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.

Fields 1936Abel 2003

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.

ICMUnder 40

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.

AnnualNorwegian

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.

SinaiDeligne

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.

Index TheoremPerelmanPerfectoids

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.

Optimal TransportBoltzmannLandau Damping

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.

Related Subject Courses

History of Mathematics,History of Math & Physics,Perelman & Geometrization,Mathematics,Differential Geometry,Probability & Statistics,Quantum Field Theory.

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