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However "distinct" may have the weaker meaning of not all coinciding. So, in case I would therefore use pairwise, for clarity (see e.g. here), like in the other situations you listed. The fact is tha …

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 …

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.

An instance of (2): the proof of the individual ergodic theorem by Garcia, using a "maximal ergodic lemma" is considerably shorter and simpler than the original one of Birkhoff.

Trying an educated guess: the practice stopped in connection with Johannes Gutenberg's invention of the printing press. After that, it became harder and harder, and not so worthwhile, keeping one's ow …

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 …

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 …

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 …

One persistent (and quite annoying) myth is the one about the incident between Leonard Euler and Denis Diderot visiting the court of Catherine II at St.Petersburg in 1773. This article documents its o …

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 …

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 …

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 …

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

I think it is also worth looking at the case $p=-1$, in the spirit of your context. It also provides a nice way to introduce the logarithm and the exponential function (quite closely to the historica …

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 …