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Cormack and Hounsfield received the 1979 Nobel prize in medicine for their work on CT scans. Cormack, a physicist, published his mathematical work on this in 1963, to essentially no response. Hounsfie …

I think the Busemann-Petty problem is an example like what you're asking, although changes in opinion would be due to progress (positive and negative) rather than any heuristic analysis. A great de …

In the early 1900s, Dickson introduced what he called generalized quaternion algebras over any field $K$ of characteristic not 2. These are exactly what we'd call quaternion algebras over $K$. His def …

Do you insist that the formula be interpreted as the value of a residue, hence requiring that it be known that the zeta-function of every number field is meromorphic around $s = 1$? It goes back to De …

Euler found values of the Riemann zeta-function by artful manipulations of divergent series, e.g., interpreting a function that's $(-1)^{n/2}$ at even $n > 0$ and $0$ at odd $n > 0$ as $\cos(\pi n/2)$ …

Since you reach back to Euler, who proved Fermat's little theorem in the form $a^p \equiv a \bmod p$ by using induction on $a$ and the binomial theorem, I think your "Frobenius endomorphism" is the $p …

here are some references: "Plane Algebraic Curves" by Brieskorn and Knorrer, around page 370. "Plane Algebraic Curves" by Fischer, Appendix 4. The link https://www.maa.org/sites/default/files/pd …

The cached page http://webcache.googleusercontent.com/search?q=cache:q5q43iNq1SQJ:siba2.unile.it/ese/issues/1/690/Notematv27n1p5.ps+normal+basis+theorem&cd=3&hl=en&ct=clnk&gl=us&client=safari gives …

Eilenberg and Mac Lane's papers on category theory started appearing: "Natural Isomorphisms in Group Theory" in the Proc. National Acad. Sci. USA in 1942 and "General Theory of Natural Equivalences" i …

Modular forms were actively studied by number theorists Hecke and Siegel in the 1930s, but it was not widely appreciated. Around the same time Hardy, in a series of lectures on Ramanujan's work deliv …

Ring came from Zahlring, which was Hilbert's term for what we would essentially call a ring of algebraic integers. Dedekind earlier used the term ordnung (= order, taken from the Linnean classificati …

See Whitney's paper from 1935 where he defined tensor products of abelian groups. There you will find the terms natural homomorphism and (especially) natural isomorphism. Whitney makes no attempt to g …

This result of Euler is the last theorem in http://eulerarchive.maa.org/docs/originals/E072.pdf, and if you prefer English to Latin look at the last theorem in http://eulerarchive.maa.org/docs/transla …

Maybe there are some perceptions of the analogy in the work of Gauss, but for certain the close relation between Z and F[x] where F is a finite field was established in 1857 in a paper of Dedekind, wh …

There are many interesting films at the site http://www.etudes.ru/ (not in English): curves of constant width, Pick's theorem, geometry of polyhedra, an infinite staircase with the harmonic series, me …