A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are lazy."
Karol Borsuk was a Polish mathematician. His main interest was topology, while he obtained significant results also in functional analysis.
In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert Seifert. In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture. He also established the conjecture for perturbations of the Hopf fibration.
Mary Ellen Rudin was an American mathematician known for her work in set-theoretic topology. In 2013, Elsevier established the Mary Ellen Rudin Young Researcher Award, which is awarded annually to a young researcher, mainly in fields adjacent to general topology.
Jenny Harrison is a professor of mathematics at the University of California, Berkeley.
Andrzej Wojciech Trybulec was a Polish mathematician and computer scientist noted for work on the Mizar system.
David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects.
The Borsuk problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk.
John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.
Włodzimierz Kuperberg is a professor of mathematics at Auburn University, with research interests in geometry and topology.
Greg Kuperberg is a Polish-born American mathematician known for his contributions to geometric topology, quantum algebra, and combinatorics. Kuperberg is a professor of mathematics at the University of California, Davis.
Gil Kalai is an Israeli mathematician and computer scientist. He is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics and of computer science at Yale University, United States.
János Kollár is a Hungarian mathematician, specializing in algebraic geometry.
Eduard J. Zehnder is a Swiss mathematician, considered one of the founders of symplectic topology.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Colin Rourke is a British mathematician who worked in PL topology, low-dimensional topology, differential topology, group theory, relativity and cosmology. He is an emeritus professor at the Mathematics Institute of the University of Warwick and a founding editor of the journals Geometry & Topology and Algebraic & Geometric Topology, published by Mathematical Sciences Publishers, where he is the vice chair of its board of directors.
Mary Wynne Warner was a Welsh mathematician, specializing in fuzzy mathematics. Her obituary in the Bulletin of the London Mathematical Society noted that fuzzy topology was "the field in which she was one of the pioneers and recognized as one of the leading figures for the past thirty years."
Viktor L. Ginzburg is a Russian-American mathematician who has worked on Hamiltonian dynamics and symplectic and Poisson geometry. As of 2017, Ginzburg is Professor of Mathematics at the University of California, Santa Cruz.
Paul Alexander SchweitzerSJ is an American mathematician specializing in differential topology, geometric topology, and algebraic topology.
Grzegorz Świątek is a Polish mathematician, currently a professor at the Warsaw University of Technology. He is known for his contributions to dynamical systems.
