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How are the best of the best recognized in Mathematics?

Mathematicians are often touted as the smartest people on the planet but then you hear about the best and brightest winning the Nobel Prize in Physics, Chemistry, Literature, Medicine, Economics... Peace... but not MATHEMATICS. I haven't really thought too much about it until I started to research for this post. I knew Mathematicians had their own awards and just left it at that. Well, let's take a look at what was up with Alfred Nobel and then talk about the biggest math prizes.

Source: Wikipedia

Alfred Nobel

Born
Alfred Bernhard Nobel

21 October 1833
Stockholm, Sweden
Died10 December 1896 (aged 63)
Sanremo, Italy
Nobel was a Swedish chemist and inventor. He holds 355 patents with dynamite being the most well known. After being criticized for making a fortune off of the production of armaments, he decided to leave his fortune to the Nobel Prize Institute to change his legacy. His last will and testament set aside monies to establish the Nobel Prizes. These prizes were to be awarded annually without regard to nationality.

Nobel was a solitary man who never married. He traveled for business much of his life and was able to speak proficiently in Swedish, French, German, Russian, English, and Italian.

Nobel didn't include Mathematics in his creation of the Nobel Prizes, not because he hated math, but because he felt math was a tool for the sciences and therefore mathematics would be recognized through the awards in Physics and Chemistry. Despite not having a specific award for mathematics many mathematicians have been awarded Nobel Prizes since 1901.
  • 1902 Lorentz (Physics)
  • 1904 Rayleigh (Physics)
  • 1911 Wien (Physics)
  • 1918 Planck (Physics)
  • 1921 Einstein (Physics)
  • 1922 Bohr (Physics)
  • 1929 de Broglie (Physics)
  • 1932 Heisenberg (Physics)
  • 1933 Schroedinger (Physics)
  • 1933 Dirac (Physics)
  • 1945 Pauli (Physics)
  • 1950 Russell (Literature)
  • 1954 Born (Physics)
  • 1962 Landau (Physics)
  • 1963 Wigner (Physics)
  • 1965 Schwinger (Physics)
  • 1965 Feynman (Physics)
  • 1969 Tinbergen (Economics)
  • 1975 Kantorovich (Economics)
  • 1983 Chandrasekhar (Physics)
  • 1994 Selten (Economics)
  • 1994 Nash (Economics)
Now that we have talked about what award isn't specifically for mathematics let's get in to the top two that are for mathematics.

Fields Medal

Front of the Fields Medal
Source: Wikipedia
Back of the Fields Medal
Source: Wikipedia
J.C. Fields, a Canadian Mathematician, proposed an award to recognize both existing work and the promise of future achievement, and donated the funds to establish the medal.

Starting in 1936, the International Congress of the International Mathematical Union awards medals (up to four) to mathematicians under the age of 40. These medals are given every four years. While it is often described as the Nobel Prize of Mathematics, the Fields Medal is regarded as the second most prestigious international awards, after the Abel Prize.

A Fields Medal can only be awarded to a person under 40 once. 60 people have won the medal as of 2018, with the exception of one PhD in Physics (Edward Witten), all recipients have had PhD in mathematics. There has only been one woman awarded the medal, Maryam Mirzakhani from Iran in 2014. The medal currently comes with a 15,000 Canadian Dollar prize.

Most Fields Medalists have been mentored by other Fields Medalists so that they fall into 4 major groups. The ethnicities of Fields Medalists have also been analyzed and most recipients are from America and Europe; begging the question how can we develop elite mathematicians that are more diverse?
Source: areppim

Abel Prize

Modeled after the Nobel Prizes, the Abel Prize is awarded each year by the King of Norway. After Nobel outlined his plans for the five original Nobel Prizes, Sophus Lie proposed the establishment of a mathematics honor in 1899. King Oscar II of Sweden and Norway was willing to establish and finance this prize in 1902, but, despite this, the Abel Prize was not established until 2001 by the Government of Norway. The laureates are chosen each year by the members of the Abel Prize board. The first Prize was set to be awarded in 2002 to honor the 200th anniversary of Niels Henrik Abel's birth, a century after its first inception. In 2005, the Bernt Michael Holmboe Memorial Prize was added to promote excellence in mathematics education.

Each march the Abel Prize Board recommends five mathematicians and the Norwegian Academy of Science and Letters declares the winner. The Prize is funded through the national budget and controlled by the Board. 24 Laureates have been chosen since 2003 with only one women, Karen Uhlenbeck in 2019.

The prize is currently 7.5 million Norwegian Kroner.

Winners of Both Prizes

At this time only 5 people have been awarded both the Fields Medal and the Abel Prize. Due to the relative "newness" of the Abel Prize there are bound to be many more who earn both in their careers.

Jean-Pierre Serre ('54, '03)
Michael Atiyah ('66, '04)
John G. Thompson ('70, '06)
John Milnor ('62, '11)
Pierre Deligne ('78, '13)

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