Feb 3, 2022

Mathematicians Prove 30-Year-Old André-Oort Conjecture

Posted by in categories: information science, mathematics

“The methods used to approach it cover, I would say, the whole of mathematics,” said Andrei Yafaev of University College London.

The new paper begins with one of the most basic but provocative questions in mathematics: When do polynomial equations like x3 + y3 = z3 have integer solutions (solutions in the positive and negative counting numbers)? In 1994, Andrew Wiles solved a version of this question, known as Fermat’s Last Theorem, in one of the great mathematical triumphs of the 20th century.

In the quest to solve Fermat’s Last Theorem and problems like it, mathematicians have developed increasingly abstract theories that spark new questions and conjectures. Two such problems, stated in 1989 and 1995 by Yves André and Frans Oort, respectively, led to what’s now known as the André-Oort conjecture. Instead of asking about integer solutions to polynomial equations, the André-Oort conjecture is about solutions involving far more complicated geometric objects called Shimura varieties.

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