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46-610: The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields . The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as

92-543: A chance at last to meet a mathematician whom I know only through his work and for whom I have the greatest respect and admiration." In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, because of martial law introduced in Poland on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at

138-471: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include

184-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while

230-766: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages

276-712: Is Docet Omnia , Latin for "It teaches everything"; its goal is to "teach science in the making" and can be best summed up by Maurice Merleau-Ponty 's phrase: "Not acquired truths, but the idea of freely-executed research" which is inscribed in golden letters above the main hall. The Collège has research laboratories and one of the best research libraries of Europe, with sections focusing on history with rare books, humanities , social sciences and also chemistry and physics . As of June 2009, over 650 audio podcasts of Collège de France lectures are available on iTunes. Some are also available in English and Chinese . Similarly,

322-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics

368-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics

414-479: Is made of 14KT gold, has a diameter of 63.5mm, and weighs 169g. Translation: "Mathematicians gathered from the entire world have awarded [understood but not written: 'this prize'] for outstanding writings." In the background, there is the representation of Archimedes' tomb , with the carving illustrating his theorem On the Sphere and Cylinder , behind an olive branch. (This is the mathematical result of which Archimedes

460-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing

506-553: Is often described as the Nobel Prize of Mathematics . Unlike the Nobel Prize, the Fields Medal is only awarded every four years. The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on

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552-624: The Collegium Trilingue in Louvain , at the urging of Guillaume Budé . Of humanist inspiration, the school was established as an alternative to the Sorbonne to promote such disciplines as Hebrew , Ancient Greek (the first teacher being the celebrated scholar Janus Lascaris ) and Mathematics . Initially called Collège royal , and later Collège des trois langues (Latin, ancient Greek and Hebrew), Collège national , and Collège impérial , it

598-526: The Collège de France 's website hosts several videos of classes. The classes are followed by various students, from senior researchers to PhD or master's students, or even undergraduates. Moreover, the "leçons inaugurales" (first lessons) are important events in Paris intellectual and social life and attract a very large public of curious Parisians. The Collège was established by King Francis I of France , modeled after

644-634: The Pythagorean school , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c.  AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of

690-656: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of

736-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of

782-541: The 1983 Warsaw congress. In 1990, Edward Witten became the first physicist to win the award. In 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri I. Manin , with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem . Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts of this award frequently make reference that at

828-542: The 1997 film, Good Will Hunting . In the movie, Gerald Lambeau ( Stellan Skarsgård ) is an MIT professor who won the award prior to the events of the story. Throughout the film, references made to the award are meant to convey its prestige in the field. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of

874-472: The Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has been CA$ 15,000. Fields was instrumental in establishing the award, designing the medal himself, and funding the monetary component, though he died before it was established and his plan was overseen by John Lighton Synge . The medal

920-468: The Fields Medal. The most recent group of Fields Medalists received their awards on 5 July 2022 in an online event which was live-streamed from Helsinki, Finland. It was originally meant to be held in Saint Petersburg , Russia, but was moved following the 2022 Russian invasion of Ukraine . The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and

966-453: The Fields medalists have been officially cited for particular mathematical achievements, while in other years such specificities have not been given. However, in every year that the medal has been awarded, noted mathematicians have lectured at the International Congress of Mathematicians on each medalist's body of work. In the following table, official citations are quoted when possible (namely for

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1012-730: The ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe. Léon Motchane , founder and director of the Institut des Hautes Études Scientifiques , attended and accepted Grothendieck's Fields Medal on his behalf. In 1970, Sergei Novikov , because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal. In 1978, Grigory Margulis , because of restrictions placed on him by

1058-578: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became

1104-399: The Nobel Prize of Mathematics , although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU , the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14,

1150-459: The Soviet government, was unable to travel to the congress in Helsinki to receive his medal. The award was accepted on his behalf by Jacques Tits , who said in his address: "I cannot but express my deep disappointment—no doubt shared by many people here—in the absence of Margulis from this ceremony. In view of the symbolic meaning of this city of Helsinki, I had indeed grounds to hope that I would have

1196-450: The arts". As of 2021, 21 Nobel Prize winners and 9 Fields Medalists have been affiliated with the Collège. It does not grant degrees. Each professor is required to give lectures where attendance is free and open to anyone. Professors, about 50 in number, are chosen by the professors themselves, from a variety of disciplines, in both science and the humanities . The motto of the Collège

1242-429: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Coll%C3%A8ge de France Research and teaching are closely linked at the Collège de France , whose ambition is to teach "the knowledge that is being built up in all fields of literature, science and

1288-500: The earliest known mathematicians was Thales of Miletus ( c.  624  – c.  546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c.  582  – c.  507 BC ) established

1334-413: The first Iranian as well as the first woman to win the Fields Medal, and Artur Avila became the first South American and Manjul Bhargava became the first person of Indian origin to do so. In 2022, Maryna Viazovska became the first Ukrainian to win the Fields Medal, and June Huh became the first person of Korean ancestry to do so. The medal was designed by Canadian sculptor R. Tait McKenzie . It

1380-494: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of

1426-886: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,

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1472-629: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"

1518-569: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at

1564-470: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to

1610-478: The part of the recipients and a stimulus to renewed effort on the part of others." Moreover, an individual can only be awarded one Fields Medal; winners are ineligible to be awarded future medals. First awarded in 1936, 64 people have won the medal as of 2022. With the exception of two PhD holders in physics ( Edward Witten and Martin Hairer ), only people with a PhD in mathematics have won the medal. In certain years,

1656-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in

1702-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate

1748-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced

1794-478: The time of the award Wiles was over the age limit for the Fields medal. Although Wiles was slightly over the age limit in 1994, he was thought to be a favorite to win the medal; however, a gap (later resolved by Taylor and Wiles) in the proof was found in 1993. In 2006, Grigori Perelman , who proved the Poincaré conjecture , refused his Fields Medal and did not attend the congress. In 2014, Maryam Mirzakhani became

1840-1303: The years 1958, 1998, and every year since 2006). For the other years through 1986, summaries of the ICM lectures, as written by Donald Albers, Gerald L. Alexanderson , and Constance Reid , are quoted. In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The upcoming Fields Medal ceremony is scheduled for 2026, taking place in Philadelphia , US. Moscow State University , Russia University of Maryland-College Park , US University of Florida , US Collège de France , France Ohio State University , US Vanderbilt University , US École polytechnique , France University of California, San Diego , US University of Cambridge , UK Rutgers University , US Rutgers University , US University of California, Berkeley , US Princeton University , US Institute for Advanced Study , US Institute for Advanced Study, US St. Petersburg State University , Russia Institut Henri Poincaré , France Institut Henri Poincaré , France CNRS , France Instituto Nacional de Matemática Pura e Aplicada , Brazil Instituto Nacional de Matemática Pura e Aplicada , Brazil University of Geneva , Switzerland University of Geneva , Switzerland The medal

1886-938: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in

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1932-464: Was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas , and it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist. In total, 64 people have been awarded

1978-550: Was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the American mathematician Jesse Douglas , and it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He retains this distinction. In 1966, Alexander Grothendieck boycotted

2024-484: Was named Collège de France in 1870. In 2010, it became a founding associate of PSL Research University (a community of Parisian universities). The faculty of the Collège de France currently comprises fifty-two Professors, elected by the Professors themselves from among Francophone scholars in subjects including mathematics, physics, chemistry, biology, history, archaeology, linguistics, oriental studies, philosophy,

2070-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support

2116-431: Was reportedly most proud: Given a sphere and a circumscribed cylinder of the same height and diameter, the ratio between their volumes is equal to 2 ⁄ 3 .) The rim bears the name of the prizewinner. The Fields Medal has had two female recipients, Maryam Mirzakhani from Iran in 2014, and Maryna Viazovska from Ukraine in 2022. The Fields Medal gained some recognition in popular culture due to references in

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