Vaniver comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 113 - Less Wrong Discussion
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(Not a serious suggestion)
Using the Axiom of Choice and partial transfiguration, Harry divides himself into two exact copies, one of which is killed by the Death Eaters and the other of which escapes.
Mathematical progress ground to a standstill in March of 2015, when thousands of researches abandoned their work to search for a constructive proof of the Banach–Tarski theorem.
It's a little vague how to define ‘constructive’, but we pretty much already know that there isn't one. https://en.wikipedia.org/wiki/Solovay_model