"No". That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. Yet, I am a mathematics educator who was o …

A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionis …

One user on MSE made an interesting question, which was unanswered so I suggested him to post it here but he refused for personal reasons and said I could ask it here. The questio …

Is there any field of mathematics that deals with the role of the observer? E.g., some formulation in which a set is changed, in some unspecified way, when it is observed? Or maybe …

My question concerns what is meant by "nonconstructive", and whether it has ever been defined in terms of computational complexity. The wikipedia article on constructive proof beg …

It sometimes happens that 1D problems are easier to solve by somehow adding a dimension. For example, we convert linear differential equations for a real unknown to a complex unkn …

In the Stanford Encyclopedia of Philosophy there is an entry on mathematical explanation. The basic philosophical question is: What makes a proof explanatory? Two main "models" o …

In Believing the axioms (I and II), Penelope Maddy proposes five "rules of thumb" that she then uses to justify large cardinal axioms in set theory. These extrinsic rules are model …

The history of mathematics over the last 200 years has many occasions when the fundamental assumptions of an area have been shown to be flawed, or even wrong. Yet I cannot think of …

I am graduate student and have a decent understanding of logic and set theory. Recently I have got interested in the philosophy of mathematics and set theory. I have read a numbe …

I know that early axiomatizations of real arithmetic (in the first half of the nineteenth century) were often inadequate. For example, the earliest axiomatizations did not include …

The title of the question is also the title of a talk by Vladimir Voevodsky, available here. Had this kind of opinion been expressed before? EDIT. Thanks to all answerers, comm …

Consider the following theorem of Koepke-Koerwien-Siders: "A set x of ordinals is ordinal computable [either by ordinal Turing machines or ordinal register machines--my comment] i …

Does there exist a set theory T-which has not yet been proved to be inconsistent-and in which one can prove the existence of (1) the empty set (2) sets that are singletons and (3) …

What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. …