1. The Fields Medal: A Prize for Young Mathematicians Every Four Years
The Fields Medal is presented at the International Congress of Mathematicians, a gathering of mathematicians from around the world. This event happens once every four years. There is a strict rule regarding age. To be eligible, a mathematician must not have reached their 40th birthday before January 1 of the year the prize is awarded. A mathematician whose 40th birthday is January 1 of the award year is still eligible. [1][7].
The selection committee chooses at least two winners. However, there is a strong preference for selecting four winners. The rules state that a maximum of four medals can be awarded at any single congress [7].
2. How Leftover Money from the 1924 Toronto Conference Started the Medal
The idea for the medal began at the 1924 International Congress of Mathematicians held in Toronto, Canada. At this meeting, a resolution was passed to award two gold medals at each future congress. The medals were created by J.C. Fields, a Canadian mathematician who served as the secretary of that conference [1].
After the conference accounts were closed, there was a surplus of about $2,700. According to the Dictionary of Canadian Biography, Fields proposed using this leftover money to fund the medals [2]. That leftover money helped launch the award. was the approximately $2,700 remaining after the meeting.
3. Why Fields Wanted a Prize Without a Country's or Person's Name
Fields wanted the prize to be chosen by an international committee. He did not want the award to carry the name of any specific country or individual. Only the winners’ names are engraved on the medal’s edge. [3][4].
On the front of the medal, there is a profile of Archimedes, the ancient Greek scholar, along with his name in Greek. There is also a Latin inscription: "TRANSIRE SUUM PECTUS MUNDOQUE POTIRI." The inscription means "Transcend your human limitations and master the world" [3][4]. The back of the medal contains text stating that mathematicians from all over the world present the award to honor outstanding achievements [3].
Despite the intention to avoid personal names, the prize is now called the "Fields Medal." It is ironic that the award later came to be known by the name of the person who wanted to remove names from it.
4. How the Medal Plan Was Approved After Fields Died
Fields worked for six years to establish the prize. In December 1930, he gained the support of the American Mathematical Society and reached out to European societies. However, he died on August 9, 1932. The following month, in September 1932, the Council of the International Mathematical Union accepted the proposal at a meeting in Zurich [2][3].
In his will, Fields left about $45,000 to be used for a small cash prize awarded with each medal. The exact amount varies slightly depending on the source [2]. The first awards were given in 1936 at the Oslo Congress to Jesse Douglas from the United States and Lars Ahlfors from Finland [4]. The cash prize component began later, at the 1950 congress in Cambridge, USA [2].
5. Why the Fields Medal Has an Age Limit of 40
The International Mathematical Union states that the purpose of the prize is to honor both existing achievements and the expectation of future work [1]. The focus on younger mathematicians connects to this expectation of what they will do next. Initially, only two prizes were given. However, as mathematics expanded, the rules were changed in 1966 to allow up to four winners per congress [1].
There are also examples of people who were not eligible due to the age limit. In 1998, Andrew Wiles proved Fermat's Last Theorem, a problem that had remained unsolved for a long time. Because he was over the age limit, he could not receive the Fields Medal. Instead, the International Mathematical Union offered him a special silver plaque [1].
In 2006, Grigori Perelman declined to accept the Fields Medal [1].
SAFETY NOTE: Why are only young people eligible? Think about this question: Why are only young people eligible? You could discuss it with an adult or teacher.
6. Japan's Three Fields Medal Winners and the 2026 Recipients
Three mathematicians from Japan have won the Fields Medal. They are Kunihiko Kodaira (1954), Heisuke Hironaka (1970), and Shigefumi Mori (1990). All three specialized in algebraic geometry, according to the Science Portal by the Japan Science and Technology Agency [5].
Only three women have won the prize so far. Maryam Mirzakhani from Iran was the first in 2014. Maryna Viazovska won in 2022. Hong Wang won in 2026 [1].
The most recent winners were announced on July 23, 2026, at the opening ceremony of the International Congress of Mathematicians in Philadelphia, USA. Four people were named [6]. One of them, Hong Wang, is recognized for solving the Kakeya problem in three dimensions in the field of harmonic analysis. The details are complex, so for now, just remember the name [6].
7. Calculating When the Next Mathematics Congress Will Be Held
If you want to learn more, you can try a simple calculation. The congress happens every four years. The next one after 2026 is scheduled for 2030. Calculate how old you will be in 2030. Then work out which birth dates would make someone eligible for the 2030 prize. Remember, they must not have turned 40 before January 1, 2030. This helps you feel the meaning of the age limit.
You can also visit a library or school library to find books about Kunihiko Kodaira, Heisuke Hironaka, or Shigefumi Mori, or books that introduce the Fields Medal.