Philosophy

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

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

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

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

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

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

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

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

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

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