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Representation theory transforms abstract algebra groups into things like simpler matrices. The field’s founder left a list of 43 problems for others to study, iterate on, and prove.
The three-part original paper is more than 300 pages long. (Britton later published a 282-page paper attempting to solve the problem, but his paper contained a serious gap.) 1960-1970 Fondements de la Géometrie Algébrique, Éléments de géométrie algébrique and Séminaire de géométrie algébrique. Grothendieck's work on the foundations ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The proof's method of identification of a deformation ring with a Hecke algebra (now referred to as an R=T theorem) to prove modularity lifting theorems has been an influential development in algebraic number theory. Together, the two papers which contain the proof are 129 pages long [4] [5] and consumed over seven years of Wiles's research time.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition , multiplication , and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics .
George Bernard Dantzig (/ ˈ d æ n t s ɪ ɡ /; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.
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