# How do mathematicians think about the existence of numbers?

Question: How do mathematicians think about the existence of numbers? And how did Newton, Euler, and other famous mathematicians thought about this concept?

I know that existence of numbers is a big ongoing debate in the philosophy of mathematics. I've searched online about this and found a lot of information (e.g. Aristotelianism, platonism, etc) , but nothing about the famous mathematicians.

Thank you

-
Relatively few mathematicians have given detailed expositions of their views. The problem belongs to a branch of knowledge that is equally serious, but different. –  André Nicolas Dec 10 '12 at 23:25
I heard that Gödel believed existence of real numbers. I would like someone to confirm this. –  Makoto Kato Dec 11 '12 at 0:17
What do you mean by "the existence of numbers"? (I am not sure what you mean either by "existence" or by "numbers.") –  Qiaochu Yuan Dec 11 '12 at 0:57
It has been said (I forget the source) that in their work, all mathematicians are naive Platonists, but in discussing the matter, many take a Formalists position. I am not comfortable with the use of the universal quantifier, particularly since as far as I know the assertion has not been experimentally tested. –  André Nicolas Dec 11 '12 at 1:45