01/08/2018

Germany, India, Iran, and Italy win the Fields Medal.

Notable and promising, four researchers born in different countries – Germany, India, Iran, and Italy – are the winners of the most important prize in world mathematics, the Fields Medal. Awarded for the first time in 1936, the prize recognizes outstanding work and encourages new achievements.

Awarded every four years at the world's largest gathering in the field, the International Congress of Mathematicians (ICM), this year it will be awarded to Caucher Birkar, Alessi Fegalli, Peter Scholze and Akshay Venkatesh, at a ceremony during the opening of ICM 2018, on August 1st, at Riocentro.

Conceived by Canadian mathematician John Charles Fields to celebrate great achievements in the field, the medal has already been awarded to 56 scholars of various nationalities, including Artur Avila, an extraordinary researcher at IMPA, who was honored in 2014 in South Korea. Due to its importance to the field, the award is cited as equivalent to a Nobel Prize in Mathematics.

Fields Medal winners are selected by a committee of leading experts appointed by the International Mathematical Union (IMU), the supranational organization that sponsors the ICMs. Every four years, up to four researchers under 40 years of age are chosen. In addition to the medal, there is a cash prize of 15,000 Canadian dollars.

Meet the winners of the 2018 Fields Medal:

Caucher Birkar (Cambridge University)

Caucher Birkar's dedication to the winding and multidimensional world of algebraic geometry – with its ellipses, lemniscates, Cassini ovals, among so many forms defined by equations – earned him the Philip Leverhulme Prize in 2010. This award is given to exceptional academics with particularly promising careers. Besides being well-deserved, considering Birkar's substantial contributions to the field of algebraic geometry, winning the Philip Leverhulme Prize was also a prediction: eight years later, the researcher from the University of Cambridge, in the United Kingdom, at the age of 40, joins the select group of Fields Medal winners.

Birkar, who in 2018 had already experienced recognition for his work with the London Mathematical Society Prize, was born in 1978 in the small town of Marivan, a Kurdish province in Iran with about 200,000 inhabitants, on the border with Iraq. He grew up with an interest sparked by algebraic geometry, a field of intersection between formulas and forms that, centuries earlier and in the same region, had attracted the attention of Omar Khayyam (1048-1131) and Sharaf al-Din al-Tusi (1135-1213).

After obtaining a bachelor's degree in Mathematics from the University of Tehran, Birkar moved to the United Kingdom, where he became a British citizen. In 2004, he completed his PhD at the University of Nottingham with the thesis "Topics in modern algebraic geometry". His main area of interest is birational geometry. He has dedicated himself to fundamental aspects of key problems in modern mathematics – such as minimal models, Fano manifolds, and singularities. His work has solved long-standing conjectures.

In 2010, the year he was awarded the Fondation Sciences Mathématiques de Paris prize, Birkar – together with Paolo Cascini (Imperial College London), Christopher Hacon (University of Utah), and James McKernan (University of California, San Diego) – wrote the paper “Existence of minimal models for varieties of log general type,” considered groundbreaking in the field. For this work, the quartet also received the 2016 Moore Prize from the American Mathematical Society.

Alessio Figalli (ETH Zurich)

Born in Naples, Italy, on April 2, 1984, Alessio Figalli discovered his interest in science late in life. Until high school, his greatest interest was playing soccer. Training for the International Mathematical Olympiad (IMO) sparked his interest in the subject, and upon entering the prestigious Scuola Normale Superiore di Pisa, he chose mathematics.

Figalli completed his doctorate in 2007 at the École Normale Supérieure de Lyon in France, under the supervision of Cédric Villani, who was also awarded the Fields Medal. In 2010.

Figalli was a researcher at the National Center for Scientific Research (CNRS), the École Polytechnique (both in France), and the University of Texas (USA). He is currently a professor at the renowned Swiss Federal Institute of Technology (ETH) in Zurich.

He is a specialist in partial differential equations and calculus of variations, a classical area of mathematics that goes back to fundamental laws of physics, such as the law of least action ("law of least effort"). He has important results in the area of optimal transport and its relations with the so-called Monge-Ampère equations. Among his most recent works, the proof of De Giorgi's Conjecture in dimension less than or equal to 5 stands out.

Figalli was a guest speaker at ICM 2014, held in Seoul, the capital of South Korea, 4 years ago. He has won the Peccot-Vimont Award (2011), the EMS Award (2012), the Cours Peccot Award (2012), the Stampacchia Medal (2015), and the Feltrinelli Award (2017), among other distinctions.

Peter Scholze (University Bonn)

At just 30 years old, the German Peter Scholze, born in the city of Dresden, is considered by the scientific community to be one of the most influential mathematicians in the world. At 24, he had already become a full professor at the University of Bonn. Scholze has impressed his colleagues with his intellectual capacity since adolescence, when he won three gold medals and one silver medal at the International Mathematical Olympiad (IMO).

Peter Scholze completed his undergraduate and master's degrees in record time, five semesters, and began to gain notoriety in the world of mathematical research at the age of 22, after simplifying a complex mathematical proof in number theory from 288 to 37 pages. A specialist in arithmetic algebraic geometry, he stands out for his ability to deeply understand the nature of mathematical phenomena and simplify them in presentations.

At age 16, while still a student at the Heinrich-Hertz-Gymnasium—a school that places great emphasis on mathematics and natural sciences—Scholze wanted to study Andrew Wiles' solution to Fermat's Last Theorem. Upon encountering the complexity of the result, he realized he was on the right track in choosing mathematics as a profession.

Scholze was an invited speaker at the ICM 2014 in Seoul, South Korea, and will be a plenary speaker this year at the Rio de Janeiro Congress. He has been recognized for his contributions to the field of arithmetic algebraic geometry and has accumulated some of the most important awards in mathematics, such as the European Mathematical Society Prize (2016), the Leibniz Prize (2016), the Fermat Prize (2015), the Ostrowski Prize (2015), the Cole Prize (2015), the Clay Research Fellowship (2014), the SASTRA Ramanujan Prize (2013), the Prix und Cours Peccot (2012), and now, the Fields Medal (2018).

Akshay Venkatesh (IAS)

Winning the highest honor among mathematicians in the world before the age of 40 is remarkable, even though Akshay Venkatesh's life has been marked by precocity. Born in New Delhi, the capital of India, in 1981, and raised in Australia, at the age of 12 he became a medalist at the International Mathematical Olympiad (IMO). From then on, he immersed himself in the field, beginning a remarkable career. He entered the Bachelor's degree program in Mathematics and Physics at the University of Western Australia when he was still a teenager of 13.

At age 20, he completed his PhD at Princeton University and soon became a professor at MIT (Massachusetts Institute of Technology), occupying a prestigious position offered to recently graduated PhDs of great distinction in the field of Pure Mathematics, previously held by famous researchers such as the American John Nash (1928-2015).

Upon leaving in 2004, he became a Clay Research Fellow and was appointed associate professor at the Courant Institute of Mathematical Sciences, New York University. Since the age of 27, he has been a professor at Stanford University and, as of this year, at the School of Mathematics of the Institute for Advanced Study (IAS).

Venkatesh has his roots in Number Theory – an area dealing with abstract questions with no known application until the advent of cryptography – but he also moves with ease through related topics such as Representation Theory, Ergodic Theory, and Automorphic Forms. Armed with a meticulous investigative sense, creativity, and a vision that transcends boundaries, detecting impressive connections between diverse areas, he has been making fundamental contributions to multiple fields of mathematical research.

Not surprisingly, his research had already been recognized with prestigious awards such as Ostrowisk (2017), Infosys (2016), SASTRA Ramanujan (2008) and Salem (2007). A guest speaker at ICM 2010, he will repeat the feat in August in Rio.