# The Nobel Prize for Mathematics

The Heidelberg Laureate Forum is an annual opportunity to celebrate some of the world’s top mathematicians and computer scientists, by gathering together the recipients of prestigious maths and computer science prizes, including the Abel Prize, the Fields Medal, the Nevanlinna Prize, the ACM A.M. Turing Award and the ACM Prize in Computing.

However, the origins of the HLF are inseparably linked to the existence of the Lindau Nobel Laureate Meetings, which took place from June 30 – July 5, and celebrate the laureates of a much more famous and highly-regarded set of prizes – the Nobel Prizes. Known throughout the world as the pinnacle of scientific achievement, Nobel Prizes are awarded in Chemistry, Physics, Medicine and Economics (as well as Literature and Peace). But no specific prize exists for maths, or for computer science – which meant mathematicians and computer scientists couldn’t make the journey to Lindau to celebrate with their peers. The HLF was created to remedy this, by recognising equivalent levels of achievement through the other awards.

It’s not clear why the Nobel Prize categories specifically exclude maths (computer science did not yet exist) – untrue rumours circulate about the originator of the prizes, Alfred Nobel, refusing to include maths as a prize category due to a grudge against a prominent mathematician, who his wife supposedly had an affair with. This is easily called into question, given that Nobel himself never married. Several sources surmise that the real reason is more likely to be either that Nobel himself didn’t rate mathematics enough to award a prize for it, or that he was aware of existing prizes in maths being given out by the King of Sweden at that time, so didn’t think it was worth including.

But even though the Nobel Prize isn’t awarded for mathematics, that doesn’t mean it’s never been awarded to a mathematician. Here are some examples of mathematicians who’ve managed to bend the rules (isn’t that what maths is all about really?) and, either individually or jointly with someone else, be awarded one of Alfred’s coveted gold medals.

#### Economics

Given that there is a Nobel in economics – formally, the Nobel Memorial Prize in Economic Sciences – which as a discipline makes heavy use of mathematics, you’d imagine there might be some mathematicians who have managed to win this. One of the most famous Economics Nobel winners who’s broadly considered to be a mathematician is **John Forbes Nash**, who won in 1994 for his work in the 1950s on the emerging field of game theory. He remains the only person to have won both a Nobel Prize in Economics and an Abel Prize.

Game theory is the study of the mathematical structures behind situations – the way incentives motivate people to make decisions, and how rational people might choose to behave given particular conditions. The most famous example of the type of reasoning involved is the prisoners’ dilemma – a setup in which two people have to choose whether to cooperate or be selfish, with different rewards or punishments for each. It’s often used as a model, not just for simple game-based situations, but for studying behaviour in economics, and even international politics.

Nash was jointly awarded the Nobel for his work on the concept of Nash Equilibrium: studying particular states within a game where each player, in full knowledge of the other players’ strategies and motivations, has no incentive to change their strategy – the system has reached equilibrium. While such equilibria can be described by considering simple N-player games, the resulting conclusions about behaviour can be applied to larger, more complex systems, and be used along with probability – each player’s strategy might mean they would take different actions with given probabilities.

In addition to his work in economics, Nash did work in other areas of maths, including geometry and differential equations – but he’s best known for his study of game theory, as it has such broad applications. And he isn’t the only game theorist to have been given a Nobel in Economics for their work – **Robert J. Aumann** was jointly awarded a Nobel for Economics in 2005 for his work on conflict and cooperation through game-theory analysis.

Other mathematicians have also been awarded Economics Nobels: **Kenneth Arrow**, who was jointly awarded the prize in 1972 for contributions to economic equilibrium theory, is also well-known for a result called *Arrow’s Impossibility Theorem*.

This is a mathematical statement about voting systems, which says that if you have three or more parties to choose between, and would like to choose a voting system which meets a set of standard fairness criteria (including things like, adding in additional options to the poll shouldn’t change which of two existing options is in the lead), then no possible system can satisfy all these criteria. Arrow first published the theorem in his doctoral thesis, and it’s often quoted in discussions about voting theory.

A colleague of Arrow, **Gerard Debreu**, won an Economics Nobel in 1983 for “having incorporated new analytical methods into economic theory and for his rigorous reformulation of the theory of general equilibrium” – using fixed-point theorems from mathematics to make statements about economic equilibria. Another Nobel Economist from 1975, **Leonid Kantorovich**, applied mathematical techniques to the theory of optimal allocation of resources. Kantorovic widely is regarded as the founder of linear programming – the field of studying systems of linear relationships to find optimal values.

#### Other subjects

You’d probably also imagine that the Nobel in physics might have some overlap with the world of mathematics – **John Bardeen**, who has shared two Physics Nobels in 1956 and 1972, and **Max Born** and **Walther Bothe**, who shared one in 1954, are all considered to be mathematicians as well as physicists; Bardeen studied on the graduate program in mathematics at Princeton University, while Born had a PhD in mathematics, having studied at Göttingen with Felix Klein, David Hilbert and Hermann Minkowski.

Nobel-prize winning chemists can also be mathematicians – **John Pople** (1998) and **Herbert Hauptman **(1985) both did maths degrees before winning a Nobel in chemistry – and Hauptman’s prize was awarded for a mathematical approach to determining molecular structures.

Even outside of the scientific disciplines, mathematicians have still managed to win Nobels. Mathematician and philosopher **Bertrand Russell** was awarded the Nobel Prize for Literature in 1950 “in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought”. Russell was famously anti-war, and was sent to prison during World War I for has pacifism.

Within maths, Russell is well known for his work on logic and the fundamental principles of mathematics – *Principia Mathematica*, which Russell wrote with Alfred Whitehead and published in 1910, is an attempt to write out the basic axioms underlying mathematics in order to understand them fully. It famously contains a proof that 1+1 = 2, spanning several hundred pages (it was very thorough). *Russell’s paradox*, a classical mathematical paradox, considers a way of defining sets of things – and in particular, asks the question: if you define a set as containing all the sets that do not contain themselves – does that set then need to contain itself?

The message you’re hopefully getting here is that while mathematics can be considered a discipline in itself, and having awards for incredible achievements in mathematics is important, it’s actually a subject which crosses over with many other types of research and thinking.

Maths is a language that helps us understand and interpret what we see in the world around us – so people working in science need to at least get along with it, if not embrace it as part of their work. We hope the Lindau laureates had a great week at their celebration, and that they can continue to use mathematical ideas to make the world a better place.

Katie Steckles wrote (15. July 2019):

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[…] Russell’s paradox, a classical mathematical paradox, considers a way of defining sets of things – and in particular, asks the question: if you define a set as containing all the sets that do not contain themselves – does that set then need to contain itself?More peaceably might be asked whether the designation of a set as

»containing all the sets that do not contain themselves«could constitute a definition of a set to begin with. (Apparently, it can’t.)

More embracing of the barbers, or the undertakers, in the world around us might then be to consider defining

– one set as

»containing all the sets that do not contain themselves, and also itself«, or– another set as

»containing all the sets that do not contain themselves, but not itself«.p.s.

Markus Pössel schrieb (16. Juni 2019 @ 17:25):

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Da es hier wieder zu aus meiner Sicht eher nebensächlichen Dingen sehr länglich wird, […]… fasse ich das in der Auseinandersetzung mit Koordinaten-“Nutzern” Wesentliche auf Bierdeckelgröße zusammen:

Aus Abständen, deren Werte durch Einsatz einer bestimmten definierten Messoperation ermittelt wurden, also z.B. (in der Wikipedia-Notation für Abstände im allerengsten Sinne)

und aus (der Umkehr-Funktion)

irgendeiner eins-zu-eins-umkehrbaren aber ansonsten beliebigenKoordinaten-Zuordnungergibt sich jeweils die Funktions-Komposition

.

Frank Wappler schrieb (15. July 2019 @ 10:56):

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[…] Aus Abständen […]und aus (der Umkehr-Funktion)

irgendeiner eins-zu-eins-umkehrbaren aber ansonsten beliebigenKoordinaten-Zuordnungergibt sich jeweils die Funktions-Komposition […]

Korrektur (hinsichtlich der Notation von Funktions-Kompositionen): Es ergibt sich

.