The abc conjecture is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers and that are relatively prime and satisfy . The conjecture essentially states that the product of the distinct prime factors of is usually not much smaller than . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician Dorian Goldfeld described the abc conjecture as "The most important unsolved problem in Diophantine analysis".
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
Paul Erdős was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. Erdős pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.
Don Bernard Zagier is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics (ICTP).
The Courant Institute of Mathematical Sciences is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research centers in the world. Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the Stern School of Business and the economics department of the College of Arts and Science.
Peter Clive Sarnak is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007. He is also Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Sir Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
Michael Barr is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University.
In number theory, Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known abc conjecture. It is named for Lucien Szpiro, who formulated it in the 1980s. Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld, in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem.
Alan Baker was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.
Sergei Gukov is a professor of mathematics and theoretical physicist. Gukov graduated from Moscow Institute of Physics and Technology (MIPT) in Moscow, Russia before obtaining a doctorate in physics from Princeton University under the supervision of Edward Witten.
Robert Edward "Rufus" Bowen was an internationally known professor in the Department of Mathematics at the University of California, Berkeley, who specialized in dynamical systems theory. Bowen's work dealt primarily with axiom A systems, but the methods he used while exploring topological entropy, symbolic dynamics, ergodic theory, Markov partitions, and invariant measures "have application far beyond the axiom A systems for which they were invented." The Bowen Lectures at the University of California, Berkeley, are given in his honor.
Lucien Serge Szpiro was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research at the CNRS.
Ronald Brown FLSW is an English mathematician. Emeritus Professor in the School of Computer Science at Bangor University, he has authored many books and more than 160 journal articles.
Sujatha Ramdorai is an algebraic number theorist known for her work on Iwasawa theory. She is a professor of mathematics and Canada Research Chair at University of British Columbia, Canada. She was previously a professor at Tata Institute of Fundamental Research.
Guanrong Chen (陈关荣) or Ron Chen is a Chinese mathematician who made contributions to Chaos theory. He has been the chair professor and the founding director of the Centre for Chaos and Complex Networks at the City University of Hong Kong since 2000. Prior to that, he was a tenured full professor at the University of Houston, Texas. Chen was elected Member of the Academy of Europe in 2014, elected Fellow of The World Academy of Sciences in 2015, and elected IEEE Fellow in 1997. He is currently the editor-in-chief for the International Journal of Bifurcation and Chaos.
David Nualart is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.
Scott Sheffield is a professor of mathematics at the Massachusetts Institute of Technology. His primary research field is theoretical probability.
Jennifer Shyamala Sayaka Balakrishnan is an American mathematician known for leading a team that solved the problem of the "cursed curve", a Diophantine equation that was known for being "famously difficult". More generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is the Clare Boothe Luce Associate Professor at Boston University.
Tsachik Gelander is an Israeli mathematician working in the fields of Lie groups, topological groups, symmetric spaces, lattices and discrete subgroups. He is a professor in Northwestern University.
