The awards and rewards of grasping infinity

With so much news being about the scarcity of things, it may be easy to overlook news about infinity, or rather our understanding of it. Last July, two scholars were awarded one of the highest honors in math for solving a problem that had stumped mathematicians for seven decades: whether two variations of infinity expressed in sets of numbers are the same. It turns out they are. Not only was the proof a surprise, and an elegant one, it may bring practical applications.

The award, called the Hausdorff medal, was given to Maryanthe Malliaris of the University of Chicago and Saharon Shelah of the Hebrew University of Jerusalem and Rutgers University for a 2016 paper in the Journal of the American Mathematical Society. Their breakthrough, proved over 60 pages of complex calculations, was in applying one field known as model theory to another field called set theory. This allowed them to overturn conventional understanding about the sizes of infinite sets.

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