An antifoundationalist is a person who rejects foundationalism.

Strong foundationalism is a philosophy that holds that all beliefs and knowledge must be justified by a set of indubitable foundational beliefs or principles. These foundational beliefs serve as the basis for all other beliefs and can provide certainty and justification for our knowledge. Critics argue that finding such indisputable foundations is difficult, if not impossible.

Descartes was most concerned with the problem of skepticism and uncertainty in knowledge. He aimed to establish a foundation of certain knowledge that could not be doubted, leading to his famous statement "Cogito, ergo sum" (I think, therefore I am). This led him to develop the philosophy of foundationalism, which seeks to build knowledge from clear and distinct ideas.

Descartes' doubt is often associated with his method of radical skepticism, which posits that doubt should be applied to all beliefs that can be doubted in order to reach certain knowledge. This led to the development of the famous phrase "Cogito, ergo sum" (I think, therefore I am) as a foundational certainty. Descartes' doubt also influenced the development of epistemological theories, such as foundationalism and coherentism, which seek to address the issue of how certain knowledge can be attained in the face of doubt.

The easy answer is: yes. Lots of famous philosophers (for example, Spinoza, Kant, Aquinas, Descartes) have written "proofs". The question of whether it's possible to "prove" anything philosophically is obviously open and obviously depends on how rigorous a "proof" you want. The term "proof", broadly understood, is usually replaced with "argument" in philosophy. An argument is an attempt to show how a certain conclusion follows from a set of premises. etc. Specifically relevant to this issue are: http://en.wikipedia.org/wiki/Argument http://en.wikipedia.org/wiki/Formal_proof http://en.wikipedia.org/wiki/Foundationalism