What Can We Gain by Losing Infinity? | Quanta Magazine
Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.
A properly delicious heresy to start the week on. This Quanta profile follows mathematician Doron Zeilberger, standard-bearer for ‘ultrafinitism’ — the fringe conviction that there is, in the end, a largest number, and that infinity is a fiction we’ve talked ourselves into.
Drop infinity, he argues, and mathematics becomes more honest, more concrete, more usable — those parallel lines really do meet somewhere eventually. Centuries of history and most of his colleagues think he’s wrong. Whether or not he ‘wins’, it’s fun to be reminded that even the most settled-seeming foundations are still up for grabs.
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