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The McKay conjecture turns a key theme in mathematics into a concrete tool for group theorists

Quanta Magazine
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The McKay conjecture is one of the biggest open problems in the mathematical realm known as group theory.

After the conjecture was posed in the 1970s , dozens of mathematicians tried their hand at proving it.

But a full proof seemed out of reach.

Now, 20 years after she first learned about the problem, Britta Späth and Marc Cabanes have finally proved it.

A mathematician named Marty Isaacs proved that it held for a large class of groups.

But mathematicians got stuck in proving the McKay conjecture for all finite groups.

The next major advance on the problem required the completion of one of the most herculean mathematical projects in history.

The project ultimately required thousands of proofs and took more than 100 years to complete.

Britta Späth spent years working on a new version of the McKay conjecture.

She and her co-workers proved the last case of a class of Lie-type groups that remained open.