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Mathematician Disproves 80-Year-Old Algebra Conjecture

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

Click to view the original at quantamagazine.org

Hasnain says:

“Once Gardam releases the details of his algorithm, it will be open season for other mathematicians to explore the Hantzsche-Wendt group and potentially other groups. “The hope is that we will learn something new — a new trick which will allow us to build examples,” Kielak said.

Already, knowing that the conjecture is false has changed the mindsets of many mathematicians. “Psychologically, this is a very big difference,” Kielak said. “Probably in a year’s time, we’re going to have infinitely many” counterexamples.”

Posted on 2021-04-15T06:07:39+0000