The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, uses number ...

The Journal of Integral Equations and Applications, Vol. 4, No. 2 (SPRING 1992), pp. 273-307 (35 pages) This paper formulates several axioms for the ordering structure of state spaces and establishes ...

The Annals of Probability, Vol. 34, No. 2 (Mar., 2006), pp. 663-727 (65 pages) We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely ...

When you buy through links on our articles, Future and its syndication partners may earn a commission. Mathematicians have solved a longstanding algebra problem, providing a general solution for ...

Computers fail at even simple math more often than many of us realize and that flaw is rooted in the architecture of the machines themselves. Using machine learning, Google might have discovered a way ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...