5 min read · 2020-06-01 · Mathematicians try to figure out when problems can be solved using current knowledge — and when they have to chart a new path instead.
“I think one of the reasons we were stonewalled was not because we didn’t have the right techniques, but because the problem wasn’t put in the right conceptual framework,” McMullen said. “The changed question suggested the changed techniques.”
~20 min read · 2020-02-24 · For over six years now, I've been studying mathematics on my own in my spare time - working my way through books, exercises, and online courses. In this post I'll share what books and resources I've…
6 min read · 2020-03-04 · Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.
3 min read · Sep 14th · The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.
One surprising consequence of Hausdorff’s definition is that objects could have non-integer dimensions.
The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to one, a pigeon on the ground free to move in two and an eagle in the air enjoying three.