Gerd Faltings, who proved the Mordell conjecture, wins the Abel Prize

4 comments

• nhatcher4 days ago
  Oh wow! I wouldn't have expected this so many years later. Mordel's conjecture implies asva special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers. Brings me back!
• 0111011015 hours ago
  A point is that which has no breadth.<p>The line is a breadthless legth.<p>Mordell conjecture is that only circles or figure contain infinite points, whereas curves with exponents over 3 are finite accumulations.
• ljsprague3 hours ago
  &quot;He proved that if a curve’s equation has a variable raised to a power higher than 3, then it must have a finite number of [rational] points.&quot;
  • OgsyedIE1 hour ago
    This must be an incorrect description of what has actually been proved, since x^4 is a counterexample.
    • raphlinus12 minutes ago
      My understanding, which is to be taken with a grain of salt, is that there&#x27;s an additional constraint, not stated in the Scientific American article, that the plane curve be <i>irreducible.</i> The example of x^4 is reducible, it&#x27;s x^2 * x^2 among other thing. The actual conjecture is expressed in terms of genus, but this follows from the genus-degree formula.
• RonSFriedman864 days ago
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