Luis Caffarelli, 74, has won the 2023 **Abel Prize** “for his seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge-Ampère equation”, his citation read.

First awarded in 2003, the Abel prize “recognises pioneering scientific achievements in mathematics”. It is named after Norwegian mathematician Niels Henrik Abel (1802-29), who in his short life made pioneering contributions in a multitude of fields. It is often considered to be an equivalent of the **Nobel prize** – **which does not have a category for mathematics **– and has been modelled as such.

The prize includes a monetary award of 7.5 million kroner (roughly $ 720,000) and a glass plaque designed by Norwegian artist Henrik Haugan. It is awarded by The Norwegian Academy of Science and Letters, on behalf of the Ministry of Education.

## Who is Luis Caffarelli and why did he win the Abel prize?

Caffarelli was born and raised in Buenos Aires, Argentina, making him the first Abel laureate from South America. Currently, he is a professor at the University of Texas, Austin. He is married to fellow Argentinian mathematician Irene Martínez Gamba, who teaches at UT, Austin as well.

Cafarelli has been one of the leading figures in the study of partial differential equations for over five decades. According to his Abel citation, “Partial differential equations arise naturally as laws of nature, whether to describe the flow of water or the growth of populations. These equations have been a constant source of intense study since the days of Newton and Leibniz.”

The Abel citation states that Caffarelli has made “groundbreaking contributions” that have “radically changed our understanding of classes of nonlinear partial differential equations with wide applications. The results are technically virtuous, covering many different areas of mathematics and its applications.” Notably, he has been recognised for “combining brilliant geometric insight with ingenious analytical tools and methods” in this field of mathematics.

“Mathematics is like a Swiss army knife: the same tool can be applied to many different problems. The tools that Caffarelli has come up with have been applied to many different problems, from equations describing nature to financial mathematics”, Helge Holden, the chair of the Abel committee, told *The Guardian*.

## What is the Abel Prize?

The prize was established by the Norwegian Parliament (Stortinget) in 2002, marking the 200th anniversary of Niels Henrick Abel’s birth. Notably, the prize was first proposed in 1899, when Norwegian mathematician Sophus Lie proposed establishing a prize named after Abel when he learned that Alfred Nobel’s plans for annual prizes would not include a prize in mathematics. This plan never materialised.

In 2001, as Abel’s 200th birth anniversary drew close, a working group was formed to develop a proposal for such a prize. This group presented a proposal to the Norwegian prime minister, who soon announced the creation of the Abel prize.

The Abel Prize is awarded and administered by the Norwegian Academy of Science and Letters on behalf of the Norwegian government. It is financed by the Norwegian government which also does not tax the prize money. The recipients are chosen by the Abel Committee, which comprises expert mathematicians, all appointed by the Norwegian Academy of Science and Letters, under the advice of the International Mathematical Union (IMU) and the European Mathematical Society (EMS).

## Who was Niels Henrick Abel?

Niels Henrik Abel (1802-1829) was a Norwegian mathematician who left a big impact on a number of fields in his rather short life. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 250 years.

He was also an innovator in the field of elliptic functions, discoverer of what would later be known as Abelian functions. He made all his discoveries while living in crippling poverty. He died of tuberculosis at the age of 26.

Commenting on the richness of Abel’s work in his shirt lifespan, French mathematician Charles Hermite once said, “ Abel has left mathematicians enough to keep them busy for five hundred years.”

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