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divisbyzero.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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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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www.fas.harvard.edu
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| | | | | [AI summary] The text discusses the Faculty of Arts and Sciences at Harvard University, highlighting its academic departments, research, and notable faculty member Professor Michael Puett. | |
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mycqstate.wordpress.com
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| | | This post is a follow-up on some somewhat off-hand comments that I made earlier regarding the notion of truth in a "proof-based" discipline such as pure mathematics or theoretical computer science. Since the former is easier to circumscribe and also has a larger literature available on it, for the purposes of the post I will... | ||
