David Seetapun is an English logician and former investment banker.
During the fall of 1990, David Seetapun was said to have "used a very interesting 0′′′- priority argument to prove that every r.e. degree 0 < a < 0′ is locally noncappable, namely (∀a) 0 < a < 0′ (∃c) a < c (∀b) b < c [a∩b = 0 => b = 0]". [1] Seetapun received a PhD in logic from Cambridge in 1991, the topic was "Contributions to recursion theory". He went on to a post-doctoral position at Berkeley where in 1995 he published an influential article with his post-doctoral adviser Theodore Slaman applying reverse mathematics to Ramsey's theorem. [2] [3] [4] He also proposed the so called "Seetapun Enigma", a mathematical puzzle that was not solved until 2010 by Chinese undergraduate student Liu Lu.
After leaving academia, he took a job for Credit Suisse , but was offered a job by Goldman Sachs. Seetapun made a reputation for himself managing a trading venture with mathematical models, and has been cited as "Goldman's top London proprietary options trader", making over $500m. [5] He left Goldman in March 1998, when he was rehired by Credit Suisse. In 1998 his models started to fail causing a loss of his own funds as well as for the firm. [6] He currently works at Waymo, which was formerly Google's self-driving car project.
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.
Mathematics is an area of knowledge that includes such topics as numbers, formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes.
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
In mathematical logic, model theory is the study of the relationship between formal theories, and their models. The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory.
Alonzo Church was a renowned American mathematician, logician, philosopher, professor and editor, who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem, the Frege–Church ontology, and the Church–Rosser theorem. He also worked on philosophy of language. Alongside his student Alan Turing, Church is considered one of the founders of computer science.
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee that a particular property holds?" More specifically, Ron Graham described Ramsey theory as a "branch of combinatorics".
In combinatorial mathematics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling of a sufficiently large complete graph. To demonstrate the theorem for two colours, let r and s be any two positive integers. Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices.
Frank Plumpton Ramsey was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of Ludwig Wittgenstein and, as an undergraduate, translated Wittgenstein's Tractatus Logico-Philosophicus into English. He was also influential in persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the Cambridge Apostles, the secret intellectual society, from 1921.
Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
Leon Albert Henkin was one of the most important logicians and mathematicians of the 20th century. His works played a strong role in the development of logic, particularly in the theory of types. He was an active scholar at the University of California, Berkeley, where he made great contributions as a researcher, teacher, as well as in administrative positions. At this university he directed, together with Alfred Tarski, the Group in Logic and the Methodology of Science, from which many important logicians and philosophers emerged. He had a strong sense of social commitment and was a passionate defensor of his pacifist and progressive ideas. He took part in many social projects aimed at teaching mathematics, as well as projects aimed at supporting women's and minority groups to pursue careers in mathematics and related fields. A lover of dance and literature, he appreciated life in all its facets: art, culture, science and, above all, the warmth of human relations. He is remembered by his students for his great kindness, as well as for his academic and teaching excellence.
In computer science and mathematical logic the Turing degree or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.
In mathematical logic, a theory is categorical if it has exactly one model. Such a theory can be viewed as defining its model, uniquely characterizing its structure.
In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem X a successively harder decision problem X′ with the property that X′ is not decidable by an oracle machine with an oracle for X.
Gerald Enoch Sacks was a logician whose most important contributions were in recursion theory. Named after him is Sacks forcing, a forcing notion based on perfect sets and the Sacks Density Theorem, which asserts that the partial order of the recursively enumerable Turing degrees is dense. Sacks had a joint appointment as a professor at the Massachusetts Institute of Technology and at Harvard University starting in 1972 and became emeritus at M.I.T. in 2006 and at Harvard in 2012.
Chong Chi Tat is University Professor and Director of the Institute for Mathematical Sciences at the National University of Singapore (NUS). His research interests are in the areas of recursion/computability theory.
Stevo Todorčević, is a Yugoslavian mathematician specializing in mathematical logic and set theory. He holds a Canada Research Chair in mathematics at the University of Toronto, and a director of research position at the Centre national de la recherche scientifique in Paris.
Jean Ann Larson is an American mathematician, and a professor at the University of Florida. She is a set theorist, a historian of mathematical logic, and a professor at the University of Florida. She was the first woman to earn a doctorate in mathematics from Dartmouth College, and is known for her research in infinitary combinatorics and the theory of linear spaces.
Marcia Jean Groszek is an American mathematician whose research concerns mathematical logic, set theory, forcing, and recursion theory. She is a professor of mathematics at Dartmouth College.
The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's general meeting. The award is named after Kurt Gödel and has been given annually since 1990.