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>"The prize was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed."<p>He later abandoned mathematics and returned to obscurity.<p>[0] <a href="https://en.wikipedia.org/wiki/Grigori_Perelman" rel="nofollow">https://en.wikipedia.org/wiki/Grigori_Perelman</a>
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 "equal", they are related by β1 = 2g. Furthermore, the Euler charasteric also doesn't "equal" it. Euler charasteristic χ in terms of genus is χ = 2 − 2g, so by substitution, χ = 2 − β1.
That was a marvellously lucid presentation of the subject. I can'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've learned something.<p>There's a citation in the article to "Gardner, 1984 p. 9–10". But there'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.
From wiki:<p>In August 2006, Perelman was offered the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."
“<p>Some people are built differently, what a legend.
I always liked this 8 minute explanation of the proof: <a href="https://www.youtube.com/watch?v=PwRl5W-whTs" rel="nofollow">https://www.youtube.com/watch?v=PwRl5W-whTs</a>