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This article is from the official account of Wechat: back to Park (ID:fanpu2019), by Ni Yi (Professor of Mathematics, California Institute of Technology)
The Nobel Prize, the most famous science prize in the world, does not have a math prize, which is perhaps the biggest drawback of this award. However, because of the great influence of the Nobel Prize, other areas that have not been included also have their own "Nobel Prizes". Mathematicians have their own Fields Prize. In fact, the Fields Prize is very different from the Nobel Prize, especially its strict age limit on the winners. At first, it was not defined as the highest award in the field of mathematics, but it won the reputation of "Mathematical Nobel Prize" because of the accidental influence of political events, and now it is controversial because of age, gender and other factors. What on earth should we do with this award? Looking back on the establishment and presentation of the Fields Award, we can see that there are many intriguing things about this award, which affects the course of human wisdom.
The deficiency of the Nobel Prize on December 10, 1896, Alfred Nobel, a Swedish chemist and entrepreneur, died. According to his will, the great wealth he left behind was used to create the Nobel Prize. Since 1901, Nobel Prizes have been awarded annually to five fields: physics, chemistry, physiology or medicine, literature and peace, with only a few years vacant.
So the question arises: mathematics is the foundation of all natural sciences, why is there no math prize in the Nobel Prize?
It is not a household name that there is no math prize in the Nobel Prize. A popular rumor is that Nobel once had a grudge against Swedish mathematician G ö sta Mittag-Leffler,1846-1927 because of personal problems, so there was no mathematics prize. This is, of course, complete nonsense. There is no evidence of any feud between Nobel and Mita-Levler. In fact, as a leader of the Swedish scientific community, Mita Lefler has actively participated in the work related to the Nobel Prize. Under his strong recommendation, the Nobel Prize has the first award-winning theoretical physicist-Lorentz (Hendrik Lorentz,1853-1928), and the first female winner-Marie Curie (Marie Curie,1867-1934). Mita Lefler also held several celebratory banquets in his home for Nobel laureates. [1]
The former residence of Mita Lefler. He donated the house and established the world's first mathematics institute, now known as the Mita-Levler Institute. Wikipedia coincidentally, Fields (John Charles Fields,1863-1932), who proposed to set up a math medal in the future, has a deep friendship with Mita Levler. [2] so the establishment of the Fields Award is sometimes interpreted as Fields taking it out on Mita Lefler.
The absence of the Nobel Prize in mathematics disappointed some mathematicians. As early as 1884, Mita Lefler tried to persuade King Oscar II of Sweden (Oscar II,1829-1907) to set up a math prize to be awarded every four years. But in the end, an one-off reward was set up for the solution of multi-body problems, which was won by Henri Poincar é (1854-1912), whose winning thesis pioneered the mathematical branch of dynamical systems. In 1916, Mita Lefler proposed to set up a gold medal in mathematics to compare it with the Nobel Prize, but there was no prize. The prize was Acta Mathematica, a mathematics magazine he founded. This proposal also failed to materialize. [1]
At that time, Sweden and Norway formed a confederation called the Swedish-Norwegian Alliance. On the eve of his death, the Norwegian mathematician Sofius Lee (Sophus Lie,1842-1899) proposed the establishment of an "Abel Prize", which will be awarded from 1902 to commemorate the 100th anniversary of the birth of the talented Norwegian mathematician Niels Abel,1802-1829. Due to various reasons, Li's proposal finally failed to come true. [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, which was first awarded in 2003.
Establishment of ICM, UMI and Fields Prizes to commemorate the bicentenary of Abel's birth, Norway also applied for the 2002 International Congress of mathematicians, but lost to China. The International Congress of mathematicians (International Congress of Mathematicians, ICM) is the highest event for 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 was probably the most famous in history because the German mathematician Hilbert (David Hilbert,1862-1943) raised 23 important unsolved questions at this Congress. Since the Paris Congress, ICM has been held every four years, during which it was suspended for several years under the influence of two world wars.
At the ICM held in Rome in 1908, a Medaglia Guccia was awarded after the Italian mathematician Giovanni Guccia,1855-1914, and the winner was Severi (Francesco Severi,1879-1961). But the award did not last. [3]
The first World War seriously torn apart the international mathematical community. In 1920, at the ICM in Strasbourg, the International Mathematical Union (French-speaking Union Math é matique Internationale,UMI) was established to organize the ICM. However, the alliance is not so international: at the insistence of leading figures in French mathematics, Germany and other allied countries are excluded from the UMI, and allied mathematicians are not allowed to participate in the ICM. [5] in fact, the venue of this ICM is itself a humiliation to Germany: Strasbourg was ceded to Germany in 1871 after the Franco-Prussian War, and just returned to France in 1918 after World War I.
It was not until 1928 that Confederate mathematicians were allowed to attend the ICM in Bologna, Italy, and Hilbert received a standing ovation at the opening ceremony. However, the estrangement between countries has not been eliminated, and the activities of the International Mathematical Union are still full of political debates. In 1932, the International Mathematical Union was forced to dissolve. [5]
The 1924 ICM was held in Toronto, Canada, and it was the first time that ICM was held outside Europe. The chairman of the organizing committee is Fields, a Canadian mathematician, and the secretary is Xin Qi (John Lighton Synge,1897-1995). Fields was educated in America, then spent ten years in France and Germany, and had a good relationship with the European mathematics community. Fields put a lot of effort into preparing for the Toronto conference. At that time, the center of mathematics was in Europe, and it cost 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 Canadian dominion government and the Ontario government to solve the conference's financial problems. He visited Europe for a few more months to coordinate the various organizational work of the General Assembly. [2]
Note: the pronunciation of Synge is the same as sing, and the common translation names are "Xin Ji", "Singh", "Xin" and so on. This paper adopts the translation of Mr. Qian Weichang in "80 self-narration".
Fields spent four years editing and publishing the proceedings of the conference after the Johns Hopkins University Toronto Conference. Upon completion of this work, there is still a balance of C $2700 for the conference. So in 1931, the organizing committee led by Fields decided to take out 2500 Canadian dollars and award two gold medals at the next International Congress of mathematicians. [5]
Fields did a lot of work to successfully set up the medal. He discussed with mathematical societies in the United States, France, Germany, Italy, Switzerland and other countries and won their support. He also contacted McKinsey (R. Tait McKenzie,1867-1938), a Canadian sculptor, to design medals in his own way. Fields had planned to formally propose a medal at the International Congress of mathematicians in Zurich in September 1932, but he died of illness a month before the Congress. On his deathbed, Fields donated about C $47000 of his inheritance to the Medal Fund in the presence of Xinqi. At the International Congress of mathematicians in 1932, Xinqi's proposal to set up a permanent medal instead of Fields was accepted. [5]
Fields does not agree with UMI and ICM's exclusion of allied mathematicians. In the proposal he wrote, he repeatedly stressed that it should be an international medal with no nationality restrictions on the winners. 'The medal should be in Latin or Greek, and its design cannot be associated with any country, institution or individual,'he wrote. Fields calls this medal the International Medal for Outstanding Discovery in Mathematics (International Medals for Outstanding Discoveries in Mathematics). However, the award was eventually named the Fields Medal, against Fields' own wishes. [6]
The front and back of the Fields Medal: the Wikipedia Fields Medal is made of 14K gold. The head on the front of the medal is Archimedes, written in Latin "Transire suum pectus mundoque potiri", which means "transcend human limits and master the universe". The pattern on the back is the geometry on the Archimedes tombstone: the outer-cut cylinder of the ball. The text is also Latin "Congregati ex toto orbe mathematici ob scripta insignia tribuere", translated as "mathematicians from all over the world gather together to honor their important contribution to knowledge."
At the beginning of its establishment, the prize for the Fields Award was C $1500. The bonus has been increased several times since Warsaw ICM in 1983 and is now C $15000. This is negligible compared to the million-dollar Nobel Prize, and it is far from being compared to the scientific breakthrough award which has been very popular in recent years. But the Fields Prize has a much higher status in the eyes of the public than other math awards. Even the Wolf Prize and the Abel Prize, which are as influential as the Fields Award, are far less well-known than the Fields Award.
When I was in class in New Oriental, the author listened to President Yu Minhong's motivational speech, in which he talked about one of Yu Minhong's mathematician friends who taught at an American university. The friend's ambition was to win the Fields prize, and Yu Minhong asked him, "how much is the bonus?" After hearing his friend's answer, Yu said, "I'll give you such a little money!" Friends say the Fields Prize is worth more than that. A Fields winner can earn tens of thousands of dollars a year at any university in the United States and change careers if he or she doesn't get a Fields Award at the age of 40. Yu was satisfied with this and praised this friend for having a clear goal in life.
The early Fields Award was awarded in Fields's proposal, which is not only an recognition of existing achievements, but also an encouragement for the winners to work in the future. This rule was interpreted to mean that medals were awarded only to "young" mathematicians, although there was no clear age limit for early awards.
The first Fields Prize was presented at the International Congress of mathematicians in Oslo in 1936. The winners were 29-year-old Alfus (Lars Ahlfors,1907-1996) and 39-year-old Douglas (Jesse Douglas,1897-1965). Constantin Carath é odory (1873-1950) introduced the work of the two winners at the conference. At that time, the Fields Prize was not as beautiful as it is today, and none of the winners had ever heard of it before. Alfus was congratulated on winning the prize in advance, but he was not formally notified before entering the meeting. Douglas, another winner, arrived in Oslo, but did not attend the award ceremony because of the fatigue of the journey. Instead, his colleague Wiener (Norbert Wiener,1894-1964) took the award instead. [5]
The first Fields Prize winner Alfus and Douglas (Picture Source: IMU official website the next ICM is scheduled to be held in Cambridge, Massachusetts, USA in 1940, but it was postponed for ten years because of World War II, and it was not held until 1950. At this time, earth-shaking changes have taken place in the field of mathematics. The United States has become the new mathematical center of the world, and the new International Mathematical Union (International Mathematical Union, IMU) has been formed. Schwartz (Laurent Schwartz,1915-2002) and Selberg (Atle Selberg,1917-2007) won the Fields Prize at the conference, and Harald Bohr (Harald Bohr,1887-1951) introduced their work.
Halad Bohr (left) and his brother Nils Bohr (Niels Bohr,1885-1962), Picture Source: MacTutor History of Mathematics Archive in Bohr's speech, mentioned that the award committee agreed that the Fields Prize should be awarded to very young mathematicians, but did not clearly mean "young". In fact, the most popular candidate for this year's Fields Prize was Schwartz's fellow Frenchman, Andr é Weil,1906-1998, 44. Bohr, as chairman of the award committee, is firmly opposed to giving awards to Wei. In his view, Wey is too old and has gained wide recognition. He pointed out that giving the award to Wei could be a disaster because "it would give people the impression that the committee is trying to select the greatest math genius." In order to rule out Wei, Bohr suggested that the award age be set at no more than 42. Bohr's view caused a heated debate in the jury, according to Bohr, "it takes blood and tears" to determine the final winner. [7]
Bohr represents a tendency of the early Fields Prize, that is, the Fields Prize is not to reward the best mathematicians, but to encourage those with potential. If the Fields Prize is not self-positioned as "awarded to the best mathematicians", the ensuing comparisons and arguments can be avoided. Fields' own proposal says that "invidious comparisons" should be avoided when commenting on winners. The division caused by the international situation left too painful memories for that generation of mathematicians, so they did not want the Fields Prize judges to become the stage of political struggle.
In 1958, 31-year-old Friedrich Hirzebruch,1927-2012 was the favourite for the Fields Prize, but he was out early because jury Chairman Heinz Hopf,1894-1971 thought Heathelouch had received enough recognition and no further encouragement was needed. The same thing happened to Grotendick (Alexander Grothendieck,1928-2014) twice in 1958 and 1962. [7] at that time, the Fields Prize did not have the status of the highest prize in mathematics at all, so the Fields Prize winner was not automatically regarded as the best mathematician.
1966, Mathematics and Politics 1966 was a crucial year in the history of the Fields Prize. This year's ICM was held in Moscow, and it was in this year that the Fields Prize as we know it today was finalized.
Two years ago in 1966, the Tata Trust of India decided to set up a Tata Prize on ICM, which, like the Fields Prize, awarded two people at a time. The award could not be established because India's domestic policy at that time did not allow the Tata Foundation to remit money abroad. Fortunately, an anonymous person donated a sum of money so that the Fields Prize could be awarded to four people this year. Since then, the Fields Prize has been awarded to a maximum of four people each year. [5]
Another change in the Fields Prize is that the award committee led by Georges de Rham,1903-1990 formally set the age limit for winners at 40. Specifically, the winner's 40th birthday cannot be before January 1 of the current year. [5] perhaps because of the clear age limit, the award committee no longer has any scruples about awarding awards to famous mathematicians. The four winners of the year are Atia (Michael Atiyah,1929-2019), Cohen (Paul Cohen,1934-2007), Grotendick and Stephen Smale,1930-. Among them, Atia and Grotendick are among the greatest mathematicians of the 20th century, while Cohen and Smeer won awards for solving well-known problems in mathematical circles. It can be said that this selection has set a benchmark, and since then the Fields Award is aimed at selecting the "best mathematicians under the age of 40".
The aforementioned is a change in the system. Another thing happened this year, which made the Fields Prize really out of the circle and won the reputation of the "Nobel Prize in Mathematics".
Among the four Fields Prize winners in 1966, Grotendick and Smeer had strong political views. Grotendike did not go to Moscow to attend the conference in order to protest against the Soviet authorities. Smeer 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 "non-American activities Committee" of the United States Congress issued a subpoena to Smeer asking him to come to Congress for questioning. The congressional hearing was held on the same day that Smeer received the Fields award. Smeer visited Europe all summer and received no subpoena. On a plane to Moscow, Smeer met the Hungarian mathematician Paul Erd Erdesh (1913-1996), from whom he learned about the subpoena. [8]
When Smeer (Picture Source: On the Steps of Moscow University) arrived at the meeting in 1966, Smeer received a letter from Lang (Serge Lang,1927-2005). The letter told Smeer of a report in the San Francisco Observer that Smeer, a professor of mathematics at Berkeley, had dodged a congressional subpoena and went to Moscow, implying that Smeer had defected. [8] Smeer's colleagues were amused by the report and hastened to explain to the media that Smeer was only going to Moscow to attend the International Congress of mathematicians and receive the Fields Prize. In order to make it easier for reporters to understand, they said that the Fields Prize is equivalent to the Nobel Prize in mathematics. This statement was quoted by the major media and has been deeply rooted in the hearts of the people ever since. (some media that are not too busy have adopted the sensational title of "American math teachers are awarded by the Soviet Union". ) [7]
The controversy over the Fields Prize that "Fields Prize is equivalent to a Nobel Prize in Mathematics" is easy for the public to understand and to some extent increases the voice of the mathematical community in front of the public. Smeer was almost canceled by the National Science Foundation for his anti-war activities, but the aura of the Nobel Prize in Mathematics protected him. [7] Fields winners are given the same treatment as Nobel laureates in many places. For example, Berkeley, who works at Smeer, Fields Prize winners, like Nobel laureates, can enjoy a dedicated parking space on campus.
Although it is known as the "Nobel Prize in Mathematics", there is still a big difference between the Fields Prize and the Nobel Prize. The Nobel Prize often honors two or three collaborators on a work, such as James Watson,1928- and Francis Crick,1916-2004, who discovered the double helix structure of DNA, but the Fields Prize has never been awarded like this, although more and more important work is done by multiple mathematicians.
The bigger difference between the Fields Prize and the Nobel Prize is the age limit of the former. Some people joke that it's a good thing that math doesn't have a Nobel Prize, so mathematicians don't have to think about winning Fields after the age of 40 and don't have to wait for a late-night call from Sweden every year. Although it is a joke, the age limit of 40 does make the Fields Prize and the Nobel Prize have a different impact on the development of the discipline. The Fields Prize is awarded to young mathematicians, and the winning work is usually a hot topic of current research, and these people will be active for 20 or 30 years in the future, and their influence may last longer. There is no age limit for Nobel prizes, winners are often past their creative peak, and many have even retired. The oldest Nobel laureate, John B. Goodenough,1922-, was 97 when he won the Nobel Prize in chemistry. Therefore, to a large extent, the Nobel Prize is the recognition of the major achievements of the past, and does not often directly guide the trend of discipline development, which is particularly obvious in recent years.
In terms of the Fields Prize as the position of "the highest prize in mathematics", the age limit implies unfairness. At first glance, the age limit for Fields prizes is the same for everyone under the age of 40. However, ICM is held only once every four years, and the maximum age at which mathematicians born in different years can win the Fields Prize is different. For example, the next International Congress of mathematicians will be held in St. Petersburg in 2022, when mathematicians born in 1981 will be disqualified. The last chance for mathematicians born in 1981 to win the prize was in 2018, when they were 37 and had to compete with 40-year-old mathematicians born in 1978. You know, the time taken to produce major mathematical achievements is usually measured in years, and it takes several years to be widely recognized, and the time gap of three or four years is not negligible.
An extreme example is Schram (Oded Schramm,1961-2008), who has made extraordinary contributions in the fields of geometry, topology, probability and so on. Schram's most famous work is the SLE he introduced, that is, random Lefner evolution (Stochastic Loewner Evolution), also known as Schram-Lefner evolution (Schramm-Loewner Evolution). This theory combines stochastic processes with conformal geometry and solves many important problems in probability theory and statistical mechanics. Schram has two main collaborators, Gregory Lawler,1955- and Wendelin Werner,1968-. Among them, Werner won the Fields Award in 2006 and Lawler won the Wolf Award in 2019, mainly for their work on SLE. Part of the 2010 Fields Prize winner Smirnov Smirnov's award-winning work is also in the field of SLE.
However, as the founder of SLE theory, Schram failed to win the Fields Prize because of his age and failed to win the Wolf Prize because he died prematurely. Schram was born on December 10, 1961. After he was killed in a mountaineering accident, the New York Times obituary wrote that if Schram had been born three weeks later, he would almost certainly have won the 2002 Fields Prize. However, if a good mathematician misses the Fields Prize only because of such a small age difference, how can the Fields Prize be the highest prize in mathematics?
There is also a view that the age limit for Fields awards is unfair to women, who tend to bear the responsibility of having children when they are young, delaying scientific research for one to several years. For details, please refer to the myth of "Young mathematicians" and structural gender inequality in the field of mathematics. So far, only one female mathematician, Mirzahani (Maryam Mirzakhani,1977-2017), has won the Fields Prize.
Getty Images, even for mathematicians who meet the age requirements, the selection of the Fields Prize is hardly absolutely fair. As the saying goes, there is no first in literature and no second in martial arts. The results of sports competitions can be expressed by numbers, how can mathematical achievements be quantified? How can it be compared between different fields? The choice of Fields Prize winners is largely related to the preferences of the members of the jury. As Fields, Bohr and other ancestors expected, the selection is accompanied by a lot of controversy, including the participation of political factors. After the Fields Award was announced in 2014, Timothy Gowers,1963-, the 1998 Fields Prize winner, pointed out in a blog that many mathematicians in this class, including more than one female mathematician, also deserved the award. Of course, this situation is not unique to the 2014 session, nor is it unique to the Fields Award. The selection of any science and technology award will be similarly controversial, but the age limit of the Fields award makes most nominees have only one or two chances to win the prize, so the controversy is even more prominent.
In addition to the Fields Award, there are also some awards with no age limit in mathematics as awards for the highest achievements of mathematicians. These include Wolf Award, Abel Award, Shiing-Shen Chern Award, Scientific Breakthrough Award and so on. Among them, the Abel Prize is very similar to the Nobel Prize in terms of name, award country, award rules, bonus amount and so on. In recent years, it is often compared with the Nobel Prize by the media, which may be more in line with the positioning of the "Mathematical Nobel Prize."
Looking back on the history of Fields Prize, it was not designed as the "highest prize in mathematics" at first, but it got the reputation of "Nobel Prize in Mathematics" by mistake. However, the congenital defects of the Fields Prize in the system make it difficult for it to really assume the responsibility of "the highest prize in mathematics". Therefore, some people have suggested that the Fields Prize should be returned to its original mind and the halo of the "highest prize in mathematics" should be removed only as an inspiration to outstanding young mathematicians. [7] this may be the right attitude towards the Fields Award.
Appendix: other awards awarded by IMU in addition to the Fields Award, IMU has also established a number of awards, which are also presented at the quadrennial International Congress of mathematicians. Only one person will be awarded each of these awards. The following is a brief introduction to these awards.
The IMU abacus Award (IMU Abacus Medal), formerly known as the Nevanlinna Prize (Rolf Nevanlinna Prize), Nevanlinna (Rolf Nevanlinna,1895-1980) is a famous Finnish mathematician who served as chairman of IMU, chairman of ICM in Stockholm, Sweden in 1962, and honorary chairman of ICM in Helsinki, Finland in 1978. In memory of Nevanlinna, the University of Helsinki funded the establishment of the Nevanlinna Award to reward scientists who have made outstanding contributions to the mathematics of information science. The Nevanlinna Award, which also has an age limit of 40, has been awarded since 1982 and currently has a prize of 10,000 euros. Neville Linna's cooperation with Nazi forces was a major stain on his life, so IMU decided to rename the Neville Linna Award as the IMU abacus Award from 2022.
The Carl Friedrich Gauss Prize German Mathematical Society and IMU used the surplus funds from Berlin ICM in 1998 to set up the Gauss Prize to reward mathematical research that has a significant impact on areas other than mathematics. The Gauss Award, which has no age limit, has been awarded since 2006 and currently has a prize of 10,000 euros.
After the death of Mr. Shiing-Shen Chern (1911-2004) of the Shiing-Shen Chern Prize (Chern Medal), his family and friends funded the Shiing-Shen Chern Prize as a lifetime achievement award for mathematicians. The Shiing-Shen Chern Award has no age limit and has been awarded since 2010. The Shiing-Shen Chern Prize has a prize amount of US $500000, of which US $250000 is given to the winners and US $250000 is donated to institutions designated by the winners to support mathematical research, education and popularization.
The Lilawati Award (Leelavati Prize) was awarded at the ICM closing ceremony in Hyderabad, India in 2010 to reward the public popularization of mathematics. Infosys, a famous Indian IT company, subsequently funded the Lilawati Award as a permanent award for IMU. Lilawati is a mathematical work written by the ancient Indian mathematician Bhashgara II (approx. 1114-about 1185). The Lilawati Award is the only one of the IMU awards that was awarded at the ICM closing ceremony rather than the opening ceremony, and the only one that does not reward mathematical research. The prize for the Lilawati Award is 1 million Indian rupees.
The Ladyzhenskaya Medal (Olga Ladyzhenskaya,1922-2004) is a famous Russian mathematician who was nominated for the Fields Prize in 1958. The Russian State Mathematical Committee, St. Petersburg State University and the 2022 St. Petersburg ICM Organizing Committee jointly established the Radjenskaya Award to reward revolutionary achievements in mathematical physics and related fields. The Radjenskaya Award, which has no age limit and has a prize of 1 million rubles, will be awarded for the first time at a ceremony commemorating the centenary of the birth of Radjenskaya during ICM in 2022.
Google graffiti commemorating the 97th birthday of Radrenskaya? photo Source: Google thanks: Xu Chenyang read the first draft of this article and made valuable comments. This article is partly inspired by his speech "the Curse of Fields Award".
Reference [1] Arild Stubhaug, G ö sta Mittag-Leffler. A Man of Conviction. Springer-Verlag, Berlin, 2010. Xerox 733 pp.
[2] J. L. Synge, John Charles Fields. J. London Math. Soc. 8 (1933), no.
[3] Michael Barany, The myth and the medal. Notices Amer. Math. Soc. 62 (2015), no. 1,15-20.
[4] the official website of the Abel Prize, The History of the Abel Prize.
[5] Olli Lehto, Mathematics without borders. A history of the International Mathematical Union. Springer-Verlag, New York, 1998.
[6] Henry Tropp, The origins and history of the Fields Medal. Historia Math. 3 (1976), no.
[7] Michael Barany, The Fields Medal should return to its roots. Nature 553,271-273 (2018).
[8] Steve Smale, On the Steps of Moscow University. From Topology to Computation: Proceedings of the Smalefest (Berkeley, CA, 1990), 41-52, Springer, New York, 1993.
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