Toeplitz’ Conjecture

Does every simple closed curve in the plane contain the vertices of a square?
No one knows, but the answer to this question is positive if the curve is sufficiently regular.
Toeplitz conjecture
The black dashed curve goes through all corners of several green squares.

Life, the Universe, and Maths

For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1 to 100. This theory is true in all cases except for an unproven exception: 42.

By 2016 and over a million hours of computation later, researchers of the UK’s Advanced Computing Research Center had its solution for 42.

Sum of 3 cubes

More intriguing number facts here.


Wallace-Simson’s Line Theorem

The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.

Simon line theorem

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