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The Poincaré Conjecture, Explained

133 pointsby privatdozentalmost 4 years ago

6 comments

lglalmost 4 years ago
Also fascinating is the story of the man that eventually proved the conjecture, Grigori Perelman [0], which famously later denied the $1M Millennium prize as well as the Fields medal where he is quoted as saying:<p>&quot;The prize was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed.&quot;<p>He later abandoned mathematics and returned to obscurity.<p>[0] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Grigori_Perelman" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Grigori_Perelman</a>
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GolDDranksalmost 4 years ago
The article seems to be full of little mistakes. A torus has Betti number β1 of 2, not 1 as is on the text. Also, β1 and genus are not &quot;equal&quot;, they are related by β1 = 2g. Furthermore, the Euler charasteric also doesn&#x27;t &quot;equal&quot; it. Euler charasteristic χ in terms of genus is χ = 2 − 2g, so by substitution, χ = 2 − β1.
denton-scratchalmost 4 years ago
That was a marvellously lucid presentation of the subject. I can&#x27;t say I understood all of it, but I love to read presentations of difficult subjects expressed clearly in (more or less) plain words. It makes me think I&#x27;ve learned something.<p>There&#x27;s a citation in the article to &quot;Gardner, 1984 p. 9–10&quot;. But there&#x27;s no footnote. Would that be the late Martin Gardner, formerly of Mathematical Recreations? He also had a talent for expressing hard subjects clearly, in plain words.
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jwilberalmost 4 years ago
From wiki:<p>In August 2006, Perelman was offered the Fields Medal for &quot;his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow&quot;, but he declined the award, stating: &quot;I&#x27;m not interested in money or fame; I don&#x27;t want to be on display like an animal in a zoo.&quot; “<p>Some people are built differently, what a legend.
yargalmost 4 years ago
Shouldn&#x27;t it be renamed now that it&#x27;s proven?<p>The Poincaré-Perelman theorem seems more accurate now.
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wrnralmost 4 years ago
I always liked this 8 minute explanation of the proof: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=PwRl5W-whTs" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=PwRl5W-whTs</a>
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