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polymathprojects.org | ||
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thatsmaths.com
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| | | | | The Riemann Hypothesis Perhaps the greatest unsolved problem in mathematics is to explain the distribution of the prime numbers. The overall ``thinning out'' of the primes less than some number $latex {N}&fg=000000$, as $latex {N}&fg=000000$ increases, is well understood, and is demonstrated by the Prime Number Theorem (PNT). In its simplest form, PNT states that... | |
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www.jeremykun.com
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| | | | | Problem: Prove there are infinitely many primes Solution: Denote by $ \pi(n)$ the number of primes less than or equal to $ n$. We will give a lower bound on $ \pi(n)$ which increases without bound as $ n \to \infty$. Note that every number $ n$ can be factored as the product of a square free number $ r$ (a number which no square divides) and a square $ s^2$. | |
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gilkalai.wordpress.com
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| | | | | Gowers, Green, Manners and Tao. They reminded me of the A-team of the 1980s television series: "If you have a problem, if no one else can help, and if you can find them, maybe you can hire... the A-Team." A conjecture of Marton, widely known as "the polynomial Freiman-Ruzsa conjecture" was certainly a holy grail | |
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scottaaronson.blog
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| | | (1) Apparently Microsoft has decided to make a major investment in buildingtopological quantum computers, which will include hiring Charles Marcus and Matthias Troyer among others. See here for their blog post, and here for the New York Times piece. In the race to implementQC among the establishedcorporate labs, Microsoft thus joins the Martinis group at... | ||
