On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

Algebraic structures, encompassing groups, rings, fields and modules, have long formed the backbone of modern mathematics. Category theory, with its focus on objects and morphisms, provides a unifying ...

Transactions of the American Mathematical Society, Vol. 362, No. 7 (JULY 2010), pp. 3499-3533 (35 pages) We introduce a notion of Polish structure and, in doing so, provide a setting which allows the ...

Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research ...

Math as both profession and course of study can be a hard sell, something even Don Draper might have trouble pitching. The field unites numbers, theories, and ideas that, yes, can be physically ...

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