Jekyll2026-03-04T15:17:06+00:00/feed.xmlDavid RadcliffeMy personal website.Polynomials as finite sums of periodic functions2026-03-04T14:00:00+00:002026-03-04T14:00:00+00:00/math/2026/03/04/polynomials-as-sums-of-periodic-functionsEvery real polynomial function of degree $n$ can be expresed as the sum of $n+1$ periodic functions. The proof requires the axiom of choice.

]]>Cancellation in direct products of finite groups2026-02-28T18:12:00+00:002026-02-28T18:12:00+00:00/math/2026/02/28/cancellation-in-direct-products-of-finite-groupsLet $A$, $B$, $C$ be finite groups. If $A \times B$ and $A \times C$ are isomorphic, then $B$ and $C$ are also isomorphic. That is, the common factor $A$ can be cancelled from both sides of the equation.

I learned a beautiful proof of this result from the Usenet newsgroup sci.math in 2001, while I was completing my Ph.D. dissertation. I rewrote the proof in a plain text file, and then forgot the details.

Today, I prompted ChatGPT to rewrite the proof carefully in LaTeX. I think that the result was pretty good. You can view the proof as a PDF.

]]>Welcome to my personal website2026-01-20T15:26:27+00:002026-01-20T15:26:27+00:00/jekyll/update/2026/01/20/welcomeMy name is David Radcliffe. I am an independent mathematician (Ph.D. 2001) and a software engineer in Saint Paul, Minnesota.

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