Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan. Cartan studied at the Lycée Hoche in Versailles, then at the ENS, receiving his doctorate in mathematics. He taught at the University of Strasbourg from November 1931 until the outbreak of the Second World War, after which he held academic positions at a number of other French universities, spending the bulk of his working life in Paris. Cartan is known for work in algebraic topology, in particular on cohomology operations, the method of “killing homotopy groups”, and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Alan Mathison Turing was an English mathematician, logician, cryptanalyst and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of “algorithm” and “computation” with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence. During the Second World War, Turing worked for the Government Code and Cypher School at Bletchley Park, Britain’s codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine. After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. Towards the end of his life Turing became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s. Turing’s homosexuality resulted in a criminal prosecution in 1952, when homosexual acts were still illegal in the United Kingdom. He accepted treatment with female hormones (chemical castration) as an alternative to prison. He died in 1954, several weeks before his 42nd birthday, from cyanide poisoning. An inquest determined it was suicide; his mother and some others believed his death was accidental. On 10 September 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for the way in which Turing was treated after the war.
John Forbes Nash, Jr. is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi. Nash is the subject of the Hollywood movie A Beautiful Mind. The film, loosely based on the biography of the same name, focuses on Nash’s mathematical genius and struggle with paranoid schizophrenia.
Hans Georg Bock is a German university professor for mathematics and scientific computing. He is managing director of the Interdisciplinary Center for Scientific Computing of the University of Heidelberg since 2005, and has been vice managing director from 1993 to 2004. Hans Georg Bock is a member of the European Mathematical Society’s committee for developing countries (CDC-EMS) and responsible member for the region of Asia therein. In appreciation of his merits with respect to Vietnamese-German relations and his role in the establishment of high performance scientific computing in Vietnam, he was awarded the honorary degree of the Vietnamese Academy of Science and Technology in 2000. In 2003, he was awarded the Medal of Merit of the Vietnamese Ministry for Education and Training.
Sir Andrew John Wiles KBE FRS is a British mathematician and a professor at Princeton University, specializing in number theory. He is most famous for proving Fermat’s Last Theorem. Andrew Wiles is the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford and Patricia Wiles. His father worked as the Chaplain at Ridley Hall, Cambridge, for the years 1952-55. Wiles was born in Cambridge, England, in 1953, and he attended King’s College School, Cambridge, and The Leys School, Cambridge. Wiles discovered Fermat’s Last Theorem on his way home from school when he was 10 years old. He stopped by his local library where he found a book about the theorem. Puzzled by the fact that the statement of the theorem was so easy that he, a ten-year old, could understand it, he decided to be the first person to prove it. However, he soon realized that his knowledge of mathematics was too small, so he abandoned his childhood dream, until 1986, when he heard that Ribet had proved Serre’s ε-conjecture and therefore established a link between Fermat’s Last Theorem and the Taniyama-Shimura conjecture. Wiles earned his bachelor’s degree in mathematics in 1974 after his study at Merton College, Oxford, and a Ph.D. in 1980, after his research at Clare College, Cambridge. After a stay at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. In 1985-86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at Oxford University, and then he returned to Princeton. In October 2009 it was announced that Wiles would again become a Royal Society Research Professor at Oxford in 2011.
Thomas Andrew Lehrer is an American singer-songwriter, satirist, pianist, and mathematician. He has lectured on mathematics and musical theater. Lehrer is best known for the pithy, humorous songs he recorded in the 1950s and 1960s. His work often parodies popular song forms, such as in “The Elements”, where he sets the names of the chemical elements to the tune of the “Major-General’s Song” from Gilbert and Sullivan’s Pirates of Penzance. Lehrer’s earlier work typically dealt with non-topical subject matter and was noted for its black humor, seen in songs such as “Poisoning Pigeons in the Park”. In the 1960s, he produced a number of songs dealing with social and political issues of the day, particularly when he wrote for the U.S. version of the television show That Was The Week That Was. In the early 1970s, he retired from public performances to devote his time to teaching mathematics and music theatre at the University of California, Santa Cruz. He did two additional performances in 1998 at a London gala show celebrating the career of impresario Cameron Mackintosh.
Shing-Tung Yau is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province. Yau’s contributions have had an influence on both physics and mathematics. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today. He has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein’s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi-Yau compactification—to show that string theory is a viable candidate for a unified theory of nature.