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Serre's multiplicity conjectures: commutative algebra: Jean-Pierre Serre: 221 Singmaster's conjecture: binomial coefficients: David Singmaster: 8 Standard conjectures on algebraic cycles: algebraic geometry: n/a: 234 Tate conjecture: algebraic geometry: John Tate: Toeplitz' conjecture: Jordan curves: Otto Toeplitz: Tuza's conjecture: graph ...
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
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 ...
Homological conjectures in commutative algebra; Jacobson's conjecture: the intersection of all powers of the Jacobson radical of a left-and-right Noetherian ring is precisely 0. Kaplansky's conjectures; Köthe conjecture: if a ring has no nil ideal other than {}, then it has no nil one-sided ideal other than {}.
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 proof has appeared in "Annals of Mathematics" in March 2019. [5] The Burr–Erdős conjecture on Ramsey numbers of graphs, proved by Choongbum Lee in 2015. [6] [7] A conjecture on equitable colorings proven in 1970 by András Hajnal and Endre Szemerédi and now known as the Hajnal–Szemerédi theorem. [8]
This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. There may or may not be conjectures for all unsolved problems.
The Collatz conjecture states that all paths eventually lead to 1. The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.