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7stones.com | ||
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www.jeremykun.com
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| | | | | Problem: Prove there are infinitely many prime numbers. Solution: First recall that an arithmetic progression with difference $ d$ is a sequence of integers $ a_n \subset \mathbb{Z}$ so that for every pair $ a_k, a_{k+1}$ the difference $ a_{k+1} - a_k = d$. We proceed be defining a topology on the set of integers by defining a basis $ B$ of unbounded (in both directions) arithmetic progressions. That is, an open set in this topology is an arbitrary union of arithmetic progressions from $ -\infty$ to $ \infty$. | |
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www.quantamagazine.org
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| | | | | A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura | |
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mattbaker.blog
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| | | | | Today is the 10th anniversary of the death of Martin Gardner. His books on mathematics had a huge influence on me as a teenager, and I'm a fan of his writing on magic as well, but it was only last year that I branched out into reading some of his essays on philosophy, economics, religion,... | |
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reasonableapproximation.net
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