The world's most famous science award Nobel Prize does not have a mathematics award, which may be the biggest shortcoming of this award. But because of the huge influence of the Nobel Prize, other fields that are not included also have their own "Nobel Prizes". Mathematicians have their own Fields Medal. In fact, the Fields Medal is very different from the Nobel Prize, especially its strict age limit for winners.
It was not positioned as the highest award in the field of mathematics at first, but it won the reputation of "Nobel Prize in Mathematics" because of the accidental influence of political events; it is still controversial because of factors such as age and gender. How should we treat this award? Looking back at the establishment and presentation of the Fields Medal, we can see that there are many intriguing things in this award that have influenced the course of human wisdom.
The shortcomings of the Nobel Prize
On December 10, 1896, Swedish chemist and entrepreneur Alfred Nobel (1833-1896) died. According to his will, the vast fortune he left was used to create the Nobel Prize. Since 1901, the Nobel Prizes have been awarded every year to the five fields of physics, chemistry, physiology or medicine, literature, and peace, and only a few years are vacant. So here comes the question: Mathematics is the foundation of all natural sciences, why is there no mathematics prize in the Nobel Prize?
A popular rumor is that Nobel once had a feud with the Swedish mathematician Gösta Mittag-Leffler (1846-1927) because of personal feelings, so there was no mathematics prize. This is of course complete nonsense. There is no evidence of any feud between Nobel and Mitta-Leffler. In fact, as a leading figure in the Swedish scientific community, Mitta-Leffler was actively involved in the work related to the Nobel Prize. Under his strong recommendation, the Nobel Prize was awarded to the first theoretical physicist to win, Hendrik Lorentz (1853-1928), and the first woman to win, Marie Curie. Curie, 1867-1934). Mitta-Leffler has also hosted several celebrations for Nobel laureates in her home.
Coincidentally, Fields (John Charles Fields, 1863-1932), who proposed the establishment of the Mathematics Medal in the future, had a deep friendship with Mitta-Leeffler. Therefore, the establishment of the Fields Medal is sometimes interpreted as Fields venting his anger on Mita Leeffler. The absence of a Nobel Prize in mathematics has disappointed some mathematicians. Mitta-Leffler tried as early as 1884 to persuade King Oscar II of Sweden (Oscar II, 1829-1907) to establish a mathematical prize, awarded every four years.
But what ended up being a one-time bounty for a solution to the many-body problem was awarded to Henri Poincaré (1854-1912), whose winning paper pioneered the branch of mathematics in dynamical systems. In 1916, Mita-Leffler proposed to set up a gold medal in mathematics in comparison with the Nobel Prize, but there was no prize. The prize was Acta Mathematica, a mathematical journal he founded. This proposal also failed to materialize.
At that time, Sweden and Norway formed a common confederation Sweden-Norway Union. The Norwegian mathematician Sophus Lie (Sophus Lie, 1842-1899) proposed the establishment of an Abel Prize on the eve of his death, which will be awarded from 1902 to commemorate the genius Norwegian mathematician Abel (Niels Abel, 1802- 1829) centenary of his birth. For various reasons, Lee's proposal ultimately failed to materialize. [4] It was not until a hundred years later that the Norwegian government established the Abel Prize on the occasion of the bicentenary of Abel's birth, and awarded it for the first time in 2003.
ICM, UMI, and the establishment of the Fields Medal
To commemorate the 200th anniversary of Abel's birth, Norway also bid to host the 2002 International Congress of Mathematicians but lost to China. The International Congress of Mathematicians (ICM) is the highest meeting of mathematicians in the world. The first International Congress of Mathematicians was held in Zurich, Switzerland in 1897. The second ICM, held in Paris in 1900, is probably the most famous in history, as the German mathematician David Hilbert (1862-1943) presented 23 important unsolved problems at this congress. Beginning with the Paris Congress, the ICM was held every four years, during which it was suspended for several years due to the impact of the two world wars.
At the ICM in Rome in 1908, a Medaglia Guccia, named after the Italian mathematician Giovanni Guccia (1855-1914), was awarded to Francesco Severi (1879-1961). But the award did not last. The First World War severely tore apart the international mathematical community. At the ICM held in Strasbourg in 1920, the International Mathematical Union (French Union Mathématique Internationale, UMI) was established to organize the ICM. However, the alliance was not so international at the insistence of French mathematicians, Germany, and other Allied countries were excluded from the UMI, and allied mathematicians were not allowed to participate in the ICM. In fact, the location of this ICM is itself a humiliation to Germany: Strasbourg was ceded to Germany in 1871, after the Franco-Prussian War; in 1918, after the First World War, it had just returned to France.
Allied mathematicians were not allowed to attend the ICM in Bologna, Italy until 1928, and Hilbert received a standing ovation at the opening of the conference. However, the gap between countries has not been eliminated, and the activities of the International Mathematical Union are still full of political debate. In 1932, the International Mathematical Union was forced to dissolve.
The 1924 ICM was held in Toronto, Canada, the first time that the ICM was held outside of Europe. The chairman of the organizing committee of the conference is Fields, a Canadian mathematician, and the secretary is Xin Qi (John Lighton Synge, 1897-1995). Fields were educated in the Americas and later spent ten years in France and Germany, where he had a good relationship with the European mathematics community. Fields put a lot of effort into the organization of the Toronto conference. At that time, the center of mathematics was in Europe, and it took a lot of money to send a large number of European mathematicians across the ocean to America.
At that time, the scientific community lacked stable research funding, and Fields managed to raise a lot of money from the governments of the Dominion of Canada and the government of Ontario to solve the financial problems of the conference. He visited Europe for several months to coordinate the various organization's work of the Congress.
After the Toronto conference, Fields spent four years editing and publishing the conference proceedings. After completing this work, there is still a surplus of CAD 2,700 for the conference funds. So in 1931, the organizing committee led by Fields decided to take out 2,500 Canadian dollars and award two gold medals at the next International Congress of Mathematicians. In order to successfully set up the medal, Fields did a lot of work. He negotiated with mathematical societies in the United States, France, Germany, Italy, Switzerland, and other countries and won their support.
He also contacted the Canadian sculptor R. Tait McKenzie (1867-1938), who asked the latter to design the medal according to his own ideas. Fields was going to formally propose the establishment of the medal at the Zurich International Congress of Mathematicians in September 1932, but he, unfortunately, died a month before the Congress. Before his death, under the witness of Xin Qi, Fields donated a portion of his estate, about $47,000, to the Medal Fund. At the 1932 International Congress of Mathematicians, Xin Qi's proposal to replace Fields with a permanent medal was accepted.
Fields disagreed with the exclusion of Allied mathematicians by the UMI and ICM. In the proposal he wrote, he repeatedly emphasized that this should be an international medal, with no nationality restrictions on the winners. He wrote that the medal should use Latin or Greek, and its design should not be associated with any country, institution, or individual. Fields called the medal the International Medals for Outstanding Discoveries in Mathematics. However, the award was eventually named the "Fields Medal" against Fields' wishes.
The Fields Medal is made of 14K gold. The head portrait on the front of the medal is Archimedes, and the text is Latin Transire suum pectus mundoque potiri, which means beyond human limits and mastering the universe. The pattern on the back is the geometric figure on Archimedes' tombstone: a circumscribed cylinder of a sphere. The text is also Latin Congregati ex toto orbe mathematici ob scripta insignia tribuere, translated as mathematicians from all over the world gather to honor their important contribution to knowledge.
At its inception, the Fields Medal was awarded $1,500. Beginning with the Warsaw ICM in 1983, the bonus amount has been increased several times and is currently $15,000. This is nothing compared to the million-dollar Nobel Prize, and it is far from the scientific breakthrough awards that have been very popular in recent years. But the Fields Medal has a much higher status in the public mind than other mathematics awards. Even the Wolf Prize and Abel Prize, which are as influential in mathematics as the Fields Medal, are far less famous than the Fields Medal.
The author once listened to President Yu Minhong's inspirational speech when he was in class at New Oriental in which he talked about a mathematician friend of Yu Minhong who taught at an American university. This friend's ambition is to win the Fields Medal, so Yu Minhong asked him: How much is the bonus? After hearing his friend's answer, Yu said: I will give you this little money! The value of the Fields Medal is more than that. Fields Medal winners can get an annual salary of tens of thousands of dollars at any university in the United States. Only then was Yu satisfied and praised this friend for having a clear goal in life.
Early Fields Medal Awarding
In Fields' proposal, the medal is both a recognition of what has been accomplished and an encouragement to the recipient's future work. The rule was read to mean that medals were only awarded to young mathematicians, although there was no explicit age limit for earlier awards. The first Fields Medal was awarded at the Oslo International Congress of Mathematicians in 1936, and the winners were 29-year-old Lars Ahlfors (1907-1996) and 39-year-old Douglas (Jesse Douglas, 1897-1965).
Constantin Carathéodory (1873-1950) presented the work of the two laureates at the Congress. At that time, the Fields Medal was far less beautiful than it is today, and none of the winners had heard of it before. Alfors was congratulated in advance, but he was not formally notified before entering the venue. Although another winner, Douglas, arrived in Oslo, he was too tired from the journey and did not attend the award ceremony. Instead, his colleague Norbert Wiener (1894-1964) accepted the award instead.
The next ICM was scheduled to be held in Cambridge, Massachusetts, in 1940, but was delayed for ten years because of World War II, and it was not held until 1950. At this time, the world of mathematics has undergone tremendous changes. The United States has become the new center of mathematics in the world, and the new International Mathematical Union (IMU) has been formed. Schwartz (Laurent Schwartz, 1915-2002) and Atle Selberg (1917-2007) received the Fields Medal at this Congress, Harald Bohr (1887-1951) presents their work.
In Bohr's speech, he mentioned that the award committee agreed that the Fields Medal should be awarded to very young mathematicians, but did not make it clear what "young" meant. In fact, the most vocal candidate for the Fields Medal was Schwartz's French compatriot, 44-year-old André Weil (1906-1998). Bohr, chairman of the awards committee, was adamantly against giving Weil the award.
In his opinion, Weil is too old and has gained widespread recognition. Giving the award to Weil, he noted, could be a disaster because " it would give the impression that the committee was trying to select the greatest mathematical genius ." To exclude Weil, Bohr suggested setting the age at no age for the award. over 42 years old. Bohr's views sparked a heated debate among the jury, who, according to Bohr, "needed blood and tears" to decide the winner.
Bohr represents a tendency in the early Fields Medal awarding, that is, the Fields Medal is not to reward the best mathematicians, but to encourage those who have potential. If the Fields Medal does not position itself as awarded to the best mathematicians", it can avoid the various comparisons and debates that follow. Fields himself wrote in his proposal that invisible comparisons should be avoided when commenting on the winners. The fragmentation caused by the international situation left too painful memories for that generation of mathematicians, so they did not want the Fields Medal review to become a stage for political struggle.
In 1958, the 31-year-old Hirzebruch (Friedrich Hirzebruch, 1927-2012) was the favorite of the Fields Award, but he was out early because the chairman of the jury, Heinz Hopf (1894-1971) Think Hitzebrugge has gained enough recognition that no further encouragement is needed. The same situation happened to Grothendieck (Alexander Grothendieck, 1928-2014) twice in 1958 and 1962. At that time, the Fields Medal did not have the status of the highest award in mathematics at all, so the Fields Medal winners were not automatically regarded as the best mathematicians.
1966, Mathematics and Politics
1966 was a crucial year in the history of the Fields Medal. This year's ICM was held in Moscow, and the Fields Medal as we know it today was finalized this year. Two years before 1966, the Tata Trust of India decided to set up a Tata Award on the ICM. Like the Fields Medal, it was awarded to two people each year. The award could not be created because Indian domestic policy at the time did not allow the Tata Foundation to send money abroad. Fortunately, an anonymous person donated a sum of money, so that the Fields Medal can be awarded to four people this year. Since then, a system has been formed, and a maximum of four Fields Medals will be awarded each session.
Another change in the Fields Medal is that the award committee led by Georges de Rham (1903-1990) officially set the age limit for the winners to 40 years old. Specifically, the winner's 40th birthday cannot be before January 1st of the year of the convention. Perhaps because of the clear age limit, the award committee no longer has any scruples about awarding famous mathematicians. The four winners of this year are Atiyah (Michael Atiyah, 1929-2019), Cohen (Paul Cohen, 1934-2007), Grothendieck, and Smale (Stephen Smale, 1930-). Among them, Atiyah and Grothendieck can be ranked among the greatest mathematicians of the twentieth century, while Cohen and Smale were awarded for solving well-known problems in mathematics. It can be said that this selection has set a benchmark. Since then, the Fields Medal has aimed to select "the best mathematician under the age of 40.
The foregoing are institutional changes. Another incident happened this year, which made the Fields Medal truly out of the circle and won the reputation of the Nobel Prize in Mathematics. Of the four Fields Medal winners in 1966, both Grothendieck and Smale had strong political views. Grothendieck did not go to Moscow to attend the congress in protest of the Soviet authorities. Smale firmly opposed the Vietnam War and actively participated in many anti-war activities, so he was targeted by American politicians.
In the summer of 1966, the Un-American Activities Committee of the US Congress issued a subpoena to Smail, asking him to appear in Congress for questioning. The date of this congressional hearing coincided with the same day that Smail received the Fields Medal. Smail, who spent the summer traveling in Europe, was not served a subpoena. On the plane to Moscow, Smail met the Hungarian mathematician Paul Erdős (Paul Erdős, 1913-1996), from whom he learned about the subpoena.
After arriving at the venue, Smale received a letter from Serge Lang (1927-2005). The letter informed Smel of a report in the San Francisco Observer, which said that Smel, a professor of mathematics at Berkeley, escaped a subpoena from the U.S. Congress and went to Moscow, implying that Smel had defected. Smel's colleagues felt dumbfounded by the report and quickly explained to the media that Smel just went to Moscow to attend the International Congress of Mathematicians and receive the Fields Medal at the same time.
To make it easier for journalists to understand, they say that the Fields Medal is equivalent to the Nobel Prize in mathematics. This statement was quoted by major media and has been deeply rooted in the hearts of the people since then. (Some of the media, which is not too big to watch, still adopted the sensational headline "American mathematics teacher received Soviet reward").
The Fields Medal Controversy
The simple and crude statement that the Fields Medal is equivalent to the Nobel Prize in mathematics is easy for the public to understand, and to a certain extent, it also improves the right of the mathematics community to speak in front of the public. Smail was later almost canceled by the National Science Foundation because of his anti-war activities, but the halo of the Nobel Prize in Mathematics protected him. Many places give Fields Medal winners the same treatment as Nobel Prize winners. For example, at Berkeley, where Smale works, Fields Medal winners and Nobel Prize winners have access to dedicated parking spaces on campus.
Although it is known as the Nobel Prize in Mathematics, there is still a big difference between the Fields Medal and the Nobel Prize. The Nobel Prize often recognizes two or three collaborators of a certain work. For example, James Watson (James Watson, 1928-) and Crick (Francis Crick, 1916-2004), who discovered the double helix structure of DNA, were awarded at the same time, but The Fields Medal has never been awarded like this, although more and more important work is done by multiple mathematicians.
The biggest difference between the Fields Medal and the Nobel Prize is the age limit of the former. Someone jokes that it's a good thing that mathematics doesn't have a Nobel Prize so that mathematicians don't have to think about winning a Fields Medal after they turn 40, and don't have to wait every year for a late-night phone call from Sweden. Although it is a joke, the 40-year-old age limit does make the Fields Medal and the Nobel Prize have a different impact on the development of the discipline.
The Fields Medal is awarded to young mathematicians, usually for work that is currently hot, and these people will be active for two or three decades in the future and may have an impact for longer. There is no age limit for the Nobel Prize, and the winners are often past their creative peaks, and many have even retired. The oldest Nobel laureate, the good enough man (John B. Goodenough, 1922- ), was 97 years old when he won the Nobel Prize in Chemistry. Therefore, the Nobel Prize is largely a ratification of previous major achievements and does not often directly guide the trend of discipline development, especially in recent years.
Given the positioning of the Fields Medal as the "highest prize in mathematics", the age limit is implicitly unfair. At first glance, the age limit for the Fields Medal is 40 and under, the same for everyone. However, the ICM is only held every four years, and the maximum age at which mathematicians born in different years can receive the Fields Medal is different. For example, when the next International Congress of Mathematicians will be held in St. Petersburg in 2022, mathematicians born in 1981 will be disqualified. The last chance for a mathematician born in 1981 was in 2018 when they were 37 years old and had to compete with a 40-year-old mathematician born in 1978. You must know that the time it takes for major mathematical achievements to be made is usually measured in years, and it takes several years for them to be widely recognized. The time gap of three or four years is not negligible.
An extreme example is Oded Schramm (1961-2008), who made extraordinary contributions in the fields of geometry, topology, probability, etc. Schramm is best known for his introduction of SLE, or Stochastic Loewner Evolution, also known as Schramm-Loewner Evolution. This theory combines stochastic processes with conformal geometry to solve many important problems in probability theory and statistical mechanics. Schramm has two main collaborators, Lawler (Gregory Lawler, 1955- ) and Werner (Wendelin Werner, 1968- ). Werner won the Fields Medal in 2006 and Lawler won the Wolf Prize in 2019, mainly for their work on SLE. Part of the award-winning work of 2010 Fields Medal winner Stanislav Smirnov (1970- ) is also in the field of SLE.
However, as the founder of SLE theory, Schramm failed to win the Fields Medal due to his age and failed to win the Wolf Medal due to his untimely death. Schramm was born on December 10, 1961. After his death in a mountain climbing accident, the New York Times obituary wrote that if Schramm had been born three weeks and a day late, he would almost certainly have won the 2002 Fields Medal. But if a good mathematician misses out on the Fields Medal just because of such a tiny age difference, how can the Fields Medal be the highest prize in mathematics? There is also a view that the age limit of the Fields Medal is unfair to women because women tend to take on the responsibility of having children when they are young, which can delay scientific research for one to several years.
Even for mathematicians of the right age, the selection of the Fields Medal is hardly fair. As the saying goes, there is no first place in literature and no second in martial arts. The results of sports competitions can be represented by numbers, but how can mathematical results be quantified? How can different fields be compared? The selection of Fields Medal winners is largely tied to the preferences of jury members. As expected by predecessors such as Fields and Bohr, the selection was accompanied by a lot of controversies, and there were even political factors involved.
Following the announcement of the Fields Medal in 2014, Timothy Gowers (1963- ), the 1998 Fields Medal winner, pointed out in a blog post that many mathematicians, including more than one female mathematician, were also in this class. worthy of an award. Of course, this situation is by no means unique to the 2014 class, nor is it unique to the Fields Medal. There are similar controversies in the selection of any technology award, but the age limit of the Fields Medal means that most nominees have only one or two chances to win the award, so the controversy is more prominent.
In addition to the Fields Medal, there are several awards in the mathematics community that have no age limit as rewards for the highest achievements of mathematicians. These include the Wolf Prize, the Abel Prize, the Chern Prize, the Breakthrough Prize, and more. Among them, the Abel Prize is very similar to the Nobel Prize in many aspects such as its name, awarding country, awarding rules, and bonus amount. position.
Looking back at the history of the Fields Medal, it was not originally designed as the highest prize in mathematics, but it got the reputation of the Nobel Prize in Mathematics by accident. However, the inherent flaws in the system of the Fields Medal make it difficult to truly assume the responsibility of the highest prize in mathematics. Therefore, some people propose that returning the Fields Medal to its original intention and fading the halo of the highest award in mathematics is only regarded as an incentive for outstanding young mathematicians. This may be the correct attitude towards the Fields Medal.
Remaining awards from IMU
In addition to the Fields Medal, IMU has established a number of awards, also presented at the quadrennial International Congress of Mathematicians. These awards are given to only one person per session. These awards are briefly described below.
IMU Abacus Medal (formerly Rolf Nevanlinna Prize): Rolf Nevanlinna (1895-1980) was a famous Finnish mathematician who served as the chairman of IMU, the chairman of ICM in Stockholm, Sweden in 1962, and the honorary chairman of ICM in Helsinki, Finland in 1978. In memory of Neferlinna, the University of Helsinki funded the Neferlinna Prize to reward scientists who have made outstanding contributions to the mathematical aspects of information science. The Neferlinna Prize, which also has an age limit of 40, has been awarded since 1982 and is currently worth 10,000 euros. Neferlinna's cooperation with the Nazi forces was a major stain in his life, so IMU decided to change the Neferlinna Award to the IMU Abacus Award in 2022.
Carl Friedrich Gauss Prize: The German Mathematical Society and the IMU established the Gauss Prize with surplus funds from the ICM Berlin in 1998 to reward mathematical research that has had a significant impact on fields other than mathematics. There is no age limit for the Gauss Award, which has been awarded since 2006 and currently has a prize of 10,000 Euros.
Chern Medal: After the death of Mr. Chern (1911-2004), his family and friends funded the establishment of the Chern Award as a lifetime achievement award for mathematicians. The Chern Award has no age limit and has been awarded since 2010. The prize amount of the Chern Prize is US$500,000, of which US$250,000 goes to the laureate, and US$250,000 is donated to the institution designated by the laureate to support mathematics research, education, and popularization.
Leelavati Prize: At the closing ceremony of the ICM in Hyderabad, India, in 2010, the Rilawati Prize was presented to reward the popularization of mathematics. The well-known Indian IT company Infosys subsequently invested and made the Lilawati Award a permanent award of the IMU. Līlāvatī is a mathematical work written by the ancient Indian mathematician Bhāskara II (about 1114-1185). The Lilavati Prize is the only award among the IMU awards that are presented at the ICM Closing Ceremony rather than the Opening Ceremony and the only award that does not award mathematical research. The Lilawati Prize is worth INR 1 million.
Ladyzhenskaya Medal: Olga Ladyzhenskaya (1922-2004) was a famous Russian mathematician who was nominated for the Fields Medal in 1958. The Russian State Mathematical Committee, St. Petersburg State University, and the 2022 St. Petersburg ICM Organizing Committee jointly established the Radrenskaya Prize to reward revolutionary achievements in mathematical physics and related fields. The Radzhinskaya Prize has no age limit, the prize is 1 million rubles and will be awarded for the first time during the 2022 ICM at a ceremony marking the centenary of Radzhinskaya's birth.