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.
Are there any books/articles about this concept?
Thank you
Best Answer
The famous British mathematical physicist Roger Penrose wrote an entire book on this subject: The Road to Reality: A Complete Guide to the Laws of the Universe (Knopf, 2005). In fact you can get a very good idea of his version of the Platonic theory just from Chapter 1, pages 7-24. He sees a tripartite world, divided into physical, mental, and mathematical domains. It's an interesting approach, and perhaps deserves special attention due to his prominence within both mathematics and physics. The book itself is just over a thousand pages long, and requires some mathematical maturity to comprehend. If you have what it takes, then it is well worth the effort.