E.T. Bell called Fermat the Prince of Amateurs. One hundred years ago Ramanujan amazed the mathematical world. In between were many important amateurs and mathematicians off the beaten path, but what about the last one hundred years? Is it still possible for an amateur to make a significant contribution to mathematics? Can anyone cite examples of important works done by amateur mathematicians in the last one hundred years?
For a definition of amateur:
I think that to make the term "amateur" meaningful, it should mean someone who has had no formal instruction in mathematics past undergraduate school and does not maintain any sort of professional connection with mathematicians in the research world. – Harry Gindi
Best Answer
About ten years ago Ahcène Lamari and Nicholas Buchdahl independently proved that all compact complex surfaces with even first Betti number are Kahler. This was known since 1983, but earlier proofs made use of the classification of surfaces to reduce to hard case-by-case verification.
At the time, Lamari was a teacher at a high school in Paris. Apparently he announced his result by crashing a conference in Paris and going up to Siu (who had proved the last case in the earlier proof in 1983) with a copy of his proof. Lamari's proof was published in the Annales de l'Institut Fourier in 1999 (Courants kählériens et surfaces compactes, Annales de l'institut Fourier, 49 no. 1 (1999), p. 263-285, doi:10.5802/aif.1673), next to Buchdahl's (On compact Kähler surfaces, Annales de l'institut Fourier, 49 no. 1 (1999), p. 287-302, doi: 10.5802/aif.1674)