This page features a collection of the best resources on the philosophy of mathematics. Just to be clear, there is no single best resource on the philosophy of mathematics. The best one will depend on your preferred learning style and the amount of time you want to spend learning about it.
To get started, simply choose one of the links below:
If you want an academic overview of the philosophy of mathematics:
- Read the Stanford Encyclopedia of Philosophy article on the Philosophy of Mathematics. However, you should keep in mind that the SEP is often quite technical and this article may be difficult for beginners. It’s also quite long at around 14,000 words. Here’s a short excerpt that introduces the philosophy of mathematics:
“If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this also the case of the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way: by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics.. . . .”
If you’re looking for a somewhat shorter and more engaging introduction:
If you’d prefer a video introduction:
If you prefer audio and podcasts:
- Listen to James Franklin discuss The Philosophy of Mathematics on The Philosopher’s Zone podcast [25 mins]
While these resources are a great starting point, there’s only so much you can learn by using free online resources. If you want to learn more, check out this list of the best books on The Philosophy of Mathematics.
The Daily Idea was created to help make learning about philosophy as easy as possible by collecting the best philosophy articles, videos, podcasts, and book recommendations from across the internet and organizing them into one place. You can find a collection of links to these resources and recommendations here or try taking the 52 Book Philosophy Challenge.