1980 - 1990




  • Donaldson publishes Self-dual connections and the topology of smooth 4-manifolds which leads to totally new ideas concerning the geometry of 4-manifolds.
  • Faltings proves the "Mordell conjecture". He makes a major contribution to Fermat's Last Theorem showing that for every nn there are at most a finite number of coprime integers x,y,zx, y, z satisfying xn+yn=znx^{n} + y^{n} = z^{n}. (See THIS LINK.)



  • Margulis proves the "Oppenheim conjecture" on the values of indefinite irrational quadratic forms at integer points.


  • Zelmanov proves an important conjecture about when an infinite dimensional Lie algebra is nilpotent.


  • Langlands is the first recipient of the National Academy of Sciences Award in Mathematics. He receives it for "extraordinary vision that has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory."
  • Elkies finds a counterexample to Euler's Conjecture with n=4n = 4, namely 26824404 + 153656394 + 187967604 = 206156734 .
    Later in the year Frye finds the smallest counter-example: 958004 + 2175194 + 4145604 = 4224814 .


  • Bourgain, using analytic and probabilistic methods, solves the L(p)L(p) problem which had been a longstanding one in "Banach space" theory and harmonic analysis.