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1729 is sometimes called the Hardy-Ramanujan number. It is the smallest taxicab number, i.e., the smallest number which can be expressed as the sum of two cubes in two ...

The Diophantine equation x^2+k=y^3, which is also an elliptic curve. The general equation is still the focus of ongoing study.

A Mandelbrot set-like fractal obtained by iterating the map z_(n+1)=z_n^3+(z_0-1)z_n-z_0.

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

It is possible to place 7 cigarettes in such a way that each touches every other if l/d>7sqrt(3)/2 (Gardner 1959, p. 115).

Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

If there is an integer x such that x^3=q (mod p), then q is said to be a cubic residue (mod p). If not, q is said to be a cubic nonresidue (mod p).

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

A point p on a regular surface M in R^3 is said to be elliptic if the Gaussian curvature K(p)>0 or equivalently, the principal curvatures kappa_1 and kappa_2 have the same ...