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rjlipton.com
| | terrytao.wordpress.com
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| | Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ...
| | 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...
| | aperiodical.com
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| | This week, Katie and Paul are blogging from the Heidelberg Laureate Forum - a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top...
| | djalil.chafai.net
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| This post provides the solution to a tiny exercise of probability theory, answering the question asked by a student during the MAP-432 class yesterday. Let \( {(\Omega,\mathcal{F},\mathbb{P})} \) be a probability space equipped with a filtration \( {{(\mathcal{F}_n)}_{n\geq0}} \). Recall that a random variable \( {\tau} \) taking values in \( {\mathbb{N}=\{0,1,\ldots\}} \) is a stopping time when \( {\{\tau=n\}\in\mathcal{F}_n}...