Proving the “discrete” periodic tiling conjecture for high-dimensional lattices is a slightly different problem than proving the continuous version of the conjecture, as there are tilings that ...

Then, at the beginning of the 19th century, mathematicians constructed explicit examples of non-Euclidian geometry, disproving the conjecture. This was not the end of geometry, however.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. They were wrong.

Arithmetic Geometry and Manin's Conjecture Publication Trend The graph below shows the total number of publications each year in Arithmetic Geometry and Manin's Conjecture.

In the ensuing decades, mathematicians filled in this picture, constructing examples and developing a more concrete theory. All the evidence seemed to point to Milnor’s conjecture being true. The ...

When she was just 17 years old, Hannah Cairo disproved the Mizohata-Takeuchi conjecture, breaking a four-decade-old mathematical assumption ...

Fernando Soria, Examples and Counterexamples to a Conjecture in the Theory of Differentiation of Integrals, Annals of Mathematics, Vol. 123, No. 1 (Jan., 1986), pp. 1-9 ...

The Collatz Conjecture is a deceptively simple math problem. It has only two rules. First, pick any number. If it's even, divide it by two. If it's odd, multiply it by three and add one. This will ...

The Mizohata–Takeuchi conjecture is about identifying when this breakdown happens, especially when the underlying math is not smooth enough.