As Thurston’s article approached its 30th anniversary this year,
all but four of the 23 main questions had been settled,
including the geometrization conjecture, which the Russian
mathematician Grigori Perelman proved in 2002 in one of the
signal achievements of modern mathematics. The four unsolved
problems, however, stubbornly resisted proof. “The fact that we
couldn’t solve them for so long meant that something deep was
going on,” said Yair Minsky, of Yale University. Finally, in
March, Ian Agol, of the University of California at Berkeley,
electrified the mathematics community by announcing a proof to
“Wise’s conjecture,” which settled the last four of Thurston’s
questions in one stroke. Mathematicians are calling the result
the end of an era. “The vision of three-manifolds that Thurston
articulated in his paper, which must have looked quite fantastic
at the time, has now been completely realized,” said Danny
Calegari, of the California Institute of Technology. “His vision
has been remarkably vindicated i