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.
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada. It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers is awarded a scholarship of up to $12,000 plus tuition at Harvard University, the top 100 individual scorers have their names mentioned in the American Mathematical Monthly, and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score is often zero or one despite being primarily attempted by students specializing in mathematics.
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.
The Adams Prize is a prize awarded each year by the Faculty of Mathematics at St John's College to a UK-based mathematician for distinguished research in mathematical sciences.
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).
David William Masser is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated the abc conjecture, which has been called "the most important unsolved problem in Diophantine analysis".
The Donald E. Knuth Prize is a prize for outstanding contributions to the foundations of computer science, named after the American computer scientist Donald E. Knuth.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
The Erwin Plein Nemmers Prize in Economics is an academic prize awarded biennially by Northwestern University. It was initially endowed along with a companion prize, the Frederic Esser Nemmers Prize in Mathematics. Both are part a $14 million donation from the Nemmers brothers, who envisioned creating an award that would be as prestigious as the Nobel prize. Nine out of the past 15 Nemmers economics prize winners have gone on to win a Nobel Prize : Peter Diamond, Thomas J. Sargent, Robert Aumann, Daniel McFadden, Edward C. Prescott, Lars Peter Hansen, Jean Tirole, Paul R. Milgrom and, most recently, Claudia Goldin. Those who already have won a Nobel Prize are ineligible to receive a Nemmers prize. The Nemmers prizes are given in recognition of major contributions to new knowledge or the development of significant new modes of analysis in the respective disciplines. As of 2023, the prize carries a $300,000 stipend, among the largest monetary awards in the United States for outstanding achievements in economics.
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.
The George Szekeres Medal is awarded by the Australian Mathematical Society for outstanding research contributions over a fifteen-year period. This award, established in 2001, was given biennially in even-numbered years until 2021 and has since been given annually, for work that has been carried out primarily in Australia
James Smith Page is an Australian educationist and anthropologist, and a recognised authority within the field of peace education.
Lucien 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 French National Centre for Scientific Research.
Ronald Brown FLSW was an English mathematician. He was a Professor in the School of Computer Science at Bangor University. He has authored many books and more than 160 journal articles.
The Ruth Lyttle Satter Prize in Mathematics, also called the Satter Prize, is one of twenty-one prizes given out by the American Mathematical Society (AMS). It is presented biennially in recognition of an outstanding contribution to mathematics research by a woman in the previous six years. The award was funded in 1990 using a donation from Joan Birman, in memory of her sister, Ruth Lyttle Satter, who worked primarily in biological sciences, and was a proponent for equal opportunities for women in science. First awarded in 1991, the award is intended to "honor [Satter's] commitment to research and to encourage women in science". The winner is selected by the council of the AMS, based on the recommendation of a selection committee. The prize is awarded at the Joint Mathematics Meetings during odd numbered years, and has always carried a modest cash reward. Since 2003, the prize has been $5,000, while from 1997 to 2001, the prize came with $1,200, and prior to that with $4,000. If a joint award is made, the prize money is split between the recipients.
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 a Clare Boothe Luce Professor at Boston University.
Alex V. Kontorovich is an American mathematician who works in the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic analysis, and homogeneous dynamics.
