Andrew Wiles published his proof of Fermat's Last Theorem in the Annals of Mathematics in 1995.

Bernhard Riemann first stated the Riemann hypothesis in his paper "Über die Anzahl der Primzahlen unter einer gegebenen Grösse" published in the Journal für die reine und angewandte Mathematik in 1859.

Grigori Perelman published his proof of the Poincaré conjecture in the Annals of Mathematics in 2002.

Lothar Collatz first proposed the Collatz conjecture in his paper "Über eine neue Art von Folgen" published in the Mathematische Annalen in 1937.

Thomas Hales published his proof of the Kepler conjecture in the Annals of Mathematics in 2005.

Joseph Oesterlé and David Masser first stated the ABC conjecture in their paper "Sur l'arithmétique des courbes elliptiques" published in the Comptes Rendus de l'Académie des Sciences in 1985.

The Goldbach conjecture has not yet been proven.

William Hodge first proposed the Hodge conjecture in his paper "The Theory and Application of Harmonic Integrals" published in the Proceedings of the Cambridge Philosophical Society in 1941.

The Birch and Swinnerton-Dyer conjecture has not yet been proven.

Robert Langlands first proposed the Langlands program in his paper "Problems in the Theory of Automorphic Forms" published in the American Journal of Mathematics in 1970.

Simon Donaldson published his proof of the Yau-Tian-Donaldson conjecture in the Annals of Mathematics in 1987.

David Mumford first proposed the Mumford conjecture in his paper "Curves and their Jacobians" published in the Annals of Mathematics in 1965.

Michael Atiyah and Isadore Singer published their proof of the Atiyah-Singer index theorem in the Annals of Mathematics in 1968.

Alexander Grothendieck first proved the Grothendieck-Riemann-Roch theorem in his paper "Sur la cohomologie des faisceaux locaux" published in the Annales Scientifiques de l'École Normale Supérieure in 1957.

Pierre Deligne, David Mumford, and Finn Knudsen published their proof of the Deligne-Mumford-Knudsen formula in the Inventiones Mathematicae in 1974.