Geometry To 3D and Beyond How many spatial dimensions do we live in? How many can we directly perceive? Are the two answers the same? If they are different, what effect, if any, do any higher dimensions have on us?

Knot Theory To Be or Knot to Be Hi everyone! As I mentioned in the last article about primes, this series is a place to learn about various STEM topics that I find

Number Theory Faltings’s Theorem and the Mordell Conjecture On the number of rational solutions to polynomials.

Graph Theory Solving the Königsberg Bridge Problem This proof is accessible to ANYONE — no mathematics knowledge required! (perfect for if you are a bit bored and in isolation, like me…

Mathematics The Poincaré Conjecture (1904) The shape of the universe as it was, is now and may become in the future is very hard for us to discern empirically. Einstein helped us somewhat by showing us that matter and energy (three-dimensional phenomena) in fact may interact with the a four-dimensional phenomenon: time