineering, steam power, heat
Founder of analytical mechanics and the calculus of variations, discoverer of the Lagrange points, and author of the four-square theorem and the resolvent method that led to group theory.
calculus of variations, analytical mechanics, celestial mechanics
Bologna anatomist and physician whose frog experiments revealed animal electricity, founded electrophysiology and set Volta on the path to the pile.
anatomy, physiology, animal electricity
Musician turned astronomer who discovered Uranus and infrared radiation, built the largest telescopes of his age, showed that binary stars orbit each other, and founded the study of the structure of the Milky Way.
astronomy, optics, telescope making
Swedish pharmacist-chemist who discovered oxygen independently of Priestley, described chlorine, identified several new elements and isolated the first pure organic acids.
chemistry, pharmacy, photochemistry
Founder of quantitative chemistry who established the conservation of mass, the oxygen theory of combustion and the modern nomenclature, and with Laplace made calorimetry precise.
chemistry, calorimetry, physiology
Lombard physicist who invented the electrophorus, the condenser and the voltaic pile, the first source of continuous electric current.
electricity, electrochemistry, pneumatic chemistry
Creator of descriptive geometry and founder of the differential geometry of surfaces, who posed the optimal transport problem and helped found the École Polytechnique.
descriptive geometry, differential geometry, partial differential equations
Author of the Mécanique céleste, who established the stability of the solar system to first order, founded potential theory and made probability a science of inference.
celestial mechanics, potential theory, probability theory
Astronomer who discovered eight comets and several nebulae, reduced William Herschel's survey of the nebulae, indexed Flamsteed's catalogue, and was the first woman in England paid for scientific work.
astronomy, comets, star catalogues
French analyst who introduced Legendre polynomials, the Legendre transformation and symbol, stated quadratic reciprocity, first published least squares, and founded the theory of elliptic integrals.
number theory, elliptic integrals, calculus of variations
Loyalist soldier, Bavarian statesman and physicist whose cannon-boring experiments argued that heat is a form of motion, and founder of the Royal Institution.
thermal physics, heat transfer, photometry
Engineer, geometer and revolutionary statesman who founded the theory of machines, proved the law of energy loss in inelastic shocks, and organized the armies of the French Republic.
mechanics, geometry, foundations of calculus
Quaker teacher in Manchester who founded the chemical atomic theory, stated the law of partial pressures and gave the first scientific account of colour blindness.
chemistry, physics, meteorology
Physician turned chemist who made platinum malleable, discovered palladium and rhodium, first saw the dark lines of the solar spectrum, and invented the camera lucida and reflecting goniometer.
chemistry, metallurgy, optics
Founder of the mathematical theory of heat conduction, inventor of Fourier series and the Fourier integral, and the first to describe the atmosphere's warming of the Earth.
mathematical physics, heat conduction, Fourier analysis
Naturalist and physicist whose measurements in the Americas and worldwide magnetic network founded geomagnetism, isotherm climatology and plant geography.
geomagnetism, climatology, plant geography
Physician and polymath who established the principle of interference of light, introduced the modulus of elasticity, and proposed the three-receptor theory of colour vision.
physical optics, elasticity, physiological optics
French physicist who co-discovered the Biot–Savart law, founded polarimetry through the laws of optical rotation, and established the extraterrestrial origin of meteorites.
electromagnetism, optics, polarimetry
Founder of electrodynamics, who discovered the forces between electric currents in 1820 and gave them their first mathematical law.
electrodynamics, mathematics, chemistry
French engineer-physicist who discovered polarization by reflection, found the cosine-squared law of polarized intensity, and founded the geometric theory of ray systems.
optics, geometrical optics, polarization
Piedmontese physicist who proposed in 1811 that equal volumes of gases contain equal numbers of molecules and that elementary gases are polyatomic, the foundation of molecular formulas and of the constant that bears his name.
physics, chemistry, molecular theory
Self-taught French mathematician who proved the main nineteenth-century result on Fermat's Last Theorem before Kummer and won the Paris Academy prize for a theory of vibrating elastic plates.
number theory, elasticity, differential geometry
Founder of modern number theory and the intrinsic geometry of surfaces, and author of least squares, the normal law and Gauss's law.
number theory, algebra, differential geometry
Danish physicist and chemist who discovered in 1820 that an electric current deflects a magnetic needle, founding electromagnetism.
electromagnetism, physics, chemistry
Cornish chemist who used the voltaic battery to isolate potassium, sodium and the alkaline-earth metals, showed chlorine to be an element and invented the miner's safety lamp.
chemistry, electrochemistry, physics
French chemist and physicist who established the uniform expansion of gases and the law of combining volumes, isolated boron, named iodine and cyanogen, and founded precise volumetric analysis.
chemistry, physics, analytical chemistry
Swedish chemist who measured accurate atomic weights, introduced modern chemical symbols, discovered cerium, selenium and thorium, and named isomerism and catalysis.
chemistry, electrochemistry, mineralogy
Self-taught mathematician and science writer whose Mechanism of the Heavens brought Laplace's celestial mechanics into English and whose Connexion of the Physical Sciences prompted the coining of the word 'scientist'.
celestial mechanics, mathematical physics, physical geography
Prague priest and philosopher who gave the first rigorous definitions of continuity and convergence, proved the intermediate value theorem analytically, and anticipated modern logic and set theory.
real analysis, foundations of mathematics, logic
Scottish physicist who found the law of polarization by reflection, discovered stress birefringence and biaxial crystals, and invented the kaleidoscope and the lenticular stereoscope.
optics, polarization, crystal optics
Leading French mathematical physicist after Laplace, known for Poisson's equation, the Poisson bracket, the Poisson kernel and summation formula, and the Poisson distribution.
mathematical physics, celestial mechanics, potential theory
Founder of precision astrometry who measured the first stellar parallax and systematized the functions that bear his name.
astronomy, astrometry, geodesy
French engineer who first wrote down the general equations of elastic solids (1821) and of viscous fluids (1822), the latter now called the Navier–Stokes equations.
fluid mechanics, elasticity, structural engineering
Astronomer and physicist who discovered chromatic polarization and magnetism of rotation, championed Fresnel's wave theory, led the Académie des sciences and abolished slavery in the French colonies as minister in 1848.
astronomy, optics, electromagnetism
Bavarian optician who mapped the dark lines of the solar spectrum, introduced the diffraction grating for measuring wavelengths, and made the finest achromatic telescopes of his time.
optics, spectroscopy, optical glass and instrument making
Civil engineer who made the wave theory of light quantitative, explaining diffraction, polarization and double refraction, and invented the lighthouse lens.
physical optics, wave theory of light, engineering
Engineer officer who founded modern projective geometry with his 1822 Traité and made work the central concept of the mechanics of machines.
projective geometry, applied mechanics, hydraulic engineering
Founder of rigorous analysis and complex function theory, and creator of the stress tensor and the theory of linear elasticity.
analysis, complex analysis, differential equations
German physicist who established by experiment and theory that the current in a circuit is proportional to its driving tension and inversely proportional to its resistance.
electricity, mathematical physics, acoustics
Leipzig astronomer and geometer who introduced barycentric and homogeneous coordinates, the Möbius function and Möbius transformations, and described the one-sided Möbius band.
projective geometry, astronomy, topology
Mathematician and inventor who designed the Difference Engine and the Analytical Engine, the first design for a general-purpose programmable computer.
mathematics, mechanical computation, functional equations
English experimental physicist and chemist who discovered electromagnetic induction, the laws of electrolysis, diamagnetism and the magneto-optical effect, and introduced the concept of the field.
electromagnetism, electrochemistry, magneto-optics
Engineer and mathematician who gave work and kinetic energy their modern definitions and derived the compound centrifugal force, now called the Coriolis force, in rotating frames.
mechanics, engineering, mathematical physics
Astronomer and mathematician who surveyed the southern sky, catalogued nebulae and double stars, introduced the notation f^{-1}, and founded much of the chemistry and vocabulary of photography.
astronomy, mathematics, optics
Kazan mathematician who published the first non-Euclidean (hyperbolic) geometry in 1829 and was rector of Kazan University for nineteen years.
geometry, non-Euclidean geometry, analysis
Self-taught Nottingham miller who introduced the potential function, Green's theorem and Green's functions in his 1828 Essay.
potential theory, mathematical physics, electrostatics
French geometer and historian who systematised projective geometry around the cross-ratio, proved the screw theorem for rigid motions, founded enumerative geometry with the number 3264, and was the victim of the Vrain-Lucas forgeries.
projective geometry, enumerative geometry, kinematics
Self-taught Swiss geometer who became the leading synthetic geometer of the nineteenth century, known for the projective generation of conics, symmetrization, Steiner chains and Steiner systems.
synthetic geometry, projective geometry, geometric extremal problems
French engineer officer whose single book, Réflexions sur la puissance motrice du feu (1824), introduced the reversible cycle and the efficiency limit of heat engines and founded thermodynamics.
thermodynamics, theory of heat engines, military engineering
American physicist who built the first powerful electromagnets, discovered self-induction and the oscillatory discharge, and was the first Secretary of the Smithsonian Institution.
electromagnetism, electrical engineering, acoustics
Chemist who synthesized urea from ammonium cyanate, first isolated aluminium, beryllium and yttrium, and led the Göttingen chemical laboratory for 46 years.
organic chemistry, inorganic chemistry, analytical chemistry
Astronomer Royal for 46 years who fixed the Greenwich meridian and gave his name to the Airy disk, the Airy function, Airy isostasy and the Airy stress function.
astronomy, optics, geodesy
Geometer who introduced line coordinates, the Plücker formulas and line geometry, and physicist who first observed the magnetic deflection of the cathode glow and studied gas spectra.
analytic geometry, algebraic curves, line geometry
Self-taught instrument maker and King's College professor who co-created the first commercial electric telegraph, invented the stereoscope and popularized the Wheatstone bridge.
experimental physics, acoustics, telegraphy
Hungarian army engineer who independently discovered hyperbolic geometry and published it in 1832 as the Appendix to his father's Tentamen, together with an absolute geometry valid with or without the parallel postulate.
geometry, non-Euclidean geometry, foundations of mathematics
Proved the general quintic unsolvable by radicals, founded the theory of elliptic and abelian functions, and gave his name to commutative groups.
algebra, analysis, elliptic functions
Austrian physicist who in 1842 proposed that the observed frequency of a wave depends on the relative motion of source and observer.
physics, mathematics, astronomy
Chemist who made organic analysis routine, created the research-teaching laboratory at Giessen, and founded agricultural chemistry.
organic chemistry, analytical chemistry, agricultural chemistry
Prussian mathematician who founded the theory of elliptic and theta functions with Abel, created Hamilton–Jacobi mechanics, and introduced the Jacobian, the Jacobi identity and the Jacobi symbol.
elliptic functions, analytical mechanics, number theory
German physicist who with Gauss founded absolute electromagnetic measurement and an early telegraph, proposed the first unified force law for moving charges, and with Kohlrausch measured the ratio of units that pointed to the speed of light.
electromagnetism, geomagnetism, metrology
Founder of analytic number theory, who proved the theorem on primes in arithmetic progressions and gave the first rigorous convergence theorem for Fourier series.
number theory, analysis, Fourier series
Irish mathematician who unified optics and mechanics through a single characteristic function, created Hamiltonian mechanics, and discovered the quaternions.
optics, classical mechanics, algebra
Mathematician and logician who formulated De Morgan's laws, named mathematical induction, founded the logic of relations and was first president of the London Mathematical Society.
logic, algebra, analysis
Stettin schoolteacher whose Ausdehnungslehre founded linear algebra and the exterior product, and whose work on Sanskrit gave linguistics Grassmann's law.
linear algebra, exterior algebra, geometry
French analyst who founded the Journal de Mathématiques Pures et Appliquées, published Galois's work, constructed the first transcendental numbers and gave his name to theorems on eigenvalue problems, phase-space volume, elementary integrals and conformal maps.
analysis, differential equations, mathematical physics
Inventor of ideal numbers, who proved Fermat's Last Theorem for regular primes and found the quartic surface with sixteen nodes.
algebraic number theory, analysis, algebraic geometry
Experimental chemist who founded spectral analysis with Kirchhoff, discovered caesium and rubidium, and made gas analysis, photochemistry and calorimetry quantitative.
chemistry, analytical chemistry, spectroscopy
Astronomer who predicted the position of Neptune from the perturbations of Uranus, found the anomalous advance of Mercury's perihelion, and built the theories of all the major planets.
celestial mechanics, astronomy, meteorology
Founder of Galois theory, who linked the solvability of equations by radicals to the structure of their symmetry groups and introduced finite fields.
algebra, group theory, theory of equations
Heilbronn physician who in 1842 first published the conservation of energy as a universal principle and computed the mechanical equivalent of heat from gas data.
thermodynamics, physiology, medicine
Mathematician whose 1843 translation and Notes on Babbage's Analytical Engine explained general-purpose computation and set out a program for Bernoulli numbers.
mathematics, computing
Self-taught English mathematician who created the algebra of logic now called Boolean algebra and pioneered operator methods in analysis.
mathematical logic, algebra of logic, probability
Founder of rigorous modern analysis, who introduced the epsilon-delta style, uniform convergence and power-series foundations of complex function theory.
real analysis, complex analysis, elliptic and Abelian functions
Manchester brewer and experimenter who found the law of electrical heating and measured the mechanical equivalent of heat, the experimental basis of energy conservation.
thermodynamics, electricity and magnetism, kinetic theory of gases
Irish-born Cambridge mathematical physicist, Lucasian Professor for 54 years, known for the Navier–Stokes equations, Stokes's law, fluorescence, the Stokes parameters and Stokes's theorem.
fluid dynamics, optics, mathematical physics
Experimental physicist who made the first terrestrial measurement of the speed of light, showed that flowing water partly drags light, explained Doppler shifts of spectral lines, and founded interferometric metrology and stellar interferometry.
optics, experimental physics, astronomy
Experimental physicist who demonstrated the Earth's rotation with his pendulum and gyroscope, showed that light is slower in water than in air, measured the speed of light in the laboratory, discovered eddy-current heating, and created the silvered-glass reflecting telescope and the knife-edge test.
experimental physics, optics, mechanics
Irish physicist who first measured the absorption of infrared radiation by atmospheric gases, discovered the Tyndall effect and succeeded Faraday at the Royal Institution.
radiant heat, atmospheric physics, diamagnetism
Prolific Victorian algebraist who founded matrix algebra, gave the first abstract definition of a group, and built classical invariant theory.
algebra, invariant theory, group theory
Physician and physicist who gave the first general statement of the conservation of energy, measured the speed of the nerve impulse, invented the ophthalmoscope, founded vortex dynamics and introduced free energy.
physics, physiology, thermodynamics
Founder of the St Petersburg school who proved Bertrand's postulate, created minimax approximation and Chebyshev polynomials, and gave the general law of large numbers.
number theory, approximation theory, probability theory
French analyst and number theorist who proved the transcendence of e, solved the quintic with modular functions, and introduced Hermitian forms.
number theory, elliptic functions, invariant theory
Chemist and microbiologist who discovered molecular chirality, showed that fermentation and many diseases are caused by living micro-organisms, and developed pasteurization and the first laboratory-attenuated vaccines.
chemistry, stereochemistry, microbiology
Founder of classical thermodynamics who stated the second law, introduced internal energy and entropy, and introduced the mean free path and the virial theorem in the kinetic theory of gases.
thermodynamics, kinetic theory of gases, mathematical physics
Berlin number theorist who stated the Kronecker–Weber theorem, dreamed of class field theory through complex multiplication, and argued that all mathematics should be built from the integers.
number theory, algebra, elliptic functions
Mathematical physicist who formulated the circuit laws, founded spectral analysis with Bunsen, and stated the law of thermal radiation that defined the black-body problem.
mathematical physics, electrical circuits, spectroscopy
Glasgow physicist who defined absolute temperature, stated the second law and the dissipation of energy, and supplied the theory and instruments of the transatlantic telegraph.
thermodynamics, electricity and telegraphy, fluid dynamics
Founder of Riemann surfaces and Riemannian geometry, and author of the 1859 paper linking the primes to the zeros of the zeta function.
complex analysis, differential geometry, analytic number theory
Italian chemist whose 1858 Sunto revived Avogadro's hypothesis to fix atomic weights, decisively at the 1860 Karlsruhe Congress, and discoverer of the Cannizzaro reaction.
chemistry, atomic theory, organic chemistry
Chemist who established the tetravalence of carbon, carbon chains and the six-membered benzene ring, founding structural organic chemistry.
organic chemistry, structural theory, aromatic chemistry
Scottish physicist who unified electricity, magnetism and light in a field theory and introduced statistical methods into physics.
electromagnetism, kinetic theory, statistical mechanics
Edinburgh natural philosopher who co-wrote the Treatise on Natural Philosophy with Kelvin, championed quaternions, and founded knot theory with the first knot tables.
mathematical physics, knot theory, graph theory
Creator of ideal theory, Dedekind cuts and the set-theoretic foundations of the natural numbers.
algebraic number theory, foundations of mathematics, abstract algebra
London chemist and physicist who discovered thallium, invented the radiometer, the Crookes tube and the spinthariscope, and also investigated spirit mediums.
chemistry, spectroscopy, vacuum physics
Russian chemist who formulated the periodic law in 1869 and used it to predict gallium, scandium and germanium.
chemistry, periodic law, physical chemistry
Italian geometer who gave the first models of Lobachevsky's hyperbolic geometry, proving it as consistent as Euclid's, and whose name survives on the Laplace–Beltrami operator.
differential geometry, non-Euclidean geometry, mathematical physics
Viennese physicist of Slovene origin who discovered the fourth-power law of thermal radiation and founded the theory of multicomponent diffusion and moving-boundary heat problems.
thermal radiation, kinetic theory of gases, heat conduction
Dutch physicist whose equation of state unified gas and liquid, explained the critical point and founded the molecular theory of phase transitions; Nobel Prize in Physics 1910.
thermodynamics, molecular physics, statistical mechanics
The king of invariant theory, who proved constructively that the covariants of binary forms are finitely generated.
invariant theory, algebra, algebraic geometry
French mathematician whose Traité des substitutions (1870) founded group theory as a discipline, and who introduced the Jordan normal form, composition series, functions of bounded variation, Jordan content and the Jordan curve theorem.
group theory, linear algebra, analysis
Experimental physicist who first photographed shock waves, explained Mach bands and the sense of rotation, and whose critique of absolute space shaped Einstein's general relativity.
experimental physics, gas dynamics, sensory physiology
American logician, scientist and philosopher who developed the logic of relations and quantifiers, existential graphs, the theory of signs and pragmatism, while measuring gravity for the U.S. Coast Survey.
logic, semiotics, philosophy of science
Yale physicist who founded chemical thermodynamics, created the ensemble formulation of statistical mechanics and introduced modern vector analysis.
thermodynamics, statistical mechanics, physical chemistry
French geometer whose work on surfaces, orthogonal systems, integration and Pfaffian forms shaped classical differential geometry, and who led the Paris Faculty of Science and the Academy of Sciences.
differential geometry, real analysis, differential equations
Physicist who founded the modern theory of sound and vibration, explained the blue sky by scattering, and discovered argon.
acoustics, optics, fluid dynamics
Manchester's first professor of engineering, who discovered the criterion for turbulence in pipes and founded lubrication theory and the averaged equations of turbulent flow.
fluid mechanics, engineering, heat transfer
Founder of the theory of continuous transformation groups, now Lie groups and Lie algebras, developed to integrate differential equations by their symmetries.
transformation groups, differential equations, geometry
Founder of statistical mechanics, author of the Boltzmann equation, the H-theorem and the statistical interpretation of entropy, and champion of the atomic theory.
theoretical physics, statistical mechanics, kinetic theory
Founder of the algebraic and birational theory of curves and surfaces, known for the AF+BG theorem, Brill–Noether theory and Noether's formula.
algebraic geometry, algebraic functions, birational geometry
Creator of set theory who proved that the real numbers are uncountable and built the arithmetic of transfinite ordinals and cardinals.
set theory, real analysis, foundations of mathematics
Swedish analyst known for the theorem on meromorphic functions with prescribed poles, founder of Acta Mathematica and of the Institut Mittag-Leffler.
complex analysis, analytic continuation, summability
Founder of modern quantificational logic, author of the logicist programme for arithmetic, and originator of the distinction between sense and reference.
mathematical logic, foundations of mathematics, philosophy of language
Geometer who defined geometry through transformation groups in the Erlangen Program, pioneered automorphic functions, and made Göttingen the world centre of mathematics.
geometry, group theory, complex analysis
Berlin algebraist who created the character theory of finite groups and left his name on results across linear algebra, differential equations and number theory.
group theory, representation theory, linear algebra
German physicist who discovered rectification at crystal contacts, built the cathode-ray tube, introduced the coupled tuned transmitter and early phased arrays, and shared the 1909 Nobel Prize in Physics with Marconi.
experimental physics, wireless telegraphy, solid-state physics
Self-taught English physicist who gave Maxwell's equations their modern vector form, founded transmission-line theory and invented operational calculus.
electromagnetism, electrical engineering, transmission-line theory
First woman to earn a modern doctorate in mathematics and to hold a full chair, known for the Cauchy–Kovalevskaya theorem and the integrable Kovalevskaya top.
partial differential equations, mechanics, Abelian functions
Experimental physicist who measured the speed of light with unprecedented accuracy, invented the interferometer used in the Michelson–Morley experiment, and became the first American Nobel laureate in science.
optics, experimental physics, metrology
French physicist who discovered the spontaneous radioactivity of uranium in 1896 and showed that beta rays are fast electrons.
physics, radioactivity, optics
Founder of stereochemistry with the tetrahedral carbon atom and a founder of physical chemistry, awarded the first Nobel Prize in Chemistry for the laws of chemical dynamics and osmotic pressure.
stereochemistry, physical chemistry, chemical kinetics
Scottish chemist who discovered argon with Lord Rayleigh and then helium, neon, krypton and xenon, completing a new group of the periodic table.
chemistry, physical chemistry, noble gases
Italian mathematician who created the absolute differential calculus (tensor calculus), introduced covariant differentiation and the Ricci tensor, and with Levi-Civita wrote the 1900 memoir that became the mathematical language of general relativity.
differential geometry, tensor calculus, mathematical physics
Dutch experimental physicist who liquefied helium in 1908 and discovered superconductivity in 1911.
low-temperature physics, thermodynamics of real gases, superconductivity
Founder of the electron theory of matter, author of the Lorentz force and the Lorentz transformation, and 1902 Nobel laureate for the theory of the Zeeman effect.
theoretical physics, electromagnetism, electron theory
Founder of physical chemistry as a discipline, author of the dilution law and the modern definition of catalysis, and 1909 Nobel laureate in chemistry.
physical chemistry, electrochemistry, catalysis
Universal mathematician who created automorphic functions, the qualitative theory of dynamical systems and algebraic topology, discovered chaos in the three-body problem, and formulated the Lorentz group of relativity.
complex analysis, differential equations, celestial mechanics
St Petersburg mathematician who created the theory of Markov chains and contributed to number theory, the moment problem, polynomial inequalities and the limit theorems of probability.
probability theory, number theory, approximation theory
Physicist who identified the electron as a universal constituent of matter, proposed the first electron model of the atom, separated isotopes of neon with positive rays, and directed the Cavendish Laboratory for 35 years.
atomic physics, electromagnetism, conduction in gases
Serbian-American engineer and inventor of polyphase induction motors and the resonant Tesla coil, whose documented engineering helped found the AC power system and whose later wireless and weapons claims grew into a lasting myth.
electrical engineering, alternating-current power, electric machines
Founder of the analytic theory of continued fractions who posed and solved the moment problem and introduced the Stieltjes integral.
analysis, continued fractions, moment problem
French analyst known for the Picard theorems on entire functions, Picard iteration, Picard–Vessiot theory and the Picard group, and permanent secretary of the Académie des Sciences from 1917 to 1941.
complex analysis, differential equations, algebraic geometry
Founder of the modern theory of stability of motion, author of Lyapunov functions and exponents, and prover of the central limit theorem by characteristic functions.
stability theory, differential equations, probability theory
Experimental physicist who produced and detected electromagnetic waves, confirming Maxwell's theory, and founded the theory of elastic contact.
electromagnetism, contact mechanics, mechanics
Originator of quantum theory, who introduced the quantum of action h in his 1900 derivation of the black-body radiation law.
theoretical physics, thermodynamics, quantum theory
Teacher of Hilbert and Minkowski, whose name is attached to the Hurwitz zeta function, the Riemann–Hurwitz formula, the Routh–Hurwitz stability criterion and the 1, 2, 4, 8 theorem on composition algebras.
number theory, complex analysis, Riemann surfaces
French physicist who discovered piezoelectricity with his brother Jacques, formulated the symmetry principle and Curie's law of magnetism, and co-discovered polonium and radium with Marie Curie.
physics, crystallography, piezoelectricity
Swedish founder of physical chemistry who proposed ionic dissociation, the Arrhenius equation for reaction rates, and the first quantitative estimate of carbon-dioxide warming.
physical chemistry, electrochemistry, chemical kinetics
Italian analyst who founded the theory of functionals and of Volterra integral equations, created the theory of elastic distortions, and with Lotka founded mathematical population dynamics.
functional analysis, integral equations, mathematical physics
Leader of Göttingen mathematics whose basis theorem, Zahlbericht, axioms of geometry, Hilbert space, Paris problems and proof theory shaped twentieth-century mathematics.
invariant theory, algebraic number theory, foundations of geometry
Creator of the geometry of numbers and of the four-dimensional spacetime formulation of special relativity.
number theory, geometry of numbers, convex geometry
Physicist who found the displacement law and the high-frequency distribution law of black-body radiation, and identified the positive particles of canal rays with crossed electric and magnetic fields.
experimental physics, thermal radiation, thermodynamics
French analyst who proved the prime number theorem, created the theory of entire functions of finite order, and introduced well-posed problems, Hadamard matrices and the study of chaotic geodesic flows.
complex analysis, analytic number theory, differential geometry
Swedish analyst whose 1903 theory of linear integral equations, with the Fredholm determinant and the Fredholm alternative, launched spectral theory and modern functional analysis.
integral equations, operator theory, partial differential equations
Polish-French physicist and chemist who showed that radioactivity is an atomic property, discovered polonium and radium with Pierre Curie, and was the first person awarded two Nobel Prizes.
physics, chemistry, radioactivity
Theoretical physicist who extended Bohr's atom to elliptic and relativistic orbits, introduced the fine-structure constant, founded the quantum free-electron theory of metals, and trained the leading Munich school of theoretical physics.
theoretical physics, mathematical physics, atomic physics
Founder of general topology and of the theory of ordered sets, creator of Hausdorff measure and dimension, who also wrote philosophy and literature as Paul Mongré.
set theory, general topology, measure theory
American experimental physicist who measured the elementary charge with the oil-drop method, confirmed Einstein's photoelectric equation, named cosmic rays and led Caltech from 1921 to 1945.
experimental physics, atomic physics, cosmic rays
Scottish physicist who invented the cloud chamber, making the tracks of single charged particles visible, and founded the modern theory of thunderstorm electricity.
atomic physics, particle detectors, cloud physics
Completed the classification of simple Lie algebras, discovered spinors, and created exterior differential forms, moving frames, connections with torsion and symmetric spaces.
Lie groups and Lie algebras, differential geometry, exterior differential systems
French physicist whose Brownian-motion and sedimentation experiments established the reality of molecules, Nobel laureate in 1926, and founder of the CNRS and the Palais de la découverte.
physical chemistry, experimental physics, Brownian motion
Experimental physicist who explained radioactivity as atomic transformation, discovered the atomic nucleus and produced the first artificial nuclear reaction.
nuclear physics, radioactivity, atomic physics
French analyst who created the first theory of measure, founded denumerable probability and the theory of games of strategy, and served as Minister of Marine.
measure theory, complex analysis, divergent series
Discoverer of Russell's paradox, inventor of the theory of types and the theory of descriptions, and co-author with Whitehead of Principia Mathematica.
mathematical logic, foundations of mathematics, philosophy
French physicist who created the Langevin equation and the theory of para- and diamagnetism, framed the twin paradox, pioneered ultrasonic sonar, and led antifascist and educational causes.
statistical physics, magnetism, relativity
Italian mathematician who co-founded tensor calculus with Ricci-Curbastro, introduced parallel transport in Riemannian geometry, regularized binary collisions in the three-body problem, and was dismissed under the 1938 racial laws.
differential geometry, tensor calculus, rational mechanics
Italian inventor and entrepreneur who developed practical long-distance wireless telegraphy, shared the 1909 Nobel Prize in Physics, and became a leading scientific official of Fascist Italy.
radio engineering, wireless telegraphy, electromagnetism
Creator of Lebesgue measure and the Lebesgue integral, the foundation of modern analysis and probability.
real analysis, measure theory, Fourier analysis
Berlin algebraist who founded much of the representation theory of finite groups and of GL(n), and whose name is attached to results across algebra, combinatorics and analysis.
representation theory, group theory, linear algebra
Founder of boundary-layer theory and of modern aerodynamics, who built the Göttingen school of fluid mechanics and served the Nazi air ministry.
fluid mechanics, aerodynamics, boundary-layer theory
Founder of modern Japanese mathematics who proved that the abelian extensions of a number field are exactly its class fields.
algebraic number theory, class field theory, analysis
Radiochemist who with Rutherford explained radioactivity as atomic transmutation, formulated the displacement law and the concept of isotopes, and later wrote on monetary economics and the geometry of tangent circles.
radiochemistry, physical chemistry, economics
Cambridge analyst who, with Littlewood and Ramanujan, created the circle method and much of modern analytic number theory, and who brought rigorous analysis into English mathematics.
analytic number theory, mathematical analysis, population genetics
British mathematical physicist who founded the theory of gravitational instability and stellar dynamics, co-derived the Rayleigh–Jeans law, and became a leading popularizer of astronomy.
mathematical physics, astrophysics, stellar dynamics
Austrian-Swedish physicist who co-discovered protactinium with Otto Hahn and, with Otto Frisch, gave the first physical explanation of nuclear fission.
nuclear physics, radioactivity, beta and gamma spectroscopy
French mathematician who introduced metric spaces and abstract compactness and made lasting contributions to functional analysis, topology and probability.
functional analysis, general topology, probability theory
Creator of special and general relativity, of the light-quantum hypothesis and of the theory of Brownian motion, and founder of relativistic cosmology.
theoretical physics, relativity, quantum theory
Discoverer of the diffraction of X-rays by crystals, author of the first relativity textbook, and a public defender of Einstein's physics in Nazi Germany.
X-ray diffraction, crystallography, special relativity
German chemist who founded radiochemistry, co-discovered protactinium with Lise Meitner, identified barium among the products of irradiated uranium with Fritz Strassmann, and received the 1944 Nobel Prize in Chemistry for the discovery of nuclear fission.
radiochemistry, nuclear chemistry
Hungarian analyst, a founder of functional analysis, known for the Riesz–Fischer and Riesz representation theorems, the L^p spaces, the theory of compact operators and subharmonic functions.
functional analysis, operator theory, real analysis
Austrian-Dutch theoretical physicist, successor of Lorentz at Leiden, known for the urn model, the adiabatic principle, Ehrenfest's theorem and the classification of phase transitions.
statistical mechanics, quantum theory, theoretical physics
Founder of modern topology through the fixed point theorem and invariance of dimension, and creator of intuitionistic mathematics.
topology, intuitionism, foundations of mathematics
Hungarian-American aerodynamicist of the vortex street, the momentum integral and turbulence theory, who founded the Jet Propulsion Laboratory and shaped US and NATO aeronautical research.
aerodynamics, fluid mechanics, turbulence
Founder of the theory of stellar interiors, proposer of hydrogen fusion as the source of stellar energy, and leader of the 1919 eclipse test of general relativity.
astrophysics, stellar structure, general relativity
Founder of modern abstract algebra and author of the theorems linking symmetries to conservation laws.
abstract algebra, invariant theory, mathematical physics
Experimental physicist who counted alpha particles with Rutherford, made the scattering measurements behind the nuclear atom and invented the Geiger–Müller counter.
nuclear physics, radioactivity, particle detection
Theoretical physicist who co-founded matrix mechanics, gave the wave function its statistical interpretation, and founded the dynamical theory of crystal lattices.
theoretical physics, quantum mechanics, solid-state physics
Leader of the Warsaw school of mathematics, pioneer of set theory and the continuum hypothesis, and creator of the Sierpiński triangle, carpet and numbers.
set theory, number theory, topology
Dutch-American physicist and chemist who created the Debye model of specific heat, the theory of polar molecules, powder X-ray diffraction and the Debye–Hückel theory of electrolytes, and whose Berlin directorship under the Nazi regime remains disputed.
theoretical physics, physical chemistry, solid-state physics
Engineer turned mathematician who brought topology into algebraic geometry, proved the Lefschetz fixed-point theorem, and founded an American school of nonlinear differential equations.
algebraic geometry, algebraic topology, differential equations
Universal mathematician who founded gauge theory and the representation theory of compact Lie groups, and proved the Weyl law and the equidistribution theorem.
analysis, Lie groups and representation theory, differential geometry
Creator of the quantum model of the atom, the correspondence principle and complementarity, and founder of the Copenhagen institute at the centre of quantum mechanics.
atomic physics, quantum theory, nuclear physics
Cambridge physicist who founded the statistical theory of turbulence and the dislocation theory of plasticity, and whose name attaches to Taylor vortices, Taylor dispersion, the Rayleigh–Taylor instability and the Taylor cone.
fluid mechanics, turbulence, hydrodynamic stability
Founder of modern probability theory, known for stable laws, Lévy processes, martingale limit theorems and the fine structure of Brownian motion.
probability theory, stochastic processes, functional analysis
Number theorist who proved the functional equation of Dedekind zeta functions, introduced Grössencharaktere and their L-functions, and created the theory of Hecke operators linking modular forms to Euler products.
number theory, modular forms, L-functions
Creator of wave mechanics and the Schrödinger equation, who named quantum entanglement and wrote What Is Life?
quantum mechanics, statistical physics, foundations of physics
Physicist whose X-ray spectra showed that atomic number is the charge of the nucleus and fixed the order and gaps of the periodic table.
X-ray spectroscopy, atomic physics, radioactivity
Analyst of variational and eigenvalue problems, co-author of the CFL condition, and founder of the mathematical institutes at Göttingen and New York University.
analysis, partial differential equations, calculus of variations
Discoverer of Bragg's law of X-ray reflection, joint Nobel laureate with his father at 25, and founder of crystal-structure analysis from rock salt to proteins.
X-ray crystallography, solid-state physics, mineralogy
Founder of modern statistical inference and experimental design and co-founder of population genetics, also a prominent advocate of eugenics and a critic of the evidence linking smoking to lung cancer.
statistics, population genetics, experimental design
Experimental physicist who discovered the neutron, showed the beta spectrum is continuous and led the British mission to the Manhattan Project.
nuclear physics, radioactivity
American physicist whose discovery of the wavelength shift of scattered X-rays established the momentum of light quanta, who mapped the latitude effect of cosmic rays and who directed the Manhattan Project's Metallurgical Laboratory.
X-ray physics, quantum physics, cosmic rays
French physicist who proposed in 1924 that every particle has a wave of wavelength h/p, founding wave mechanics.
quantum theory, wave mechanics, foundations of quantum mechanics
Founder of modern functional analysis, who introduced complete normed spaces and proved its fundamental theorems, and co-author of the Banach–Tarski paradox.
functional analysis, measure theory, real analysis
Topologist who discovered the Hopf fibration and Hopf invariant, proved the Poincaré–Hopf and Hopf degree theorems, and founded the theory of Hopf algebras and group homology.
algebraic topology, differential geometry, homological algebra
American mathematician who constructed Brownian motion rigorously, created generalized harmonic analysis and the general Tauberian theorem, developed optimal filtering and founded cybernetics.
harmonic analysis, probability theory, potential theory
Soviet experimental physicist who built record pulsed magnets at Cambridge, invented the expansion-engine helium liquefier and the low-pressure oxygen turboexpander, and discovered superfluidity, winning the 1978 Nobel Prize in Physics.
low-temperature physics, magnetism, cryogenic engineering
Number theorist whose theorems on Diophantine equations, class numbers, quadratic forms, modular forms of several variables and small divisors each founded a field.
number theory, Diophantine approximation, transcendence theory
Warsaw topologist who axiomatized closure, defined the set-theoretic ordered pair, characterized planar graphs, and led the post-war rebuilding of Polish mathematics.
topology, set theory, graph theory
Founder of the Moscow school of topology, who with Pavel Urysohn created the theory of compact spaces and who introduced the nerve of a covering.
general topology, algebraic topology, dimension theory
French physicist and chemist who with Frédéric Joliot discovered artificial radioactivity, and whose 1938 work with Pavle Savić on neutron-irradiated uranium helped lead to the discovery of fission.
radioactivity, nuclear physics, nuclear chemistry
Algebraist and number theorist who proved the general reciprocity law, introduced Artin L-functions and the braid group, and solved Hilbert's seventeenth problem.
algebraic number theory, class field theory, abstract algebra
Number theorist who introduced the local-global principle, shaped class field theory and proved the Riemann hypothesis for elliptic curves over finite fields, and who directed the Göttingen institute under National Socialism.
algebraic number theory, class field theory, arithmetic of quadratic forms
Rebuilt algebraic geometry on the foundations of commutative algebra, introducing the Zariski topology, the Main Theorem on normal varieties and the first algebraic resolutions of singularities.
algebraic geometry, commutative algebra, topology of plane curves
French physicist and chemist who with Irène Joliot-Curie discovered artificial radioactivity, showed that uranium fission releases neutrons, and led the first French Atomic Energy Commission.
nuclear physics, nuclear chemistry, radiochemistry
Discoverer of the exclusion principle, author of the theory of electron spin and the spin–statistics theorem, and proposer of the neutrino.
theoretical physics, quantum mechanics, quantum field theory
Polish-American logician who gave the semantic definition of truth, proved the decidability of real closed fields and elementary geometry, co-discovered the Banach–Tarski paradox, and founded the Berkeley school of model theory.
mathematical logic, model theory, set theory
Italian-American physicist who created Fermi–Dirac statistics and the theory of beta decay, discovered the power of slow neutrons, and led the team that built the first nuclear reactor.
nuclear physics, particle physics, statistical mechanics
Algebraist who introduced the Brauer group, founded modular representation theory and set the strategy that led to the classification of finite simple groups.
representation theory, finite group theory, algebra
Creator of matrix mechanics and the uncertainty principle, who later led the theoretical work of Germany's wartime uranium project.
quantum mechanics, nuclear physics, quantum field theory
English theoretical physicist who gave quantum mechanics its general formulation, wrote the relativistic equation of the electron and predicted antimatter.
quantum mechanics, quantum field theory, mathematical physics
American logician who created the lambda calculus, proposed Church's thesis and proved the undecidability of first-order logic.
mathematical logic, computability theory, lambda calculus
Founder of axiomatic probability theory whose work also shaped turbulence, Hamiltonian dynamics, ergodic theory and algorithmic complexity.
probability theory, real analysis, turbulence
Author of Moderne Algebra, which gave abstract algebra its modern form, and of foundational work in algebraic geometry, Ramsey theory and the history of ancient science.
abstract algebra, algebraic geometry, combinatorics
Mathematician who founded the Hilbert-space formulation of quantum mechanics, operator algebras and game theory, and defined the stored-program computer.
set theory, mathematical physics, functional analysis
Physicist who explained alpha decay as quantum tunnelling, developed the hot Big Bang theory of element formation, posed the genetic coding problem and wrote the Mr Tompkins books.
nuclear physics, astrophysics, cosmology
Theoretical physicist who founded the Berkeley school of theory, co-authored the Born–Oppenheimer approximation and the first neutron-star and black-hole calculations, and directed the Los Alamos Laboratory.
theoretical physics, quantum mechanics, nuclear physics
Founder of Bourbaki who proved the Riemann hypothesis for curves over finite fields and formulated the Weil conjectures.
number theory, algebraic geometry, arithmetic geometry
Theoretical physicist who explained the nuclear reactions that power the stars, computed the Lamb shift, led the theory division at Los Alamos and became a leading voice for arms control.
nuclear physics, astrophysics, quantum electrodynamics
Logician who proved the completeness of first-order logic, the incompleteness of arithmetic, and the consistency of the axiom of choice and the continuum hypothesis.
mathematical logic, set theory, foundations of mathematics
Number theorist and matrix theorist who linked class field theory, integral matrices and eigenvalue localization, and made linear algebra a research field in its own right.
algebraic number theory, matrix theory, group theory
Finnish-American complex analyst, one of the first two Fields Medallists, who made value distribution theory geometric and with Lipman Bers founded the modern theory of quasiconformal maps, Teichmüller spaces and Kleinian groups.
complex analysis, geometric function theory, quasiconformal mappings
Founding member of Bourbaki who introduced ideles into class field theory and constructed the Chevalley groups, simple groups attached to Lie algebras over every field.
class field theory, Lie groups, algebraic groups
Polish-American mathematician of the Lwów school who introduced measurable cardinals, conjectured the Borsuk–Ulam theorem, invented the Monte Carlo method, co-designed the hydrogen bomb and ran the Fermi–Pasta–Ulam–Tsingou experiment.
set theory, measure theory, topology
American logician who founded recursion theory as a mathematical subject, proving the normal form and recursion theorems, creating the arithmetical and hyperarithmetical hierarchies, realizability and regular expressions.
mathematical logic, recursion theory, intuitionistic logic
Astrophysicist who derived the maximum mass of white dwarfs and wrote definitive theories of stellar dynamics, radiative transfer, fluid stability and black holes.
astrophysics, stellar structure, stellar dynamics
British mathematician who defined computability with the Turing machine, led the breaking of naval Enigma, designed the ACE computer and founded the theory of biological pattern formation.
mathematical logic, computability theory, cryptanalysis
Founder of linear programming and of the Kantorovich formulation of optimal transport, and Nobel laureate in economics for the theory of optimal allocation of resources.
functional analysis, linear programming, optimal transport
Founder of the theory of Banach and C*-algebras and of the representation theory of non-compact groups, whose Moscow seminar shaped generations of mathematicians.
functional analysis, representation theory, operator algebras
Founder of Teichmüller theory through quasiconformal mappings and quadratic differentials, author of key ideas in valuation theory and Galois cohomology, and an active Nazi who led the 1933 boycott of Edmund Landau.
complex analysis, Riemann surfaces, quasiconformal mappings
Itinerant Hungarian mathematician, author of some 1,500 papers with over 500 co-authors, who founded the probabilistic method and the theory of random graphs.
number theory, combinatorics, graph theory
American mathematician and engineer who applied Boolean algebra to switching circuits and founded information theory with his 1948 paper A Mathematical Theory of Communication.
information theory, switching theory, cryptography
Norwegian number theorist who created the Selberg sieve, an elementary proof of the prime number theorem and the Selberg trace formula.
analytic number theory, automorphic forms, spectral theory
Physicist turned mathematician who created the harmonic analysis of semisimple Lie groups, from the Harish-Chandra isomorphism to the discrete series and the Plancherel formula.
representation theory, harmonic analysis, Lie groups
French mathematician who transformed algebraic topology, algebraic geometry and number theory, youngest Fields medallist and first Abel laureate.
algebraic topology, algebraic geometry, number theory
Rebuilt algebraic geometry on the theory of schemes, sheaves and topoi, creating the tools behind the proof of the Weil conjectures and much of modern number theory.
algebraic geometry, homological algebra, functional analysis
Geometer who founded topological K-theory, proved the index theorem with Isadore Singer, and joined geometry to gauge theory and quantum field theory.
geometry, topology, K-theory
Creator of the theory of buildings, BN pairs and the Tits alternative, who recast the simple groups of Lie type as symmetries of geometries.
group theory, algebraic groups, incidence geometry
Topologist who discovered exotic spheres and made defining contributions to differential topology, singularity theory, algebraic K-theory, group growth and holomorphic dynamics.
differential topology, knot theory, singularity theory
Founder of the modern theory of chaotic dynamical systems through Kolmogorov–Sinai entropy, dispersing billiards, Markov partitions and SRB measures, and a leader of rigorous statistical physics.
ergodic theory, dynamical systems, mathematical physics
Founder of the Langlands programme, which conjectures deep correspondences between Galois representations and automorphic forms through the principle of functoriality.
number theory, automorphic forms, representation theory
Founded geometric invariant theory and the modern theory of moduli spaces of curves and abelian varieties, then turned to the mathematics of vision and pattern theory.
algebraic geometry, moduli theory, geometric invariant theory
Ergodic theorist who proved the rigidity of horocycle flows and Raghunathan's conjectures on unipotent flows, the foundation of homogeneous dynamics.
ergodic theory, homogeneous dynamics, Lie groups
Topologist who computed the classifying space of surgery theory, founded minimal-model rational homotopy theory, proved the no-wandering-domains theorem and launched string topology.
algebraic topology, geometric topology, rational homotopy theory
Geometer who created the h-principle, Gromov–Hausdorff convergence, hyperbolic groups and the theory of pseudoholomorphic curves in symplectic manifolds.
Riemannian geometry, metric geometry, geometric group theory
Belgian mathematician who proved the Riemann hypothesis over finite fields and created the theory of weights, mixed Hodge structures and Deligne–Mumford stacks.
algebraic geometry, number theory, Hodge theory
Proved superrigidity and arithmeticity of higher-rank lattices, built the first explicit expanders, and solved the Oppenheim conjecture by founding homogeneous dynamics.
Lie groups, ergodic theory, homogeneous dynamics
Geometer who transformed foliation theory and 3-manifold topology, proving hyperbolization for Haken manifolds and proposing the geometrization conjecture.
low-dimensional topology, foliations, hyperbolic geometry
Co-founder of Teichmüller dynamics, known for the Hubbard–Masur theorem, the Masur–Veech theorems on interval exchanges, rational billiards, and the hyperbolicity of the curve complex with Yair Minsky.
Teichmüller theory, dynamical systems, low-dimensional topology
Theoretical physicist and first physicist to win the Fields Medal, whose work on supersymmetry, topological field theory and string theory reshaped geometry and topology.
theoretical physics, string theory, quantum field theory
Number theorist who proved Fermat's Last Theorem by establishing the modularity of semistable elliptic curves.
number theory, arithmetic geometry, Iwasawa theory
Proved the Langlands correspondence for GL(2) over function fields with Drinfeld modules and shtukas, and created quantum groups, associators and, with Beilinson, the geometric Langlands framework of opers and chiral algebras.
number theory, algebraic geometry, representation theory
Fields Medallist who connected complex dynamics, Kleinian groups and Teichmüller theory, and classified Teichmüller curves and SL2(R) orbit closures in genus two.
complex dynamics, hyperbolic geometry, Teichmüller theory
Fields Medallist who turned ideas from quantum field theory and string theory into mathematics, proving Witten's conjecture and founding homological mirror symmetry and deformation quantization of Poisson manifolds.
algebraic geometry, mathematical physics, symplectic geometry
Mathematician who used rigidity in dynamics to solve counting problems in number theory, geometric group theory and the moduli space of flat surfaces, including the magic wand theorem with Maryam Mirzakhani.
dynamical systems, homogeneous dynamics, Teichmüller dynamics
First woman to win the Fields Medal, for her work on the geometry and dynamics of Riemann surfaces and their moduli spaces.
hyperbolic geometry, Teichmüller theory, ergodic theory