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.
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.
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.
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions.
In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula, named after Hale Trotter, states that for arbitrary m × m real or complex matrices A and B,
Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields.
Stochastic quantum mechanics is an interpretation of quantum mechanics.
Lane P. Hughston is an American mathematician.
Friedrich "Fritz" Gesztesy is a well-known Austrian-American mathematical physicist and Professor of Mathematics at Baylor University, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics, ordinary and partial differential operators, and completely integrable systems. He has authored more than 300 publications on mathematics and physics.
Jan Raphael Høegh-Krohn was a Norwegian mathematician.
Philippe Blanchard has been a Professor of Mathematical Physics at Faculty of Physics, Bielefeld University since 1980. He is both director of the Research Center BiBoS and deputy managing director of the Center for Interdisciplinary Research at Bielefeld University.
Michael Röckner is a mathematician working in the fields of Stochastic analysis and Mathematical Physics.
Kalyan Bidhan Sinha is an Indian mathematician. He is a professor at the Jawaharlal Nehru Centre for Advanced Scientific Research, and Professor Emeritus for life of the Indian Statistical Institute.
Jürgen Jost is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.
Yuri Kondratiev is a Ukrainian mathematician, professor at the Bielefeld University, Germany.
Stanislav Alexeyevich Molchanov is a Soviet and American mathematician.
Ambar Niel Sengupta is an Indian-American mathematician. He is a professor of mathematics at the University of Connecticut.
Vladimir Igorevich Bogachev is an eminent Russian mathematician and Full Professor of the Department of Mechanics and Mathematics of the Lomonosov Moscow State University. He is an expert in measure theory, probability theory, infinite-dimensional analysis and partial differential equations arising in mathematical physics. His research was distinguished by several awards including the medal and the prize of the Academy of Sciences of the Soviet Union (1990); Award of the Japan Society for the Promotion of Science (2000); the Doob Lecture of the Bernoulli Society (2017); and the Andrey Kolmogorov Prize of the Russian Academy of Sciences (2018).
