Category Archives: Uncategorized

Defeating an IM


I hadn’t played a tournament since May, when I had a disastrous tournament and lost four games before withdrawing in disgust. My tournament this weekend was mostly mediocre, except for one game, in which I scored my first win against … Continue reading

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Why didn’t Euler conjecture the prime number theorem?


It shouldn’t have been too hard, based on what he knew. Let us take a look. Euler knew that the sum of reciprocal primes diverged, and he even knew the growth rate of , where the sum is taken only … Continue reading

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The Wallis Product


I had seen the Wallis product, but I did not know a derivation of it until a few weeks ago, when I discovered this gem when reading the wonderful book Sources in the Development of Mathematics by Ranjan Roy. I’m storing this … Continue reading

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One interesting thing: Counting skew ternary trees


On Monday, I attended Don Knuth’s annual Christmas Tree Lecture, where he talks about the most interesting thing he has learned about trees in the past year. This year, he talked about ternary trees and planar graphs. Among other things, … Continue reading

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Exchange sacrifices galore


Last weekend, I played the BayAreaChess Thanksgiving tournament. My play was pretty bad, but my results (2 wins, 1 draw, 2 losses against all players rated a bit higher than I) were okay, and I hit a new rating high … Continue reading

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One interesting thing: Average polynomial time algorithms


The most celebrated problem in theoretical computer science is undoubtedly the P vs. NP problem. Let me explain what it is asking. (If you already know this, feel free to skip the next few paragraphs.) Suppose we have a general … Continue reading

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One interesting thing: Erdős–Rényi random graphs


I’ve been thinking a lot about random graphs this week, so it is appropriate for my post this week to be about them. One of the most important models of random graphs is the Erdős–Rényi model. Here is the construction: we … Continue reading

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