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Nigel J. Cutland is Professor of Mathematics at the University of York. [1] His main fields of interest are non-standard analysis, Loeb spaces, and applications in probability and stochastic analysis. [1] He was Editor-in-Chief of Logic and Analysis and Journal of Logic and Analysis .
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers.
Paul Richard Halmos was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
Solomon Feferman was an American philosopher and mathematician who worked in mathematical logic. In addition to his prolific technical work in proof theory, computability theory, and set theory, he was known for his contributions to the history of logic and as a vocal proponent of the philosophy of mathematics known as predicativism, notably from an anti-platonist stance.
Edward Nelson was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical logic, he was noted especially for his internal set theory, and views on ultrafinitism and the consistency of arithmetic. In philosophy of mathematics he advocated the view of formalism rather than platonism or intuitionism. He also wrote on the relationship between religion and mathematics.
Reuben Hersh was an American mathematician and academic, best known for his writings on the nature, practice, and social impact of mathematics. Although he was generally known as Reuben Hersh, late in life he sometimes used the name Reuben Laznovsky in recognition of his father's ancestral family name. His work challenges and complements mainstream philosophy of mathematics.
Mark A. Pinsky was Professor of Mathematics at Northwestern University. His research areas included probability theory, mathematical analysis, Fourier Analysis and wavelets. Pinsky earned his Ph.D at Massachusetts Institute of Technology (MIT).
Howard Jerome Keisler is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.
Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields.
Waldyr Alves Rodrigues, Jr. born at Araraquara, SP, Brazil, obtained his B.Sc. in physics in 1968 at the University of São Paulo (Brazil), where he has been a research student of Mário Schenberg and became an assistant professor in 1969. He then moved to Torino, Italy, where he did postgraduate studies at the Scuola di Perfezionamento in Fisica Nucleare and obtained a degree in theoretical nuclear physics in 1971. Later that year, he returned to Brazil and became an associate professor at the new Physics Institute of Campinas State University (UNICAMP).
Izak (Ieke) Moerdijk is a Dutch mathematician, currently working at Utrecht University, who in 2012 won the Spinoza prize.
Sir Martin Hairer is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL and at Imperial College London. He previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.
Sergio Albeverio is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis, mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
Robert Ian Goldblatt is a mathematical logician who is Emeritus Professor in the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand. His doctoral advisor was Max Cresswell. His most popular books are Logics of Time and Computation and Topoi: the Categorial Analysis of Logic. He has also written a graduate level textbook on hyperreal numbers which is an introduction to nonstandard analysis.
Keith D. Stroyan is Professor of Mathematics at the University of Iowa. His main research interests are in analysis and visual depth perception.
Mark Herbert Ainsworth Davis was Professor of Mathematics at Imperial College London. He made fundamental contributions to the theory of stochastic processes, stochastic control and mathematical finance.
In mathematics, a Loeb space is a type of measure space introduced by Loeb using nonstandard analysis.
Leif O. Arkeryd is professor emeritus of mathematics at Chalmers University of Technology. He is a specialist on the theory of the Boltzmann equation.
In computability theory, a Friedberg numbering is a numbering (enumeration) of the set of all uniformly recursively enumerable sets that has no repetitions: each recursively enumerable set appears exactly once in the enumeration.
Karel Hrbáček is professor emeritus of mathematics at City College of New York. He specializes in mathematical logic, set theory, and non-standard analysis.
Igor Dmitrievich Chueshov was a Ukrainian mathematician. He was both a correspondent member of the Mathematics section of the National Academy of Sciences of Ukraine and a professor in the Department of Mathematical Physics and Computational Mathematics at the National University of Kharkiv.
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