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| | gilkalai.wordpress.com
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| | Topology Quasi-polynomial algorithms for telling if a knot is trivial Marc Lackenby announced a quasi-polynomial time algorithm to decide whether a given knot is the unknot! This is a big breakthrough. This question is known to be both in NP and in coNP. See this post, and updates there in the comment section. Topology seminar,...
| | thatsmaths.com
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| | In his book A Mathematician's Apology, leading British mathematician G H Hardy wrote "Amathematician, like a painter or poet, is a maker ofpatterns." He observed that the mathematician's patterns, like the painter's or the poet's, must be beautiful; beauty is the acid test [TM245or search for "thatsmaths" atirishtimes.com]. Everyone is familiar with the concept of...
| | www.jeremykun.com
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| | This post assumes working knowledge of elementary number theory. Luckily for the non-mathematicians, we cover all required knowledge and notation in our number theory primer. So Three Thousand Years of Number Theory Wasn't Pointless It's often tough to come up with concrete applications of pure mathematics. In fact, before computers came along mathematics was used mostly for navigation, astronomy, and war. In the real world it almost always coincided with the physical sciences.
| | math.andrej.com
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