You write "in mathematics, Andrew Wiles and Gregory Perelman solved more vexing problems than Einstein did in physics."
Wiles and Perelman are rightly honored for solving problems that had been posed long ago and resisted any number of efforts to solve them. But Einstein is honored not only for that, but also for being the one who posed some of the startling questions that he also answered. E.g., is the speed of light an absolute bound on causal interactions, with all coordinates and other measures being bent as necessary (and quantum phase information being hidden as necessary) to keep that bound from being passed?
Einstein's technical achievement in solving problems that everyone else recognized was very impressive: see General Relativity especially. But if that was all Einstein did, we might (only!) compare him to Maxwell or Dirac. To appreciate Einstein's achievements in terms of analogous achievements of mathematicians, you can't just compare to the achievements of people like Wiles or Perelman, you also need to compare to the achievements of people like Goedel, who is famous for both stating and proving a fundamentally important out-of-the-blue conjecture.
Wiles and Perelman are rightly honored for solving problems that had been posed long ago and resisted any number of efforts to solve them. But Einstein is honored not only for that, but also for being the one who posed some of the startling questions that he also answered. E.g., is the speed of light an absolute bound on causal interactions, with all coordinates and other measures being bent as necessary (and quantum phase information being hidden as necessary) to keep that bound from being passed?
Einstein's technical achievement in solving problems that everyone else recognized was very impressive: see General Relativity especially. But if that was all Einstein did, we might (only!) compare him to Maxwell or Dirac. To appreciate Einstein's achievements in terms of analogous achievements of mathematicians, you can't just compare to the achievements of people like Wiles or Perelman, you also need to compare to the achievements of people like Goedel, who is famous for both stating and proving a fundamentally important out-of-the-blue conjecture.