Unsolved problems in mathematics
This article reiterates the Millennium Prize list of unsolved problems in mathematics as of October 2014, and lists further unsolved problems in algebra, additive and algebraic number theories, analys...
A New Hope for a Perplexing Mathematical Proof
Three years ago, a solitary mathematician released an impenetrable proof of the famous abc conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.
The Biggest Mystery In Mathematics: Shinichi Mochizuki And The Impenetrable Proof
A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right. Sometime on the morning of 30 August 201...
Conjecture
A conjecture is a conclusions or proposition that is based on incomplete information but appears to be correct. Conjectures such as the Riemann Hypothesis or Fermat's Last Theorem have shaped much of ...
Hilbert's problems
Hilbert's problems are a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very...
Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of October 2014, six of the problems remain unsolved. A correct solution ...
A New Hope for a Perplexing Mathematical Proof
Three years ago, a solitary mathematician released an impenetrable proof of the famous abc conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.
Monomial conjecture
In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following:Let A be a Noetherian local ring of Krull dimension d and let x1, ..., xd be a s...
The Biggest Mystery In Mathematics: Shinichi Mochizuki And The Impenetrable Proof
A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right. Sometime on the morning of 30 August 201...
Lists of unsolved problems in mathematics
Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still elude solution. Most ...
Smale's problems
Smale's problems are a list of eighteen unsolved problems in mathematics that was proposed by Steve Smale in 1998, republished in 1999. Smale composed this list in reply to a request from Vladimir Arn...
M/G/1 queue
In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a Gene...
Navier-Stokes existence and smoothness
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence). Th...
Markus−Yamabe conjecture
In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a continuously differentiable map on an -dimensional real vector space has a ...
Thom conjecture
In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the formula The Thom conjecture, named after French mathematician René Thom, states that if i...
New digraph reconstruction conjecture
The reconstruction conjecture of Stanislaw Ulam is one of the best-known open problems in graph theory. Using the terminology of Frank Harary it can be stated as follows: If G and H are two graphs on ...
Fujita conjecture
In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2013.In complex manifold theory, the conjecture states that for a positive ...
Burnside's problem
The Burnside problem, posed by William Burnside in 1902 and one of the oldest and most influential questions in group theory, asks whether a finitely generated group in which every element has finite ...
Burnside's problem - Wikipedia
Morita conjectures
The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. They asked The answers were believed to be affirmative. Here a normal P-space Y is c...
Hilbert's fourth problem
In mathematics, Hilbert's fourth problem in the 1900 Hilbert problems was a foundational question in geometry. In one statement derived from the original, it was to find geometries whose axioms are cl...
Prime quadruplet
A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {p, p+2, p+6, p+8}. This represents the closest possible grouping of four primes larger than 3.
The first ...
Problems in Latin squares
In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and me...
Landau's problems
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about primes. These problems were characterised in his speech as "unattackable at the present state of sc...
Hilbert's twenty-second problem
Hilbert's twenty-second problem is the penultimate entry in the celebrated list of 23 Hilbert problems compiled in 1900 by David Hilbert. It entails the uniformization of analytic relations by means ...
Heawood conjecture
In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. It was formulated in ...
Heawood conjecture - Wikipedia
Filling area conjecture
In mathematics, in Riemannian geometry, Mikhail Gromov's filling area conjecture asserts that among all possible fillings of the Riemannian circle of length 2π by a surface with the strongly isom...
Euler brick
In mathematics, an Euler brick, named after Leonhard Euler, is a cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relati...