# Category Archives: Math

## Machine-Checked Proof

“In my view, the choice between the conventional process by a human referee and computer verification is as evident as the choice between a sundial and an atomic clock in science.” – Tom Hales (from [4]) “The rapid advance of … Continue reading

## AMS Notices Spotlight October 2017

Hello and welcome to the October AMS Notices Spotlight. As we are now into the swing of the busyness of the semester it is sometimes nice to take a break and think about math not related to our classes. With … Continue reading

## Real Numbers Base…Factorials! And A By-product

PROPOSITION 1:  For a real number  x  there exists a sequence $x_1, x_2, x_3,…$ of integers such that $\hspace{4cm} x=x_1 +\frac{x_2}{2!}+\frac{x_3}{3!} + \cdots + \frac{x_n}{n!} + \cdots, \hspace{2cm} (*)$ where $x_1$ can be any integer, but for … Continue reading

I was trying to prove a theorem in algebraic geometry which basically held if and only if this lemma held. Here’s the lemma: Lemma: Given any ring $A$, a prime ideal $\mathfrak{p} \subset A$, and a finite collection of ideals … Continue reading