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kpknudson.com | ||
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carcinisation.com
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| | | | | Gödel's theorems say something important about the limits of mathematical proof. Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be "inside" the universe it's saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it's hard to make a proof of it using nothing... | |
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njwildberger.com
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| | | | | This coming Tuesday in the Pure Maths Seminar at UNSW I will be giving a talk: Here are the details, in case you are in Sydney and are interested. The talk is at the School of Mathematics and Statistics, UNSW, Kensington campus, building the Red Centre, which is up the main walkway from Anzac Parade.... | |
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cre8math.com
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| | | | | This might sound like an odd question -- most students seem to think so when I ask it. The reason it sounds a little strange is that most students -- even when I taught at a magnet STEM high school -- think there's just one type of geometry: Euclidean geometry. This isn't surprising given the... | |
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xorshammer.com
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| | | Nonstandard Analysis is usually used to introduce infinitesimals into the real numbers in an attempt to make arguments in analysis more intuitive. The idea is that you construct a superset $latex \mathbb{R}^*$ which contains the reals and also some infinitesimals, prove that some statement holds of $latex \mathbb{R}^*$, and then use a general "transfer principle"... | ||
