Category Archives: Math

A Pretty Lemma About Prime Ideals and Products of Ideals

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

Posted in Algebra, Algebraic Geometry, Math | Tagged , , | 3 Comments

Donaldson Turns 60

“Donaldson has opened up an entirely new area; unexpected and mysterious phenomena about the geometry of 4-dimensions have been discovered. Moreover, the methods are new and extremely subtle, using difficult nonlinear partial differential equations. On the other hand, this theory … Continue reading

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An Infinite Understanding

“Have you ever thought about how strange it is that we think about infinity every day, but most people think about it only on the rarest of occasions, if ever?” This is the text message I recently sent two of … Continue reading

Posted in Math, Math in Pop Culture, Mathematics in Society | 2 Comments

Gauge Theory and Low-Dimensional Topology (Part I: Historical Context)

Hi! This month, I thought I would start a brief series of articles describing the uses of gauge theory in mathematics. Rather than discuss current research directions in gauge theory (of which there are many), I hope to give an … Continue reading

Posted in Math, Topology | Tagged , | 1 Comment

The “Idea” of a Scheme

The mathematical concept of a “scheme” seems to pop up everywhere, but it’s hard to get a good grasp on what a scheme actually is. Any time you might ask someone what a scheme is in passing, there never seems … Continue reading

Posted in Algebraic Geometry, Math | Tagged , | 1 Comment