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Tag Archives: Math
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
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
What is a Manifold? (6/6)
In posts 1-3 we were able to reduce all of the geometry of a curve in 3-space to an interval along with two or three real-valued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading
What is a Manifold? (5/6)
In our last post, we invented a new geometry by re-scaling the inner product of the usual Euclidean plane. This modification did not change any of the angles in our geometry, in the sense that if two curves intersected in a particular Euclidean … Continue reading
Mathematical Democracy: Mission Impossible? Maybe not…
In 1950, a 29-year-old PhD candidate at Columbia published a stunning theorem that later won him a Nobel Prize: “There is no such thing as a fair voting system.” Or so the legend goes. Let’s dive into this claim and … Continue reading