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Let $\theta = \tan^{-1}(t)$. Nowadays it is taught: 1º that $$ \frac{d\theta}{dt} = \frac 1{dt\,/\,d\theta} = \frac 1{1+t^2}, \tag1 $$ 2º that, via the fundamental theorem of calculus, this is equival …

Gödel had a cosmological model. Hamel, primarily a mechanician, gave any vector space a basis. Plücker, best known for line geometry, spent years on magnetism. What other mathematicians had so distant …

Today homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen? “Homomorphic” (and “homomorphism” as “property of being …

The Fourier transform of the volume form of the (n-1)-sphere in $\mathbf R^n$ is given by the well-known formula $$ \int_{S^{n-1}}e^{i\langle\mathbf a,\mathbf u\rangle}d\sigma(\mathbf u) = (2\pi)^{\nu …

Do we know what mathematician first considered, and perhaps named, what we call the group $\mathrm O(n)$, or $\mathrm{SO}(n)$, for some $n>3$? I mean it specifically as group (not Lie algebra) acting …

Today the word form can refer to (at least) three different kinds of mathematical object: A homogeneous polynomial. This was apparently started by Gauss (1801), renaming what others had called formu …

I am looking for the source and context of this quote, found e.g. at St Andrews: Only with the greatest difficulty is one able to follow the writings of any author preceding Euler, because it was …

Today this is common, but how exactly did it start? I am looking for examples in various languages, and suggest: Exclude Latin (as more “ancient” or “international” than “foreign”) Exclude French af …

The “Earliest Uses” site suggests that the expression “uniform distribution” first appeared in Uspensky (1937), and “uniformly distributed” in Sakamoto (1943). Is that true?