Mathematicians have solved the 40-year-old problem that Andrew Wiles used to help him tackle Fermat's Last Theorem.
The Taniyama-Shimura conjecture had been partially proved by Wiles while he homed in on mathematics' most notorious unsolved puzzle.
Now three of Wiles's former students - Brian Conrad and Richard Taylor at Harvard University and Fred Diamond at Brandeis University, in the United States - with Christopher Breuil of the University of Paris, France, have completed the job. They will reveal the details of the proof at a special meeting at the Mathematical Sciences Research Institute in Berkeley, US, next week.
The conjecture, first made by Yutaka Taniyama and Goro Shimura, was that all elliptic curves are modular, a concept that has underpinned the field of arithmetic geometry.
Philippe Tondeur, assistant director for mathematical sciences at the National Science Foundation, which supported the work, said: "This is a breakthrough for mathematics and will have far-reaching consequences because of the abundance of new mathematical tools developed in the
process."