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Shtetl-Optimized » Blog Archive » The 8000th Busy Beaver number eludes ZF set theory: new paper by Adam Yedidia and me

I've supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now.  Today, I'm proud to announce that Adam Yedidia, a PhD student at MIT (but an MEng student when he did most of this work),…

Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

First published Tue Sep 25, 2007; substantive revision Tue Sep 26, 2017 If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this also the case of the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from

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