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The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

An equation for a lattice sum b_3(1) (Borwein and Bailey 2003, p. 26) b_3(1) = sum^'_(i,j,k=-infty)^infty((-1)^(i+j+k))/(sqrt(i^2+j^2+k^2)) (1) = ...

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).

It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

A conjecture due to Paul Erdős and E. G. Straus that the Diophantine equation 4/n=1/a+1/b+1/c involving Egyptian fractions always can be solved (Obláth 1950, Rosati 1954, ...

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-tuple. Numbers that are not friendly are said to be solitary. There are some ...