History of Mathematics · Highest Honours
The Fields Medal & the Abel Prize
A history of mathematics told through its highest honours — the people, the theorems, and the ideas that reshaped the discipline.
About This Course
Mathematics has no Nobel Prize. The two awards that come closest are the Fields Medal, instituted in 1936 by the Canadian mathematician John Charles Fields and given every four years at the International Congress of Mathematicians to laureates under the age of forty, and the Abel Prize, established by the Norwegian government in 2002 in memory of Niels Henrik Abel and awarded annually since 2003. Together they constitute the most authoritative recognition that pure mathematics gives.
This course traces the history of modern mathematics through its laureates: the creation of algebraic geometry by Grothendieck and Deligne, the Atiyah–Singer index theorem, the proof of Fermat’s Last Theorem, Perelman’s solution of the Poincaré conjecture, the Langlands programme, ergodic theory under Sinai, dynamical systems under Avila and Mirzakhani, and the radical reorganisation of arithmetic geometry under Scholze’s perfectoid spaces. Where possible, video interviews with the laureates themselves are included.
Key Numbers
1936
First Fields Medal awarded (Oslo ICM)
2003
First Abel Prize awarded
~64
Fields medallists to date
~25
Abel laureates to date
2
Mathematicians with both prizes (Serre, Milnor)
7.5 M NOK
Abel Prize purse (~$700k)
Five Modules
M0
History of the Prizes
John Charles Fields’ bequest, the 1936 Oslo congress, the post-war canonisation of the Medal; Niels Henrik Abel’s 1802–1829 life and the 2003 inauguration of the Norwegian prize bearing his name.
M1
The Fields Medal
Awarded every four years at the ICM to mathematicians under 40. Selected laureates: Serre, Grothendieck, Atiyah, Milnor, Thurston, Witten, Connes, Tao, Mirzakhani, Avila, Scholze, Viazovska.
M2
The Abel Prize
Awarded annually by the King of Norway since 2003. Often called the “mathematical Nobel.” Laureates: Serre, Atiyah & Singer, Lax, Carleson, Thompson & Tits, Gromov, Tate, Milnor, Szemerédi, Deligne, Sinai, Wiles, Nash & Nirenberg, Meyer, Langlands, Uhlenbeck.
M3
Laureate Interviews
In-their-own-words video interviews with laureates — Yakov Sinai (2014, dynamical systems & ergodic theory), Pierre Deligne (2013, Weil conjectures & Hodge theory), and others.
M4
Key Theorems & Themes
Selected award-winning results: Atiyah–Singer index theorem, the proof of Fermat’s Last Theorem, Perelman’s geometrization, Mirzakhani on moduli of surfaces, Scholze’s perfectoid spaces, Viazovska in dimension 8.
M5
Cédric Villani — Fields 2010
In-depth treatment of Villani’s Fields-Medal-winning programme: Wasserstein geometry & synthetic Ricci curvature (Lott–Sturm–Villani), Boltzmann H-theorem hypocoercivity (Cercignani conjecture), nonlinear Landau damping (with Mouhot), and the books Optimal Transport: Old and New & Birth of a Theorem.
Other Science-Prize Courses
Other prize-and-laureate courses on CoursesHub. Each one collects laureate lectures, interviews, and short biographical sketches for one of the world’s top science honours.
Nobel Physics →
The benchmark global physics prize since 1901 — 35 laureate lectures (2013–2025).
Nobel Chemistry →
The benchmark global chemistry prize since 1901 — 37 laureate lectures (2013–2025).
Dirac Medal of ICTP →
ICTP Trieste annual award for theoretical physics, since 1985 — laureate lectures + ICTP Distinguished Conversations.
Max Planck Medal →
DPG’s highest honour for theoretical physics, since 1929 — laureate lectures plus the Lise Meitner Lecture series.
Crafoord Astronomy →
Royal Swedish Academy honours in astronomy and astrophysics.
Crafoord Geosciences →
Royal Swedish Academy honours in geosciences and climate.
Crafoord Biosciences →
Royal Swedish Academy honours in evolutionary biology and ecology.
Related Subject Courses
History of Mathematics,History of Math & Physics,Perelman & Geometrization,Mathematics,Differential Geometry,Probability & Statistics,Quantum Field Theory.