El matem????tico franc????s Henri Poincar???? (1854-1912) no s????lo realiz???? aportaciones decisivas en el campo de la topolog????a la ciencia que estudia las propiedades de las formas geom????tricas, sino que, adem????s, leg???? a la posteridad uno de los problemas matem????ticos m????s fascinantes de todos los tiempos, pues su respuesta puede contribuir a explicar la forma del universo. Desde 1904, lo que se conoce como ????conjetura de Poincar???????? ha desafiado a varias generaciones de investigadores, que han tratado infructuosamente de resolverla o refutarla. / In 1904, Henri Poincar????, a giant among mathematicians who transformed the fledging area of topology into a powerful field essential to all mathematics and physics, posed the Poincar???? conjecture, a tantalizing puzzle that speaks to the possible shape of the universe. For more than a century, the conjecture resisted attempts to prove or disprove it. As Donal OShea reveals in his elegant narrative, Poincar????s conjecture opens a door to the history of geometry, from the Pythagoreans of ancient Greece to the celebrated geniuses of the nineteenth-century German academy and, ultimately, to a fascinating array of personalitiesPoincar???? and Bernhard Riemann, William Thurston and Richard Hamilton, and the eccentric genius who appears to have solved it, Grigory Perelman. The solution seems certain to open up new corners of the mathematical universe.