'To Bless All Mankind' April 9, 2018 Issue

The awards and rewards of grasping infinity

The Monitor’s Editorial Board

Originally published in The Christian Science Monitor, September 19, 2017.

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.

While the discovery was in theoretical math, it illustrates the steady recognition among scholars and other thinkers that infinity in all its aspects may be knowable in thought despite the limitations of the physical senses. By its very nature, infinity is inexhaustible and has been a source of wonder since ancient times. The desire to grasp infinity has contributed to progress in many fields, from science to religion. In fact, the ability to come up with new understandings about reality may itself be infinite.

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