The Quest to Solve the Hardest Math Problem in History

(Image cred­it: Wikipedia user Salix alba)

In 2002, a reclu­sive Russ­ian genius named Grig­ori Perel­man put an end to more than 100 years of suf­fer­ing in the math­e­mat­i­cal com­mu­ni­ty. He solved the most dif­fi­cult math prob­lem of the 20th cen­tu­ry -the Poincaré Con­jec­ture. Its siren call had lured gen­er­a­tions of math­e­mati­cians to intel­lec­tu­al graves. It first, its sim­plic­i­ty would seduce them, and they'd become con­vinced the answer was near. But as years passed, they'd be left with noth­ing to show for their lives' toil but dead ends. By the time Grig­ori Perel­man proved the Con­jec­ture, the solu­tion was worth $1 mil­lion.

THE MAN BEHIND THE MAD­NESS

230POINCARE

Henri Poincaré

In 1885, all of Europe was talk­ing about Henri Poincaré, a 30-year-old genius who'd math­e­mat­i­cal­ly proven why the solar sys­tem holds togeth­er. When a hole appeared in his cal­cu­la­tions, he plugged it up by essen­tial­ly invent­ing chaos the­o­ry: Kings were trip­ping over them­selves to make him a knight· and Swe­den gave him a small for­tune in prize money. To this day; Poin­care holds the record for the most physics Nobel Prize nom­i­na­tions, though he never actu­al­ly won one.

But his most leg­endary achieve­ment was some­thing no one noticed until much, much later. At the turn of the cen­tu­ry: Poincaré invent­ed an entire­ly new field called alge­bra­ic topol­o­gy; and today, it's one of the most com­pli­cat­ed and vibrant branch­es of math­e­mat­ics. Think of it as a twist­ed ver­sion of geom­e­try, in which shapes stretch, bend, and fold inside out. Poincaré's goal was to clas­si­fy objects by iden­ti­fy­ing their basic form, much the same way botanists clas­si­fy new species of plants. In the process of cre­at­ing topol­o­gy, Poincaré tossed out a con­jec­ture that seemed to be true. It was a side note to a larg­er prob­lem, and he fig­ured he'd work out the details later. Lit­tle did he know; his side note would become one of the great­est chal­lenges in the math­e­mat­i­cal world.

THE VIC­TIMS

Poincaré's con­jec­ture seemed sim­ple enough. It claimed that any object with­out a loop is essen­tial­ly a sphere. Think of a knife made out of Play-Doh. With­out punch­ing a hole in it or clos­ing a loop, can you squish it into a ball? Yes, of course. Now pic­ture a pair of Play-Doh scis­sors. No mat­ter how hard you try, you can't crush it into a ball with­out clos­ing up the fin­ger holes. It's impos­si­ble. Poin­care believed that objects like the knife were relat­ed to spheres, while objects with holes and loops in them were not...............

The Quest to Solve the Hardest Math Problem in History
http://www.neatorama.com/2011/11/25/the-quest-to-solve-the-hardest-math-problem-in-history-and-the-minds-that-were-lost-along-the-way/