In the game, this is a theorem called the "first sub-boss of Multiplication World." You will prove it by mobilizing all the theorems built up so far: mul_zero, zero_mul, succ_mul, and mul_succ. The ...

I will explain examples of linear transformations of Lie groups. Regarding left-invariant vectors, I will show the equivalence between the expression viewed from the mapping of tangent vectors and the ...

To square Albert Einstein’s General Theory of Relativity with quantum mechanics requires some currently unknown physics, and that’s led some scientists to question if Einstein’s theory could use some ...

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question. Mathematics started with numbers — clear, ...

This semester I’ve been teaching an undergraduate course on Galois theory. It was all online, which meant a lot of work, but it was also a lot of fun: the students were great, and I got to know them ...