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It seems to me you are referring to Egbert Rudolf van Kampen (but the problem at the immigration office was quickly solved by a phone call to the university, the Johns Hopkins I believe). The story is …

While I think that ideally, even in a freshman course of calculus, students should receive some historical notions about the development of the ideas of infinitesimal calculus, I think that, even in a …

Today almost nobody shares anymore old Leibnitz' optimistic idea There is no ignorabimus in mathematics (in Hilbert's words). We know that there are true facts in mathematics that will never be prove …

There is a small ambiguity in the expression motivate a result. You seem to use it for (A): "explain why the authors came out with certain arguments, definitions, methods etc, in order to prove the re …

Suppose today's news is actually, that in some form "current foundations of mathematics are inconsistent". Would any mathematician stop his-her research work for this? I don't think so. Even an antino …

The solution of Hilbert's nineteenth problem, in 1957, by Ennio De Giorgi and John Nash, few months later.

According to Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, the first known occurrence is in Schoute’s Mehrdimensionale Geometrie of 1902.

A beautiful classical example from Functional Analysis is the Hausdorff moment problem: characterize the sequences $m:=(m_0,m_1,\dots)$ of real numbers that are moments of some positive, finite Borel …

Another elementary proof, based on the order structure of symmetric matrices. Let me first recall the basic definitions and facts to avoid misunderstandings: we define $A\ge B$ iff $(A-B)x\cdot x\ge0$ …

Paolo Ruffini's work on the impossibility of solving the quintic by radicals did meet a strong passive resistance. Around 1800 he proved the theorem up to a minor gap, that himself or somebody else co …

I think it's mainly a problem of most Olympiad-style problems, rather than of functional equations -you may write down bizarre and unreal equations of any type, algebraic, ODE, PDE, integral, etc. Pos …

In classic Greek, μάθημα is a neuter noun, formed by a standard procedure from the root of the verb μανθάνω, to learn, and denotes in general the object of learning. Also standard is the derivation of …

Here you can hear the pronounce by a Russian speaking person. As to the romanization, which usually does have a standard form in any language, I'd use the one of the language you are writing in your …

It has to be said that in the history of mathematics sometimes quite new profound ideas suddenly arise, so that tools, methods, and foundations are still lacking in a first phase of the new theory. T …

It seems to me that this topic is a main feature of modern mathematics, if not its characteristic feature, compared with classic mathematics: moving the complexity from individuals to the species. A c …