Article
Moshe Vardi

Published: Sep 20, 2024 | Version 1.00

Publisher: COMMUNICATIONS OF THE ACM, Vol 66, No 11

DOI: 10.82383/bebc-zc12

This work is licensed under All rights reserved

 

Description

One of the most fundamental conundrums in the philosophy of mathematics is the question of whether mathematics was discovered by humans or invented by them. On one hand, it seems hard to argue that highly sophisticated mathemati- cal objects, such as inaccessible car- dinals, were discovered. On the other hand, as Albert Einstein asked, “How can it be that mathematics, being after all a product of human thought, which is independent of experience, is so ad- mirably appropriate to the objects of reality?” The 19th century mathema- tician Leopold Kronecker offered a compromise, saying “God created the integers, all else is the work of man.”

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