Four notable and promising researchers from four nations – Germany, India, Iran, and Italy – won the most important international award in mathematics, the Fields Medal at ICM 2018. Delivered for the first time in 1936, the medal is recognizes excellent contributions made to mathematics by young researcher. The coveted prize is seen as an incentive for new and outstanding achievements. Awarded every four years at the world’s largest mathematics event – the International Congress of Mathematicians (ICM) – the 2018 medals were awarded to Peter Scholze, Akshay Venkatesh, Caucher Birkar, and Alessi Fegalli at ICM’s opening ceremony on August 1^{st}, at Riocentro.

Founded by the Canadian mathematician John Charles Fields to celebrate outstanding achievements, the Fields Medal, often likened to a Nobel Prize of Mathematics, has already been awarded to 56 international scholars. Brazilian Fields laureate Artur Avila, an IMPA researcher won a Fields Medal in 2014 in South Korea. Fields Medal winners are selected by a panel of renowned specialists nominated by the Executive Committee of the International Mathematical Union (IMU), which organizes ICM, during which 2-4 researchers under the age of 40 are awarded for outstanding contributions to math. Since 2006, a cash prize of 15 thousand Canadian dollars has accompanied the medal.

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Meet the winners of the Fields Medal 2018:

**Akshay Venkatesh**

Conquering the greatest honor among the world’s mathematicians before the age of 40 is a notable accomplishment, but the life of Akshay Venkatesh was already marked with precocious feats. Born in New Delhi in 1981, and raised in Australia, Venkatesh became a medalist at the International Mathematical Olympiad when he was 12 years old. This propelled him into the world of mathematics, and kickstarted his illustrious career. He began his bachelor’s degree in Mathematics and Physics at the University of Western Australia at the age of 13, and seven years later, aged 20, had completed his PhD at Princeton University. Venkatesh was appointed as an instructor at C.L.E. Moore, at the Massachusetts Institute of Technology (MIT), a prestigious position offered to recent graduates in the area of Pure Mathematics, previously occupied by prominent figures such as the American John Nash (1928-1915). Upon leaving MIT in 2004, he became a Clay Research Fellow and was appointed associate professor at the Courant Institute of Mathematical Sciences at New York University. He became a professor at Stanford University at the age of 27, and as of this year is a faculty member at the Institute for Advanced Study (IAS).

Venkatesh researches Number Theory – an area that deals with abstract issues and had no known application until the arrival of cryptography in the late 1970s – and he roves with ease through related topics, such as Theory of Representation, Ergodic Theory, and Automorphic Forms. Armed with a meticulous, investigative and creative approach to research, detecting impressive connections between diverse areas, Venkatesh’s contributions are fundamental to several fields of research in Mathematics. He has won several accolades for his work, including the following prizes: Ostrowisk (2017), Infosys (2016), SASTRA Ramanujan (2008) and Salem (2007). Previously a guest speaker at the 2010 ICM, Venkatesh was been invited to speak in ICM 2018.

**Alessio Figalli**

Born in Naples, Italy on April 2, 1984, Alessio Figalli discovered an interest in science later than some. Until high school, he was more interested in playing football. Preparation for the International Mathematical Olympiad (IMO) awakened his interest in the subject and he chose to study math when he joined the Scuola Normale Superiore di Pisa. Figalli completed his PhD in 2007 at the École Normale Supérieure de Lyon in France, with the guidance of Fields Medal laureate Cédric Villani. He has worked at the French National Center for Scientific Research, École Polytechnique, the University of Texas in the USA and ETH Zürich in Switzerland. A specialist in calculating variations and partial differential equations, he was invited to speak at the 2014 ICM in Seoul. He has won several awards, including: Peccot-Vimont (2011), EMS (2012), Cours Peccot (2012), Stampacchia Medal (2015) and Feltrinelli (2017).

**Caucher Birkar**

Caucher Birkar’s dedication to the winding and multidimensional world of algebraic geometry, with its ellipses, lemniscates, Cassini ovals, among so many other forms defined by equations, granted him the Philip Leverhulme prize in 2010 for exceptional scholars whose greatest achievement is yet to come. Eight years later, the Cambridge University researcher joins the select group of Fields Medal winners at the age of 40. Birkar, who was recognized earlier this year for his work as one of the London Mathematical Society Prize winners, was born in 1978 in Marivan, a Kurdish province in Iran bordering Iraq with about 200,000 inhabitants. His curiosity was awakened by algebraic geometry, an area that had attracted the attention of Omar Khayyam (1048-1131) and Sharaf al-Din al-Tusi (1135-1213) in previous centuries.

After graduating in Mathematics from Tehran University, Birkar sought refugee status in 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”. Throughout his trajectory, birational geometry has stood out as his main area of interest. He has devoted himself to the fundamental aspects of key problems in modern mathematics – such as minimal models, Fano varieties, and singularities. His theories have solved long-standing conjectures. In 2010 Birkar wrote (alongside Paolo Cascini (Imperial College London), Christopher Hacon (University of Utah) and James McKernan (University of California, San Diego)) an article called “Existence of minimal models for varieties of general log type” that revolutionized the field. The article earned the quartet the AMS Moore Prize in 2016.

**Peter Scholze**

Peter Scholze was born in Dresden, Germany on December 11, 1987. At 30 years old, he is already considered by the scientific community as one of the most influential mathematicians in the world. In 2012, at age 24, he became a full professor at the University of Bonn, Germany. Scholze impresses his colleagues with the intellectual ability he has shown since was a teenager, when he won four medals – three gold and one silver – at the International Mathematical Olympiad (IMO). The German mathematician completed his university graduate and masters in record time – five semesters – and gained notoriety at the age of 22, when he simplified a complex mathematical proof of numbers theory from 288 to 37 pages. A specialist in arithmetic algebraic geometry, he stands out for his ability to understand the nature of mathematical phenomena and to simplify them during presentations.

At age 16, still a student at the Heinrich-Hertz-Gymnasium – a school with a strong scientific focus – Scholze decided to study Andrew Wiles’ solution to Fermat’s Last Theorem. Faced with the complexity of the result, he realized that he was on the right track in choosing Mathematics as a profession. He was a guest speaker at ICM 2014 in Seoul, South Korea, and will be a plenary member this year at ICM 2018. Scholze is well decorated for his contributions to arithmetic algebraic geometry, and he has collected several major mathematics awards, such as EMS (2016), Leibniz (2016), Fermat (2015), Ostrowski (2015), Cole (2015), Clay Research 2014), SASTRA Ramanujan (2013), Prix and Cours Peccot (2012) and the Fields Medal (2018).