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Fields Medal

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The Fields Medal is a premier international award for excellence in mathematics.

Jean-Pierre Serre, Erlangen 1997
Jean-Pierre Serre, Erlangen 1997

It is presented to two, three, or four mathematicians at a time. This ceremony occurs during the International Congress of Mathematicians. This congress is a major convention held by the International Mathematical Union. Many people refer to the Fields Medal as the "Nobel Prize of Mathematics."

Atle Selberg
Atle Selberg

It is widely considered one of the highest honors a mathematician can receive. A 2013–14 reputation survey by IREG ranked it as the second most prestigious award in the field, following the Abel Prize.

The medal operates under a specific set of rules that distinguish it from other prizes. To be eligible, a mathematician must be under 40 years of age on January 1 of the award year.

Hironaka heisuke 1976
Hironaka heisuke 1976

This age restriction was a deliberate choice by the award's founder. The goal is to recognize outstanding work while encouraging future achievements. It also aims to stimulate renewed effort among the broader mathematical community. Additionally, an individual may only receive the Fields Medal once. This means a recipient is not eligible for the award in future cycles.

The history of the medal begins with the work of John Charles Fields.

Lars Ahlfors - MFO
Lars Ahlfors - MFO

He was a Canadian mathematician who was instrumental in establishing the prize. Fields designed the medal himself and provided the initial funding for the monetary component. He passed away before the award was officially established. Following his death, John Lighton Synge oversaw the implementation of his plan. The first medals were awarded in 1936 to Lars Ahlfors and Jesse Douglas.

Portrait of Jesse Douglas in c. 1932
Portrait of Jesse Douglas in c. 1932

Since 1950, the medal has been awarded every four years.

Mathematical achievements vary greatly among the recipients. In some years, the award includes official citations for specific breakthroughs. In other years, no specific reason is listed. However, every medalist has a body of work that is lectured upon during the congress. For example, Lars Ahlfors won for his research on covering surfaces related to Riemann surfaces.

Lars Ahlfors - MFO
Lars Ahlfors - MFO

Jesse Douglas was recognized for his work on the Plateau problem regarding minimal surfaces. Atle Selberg won for his work on the prime number theorem and the Riemann zeta function.

Atle Selberg
Atle Selberg

These lectures ensure that the mathematical community understands the depth of each winner's contribution.

Throughout its history, the medal has been won by a diverse group of researchers. As of 2022, a total of 64 people have been awarded the medal.

Alexander Grothendieck
Alexander Grothendieck

While most winners hold a PhD in mathematics, there are rare exceptions. Edward Witten and Martin Hairer both hold PhDs in physics. In 2014, Maryam Mirzakhani made history as the first female Fields Medalist.

Edward Witten at Harvard
Edward Witten at Harvard

The most recent group of medalists was announced on July 5, 2022. This event was live-streamed from Helsinki, Finland, after a change in location. The ceremony was originally planned for Saint Petersburg, Russia, but moved due to the 2022 Russian invasion of Ukraine.

The award also includes a financial component to support the researchers. Since 2006, the prize has included a monetary award of 15,000 dollars.

Shing-Tung Yau at Harvard
Shing-Tung Yau at Harvard

This support helps mathematicians continue their high-level research. The award serves as a bridge between recognizing past success and fueling future discovery. By focusing on mathematicians under 40, the prize ensures that the field remains vibrant and energetic. It celebrates the momentum of young minds at the peak of their creative abilities.

The Fields Medal connects the individual researcher to the global mathematical community. The award is tied to the International Congress of Mathematicians, which brings experts together from around the world. These gatherings allow for the sharing of complex ideas, such as those in topology, algebra, or analysis. The next awarding ceremony is scheduled to take place in Philadelphia during the 2026 congress.

Michael Freedman, circa 1970s (re-scanned C; headshot)
Michael Freedman, circa 1970s (re-scanned C; headshot)

Through this cycle of recognition, the Fields Medal helps define the most important directions in modern mathematics.

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🖼️ Images & Media (61)
File:Lars Ahlfors - MFO.jpg
Lars Ahlfors - MFO.jpg
File:Portrait of Jesse Douglas in c. 1932.jpg
Portrait of Jesse Douglas in c. 1932.jpg
File:LaurentSchwartz.jpg
LaurentSchwartz.jpg
File:Atle Selberg.jpg
Atle Selberg.jpg
File:Kodaira Kunihiko.jpg
Kodaira Kunihiko.jpg
File:Jean-Pierre Serre, Erlangen 1997.JPG
Jean-Pierre Serre, Erlangen 1997.JPG
File:René Thom.jpeg
René Thom.jpeg
File:Lars Hörmander.jpg
Lars Hörmander.jpg
File:John Milnor, 1993 Oct (portioned).jpg
John Milnor, 1993 Oct (portioned).jpg
File:Atiyah-Hirzebruch crop.jpeg
Atiyah-Hirzebruch crop.jpeg
File:Alexander Grothendieck.jpg
Alexander Grothendieck.jpg
File:Stephen Smale2.jpg
Stephen Smale2.jpg

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