20

The Göttingen Digitalization Center provides a digital scan of the paper H. Kornblum: "Über die Primfunktionen in einer arithmetischen Progression." Mathematische Zeitschrift 5 (1919), 100–111 online. The first page features a footnote by Landau that provides a few biographical details: Heinrich Kornblum was born in Wohlau on August 23, 1890. He volunteered ...


18

Ramanujan's Lost Notebook is one such collection of mathematical results. It consists of loose and unordered sheets of paper in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George ...


16

Bolzano. Here is a copy of an answer of mine from MathOverflow: Bernhard Bolzano .... ( interesting reading ) Much of his work was unpublished until much later (for reasons see the link), thus remaining largely unknown. For example, a theorem of Weierstrass is now known as the "Bolzano-Weierstrass theorem", acknowledging that Bolzano had proved it ...


12

Date: 1930's. There is the story of the "ergodic theorem". Young mathematician John von Neumann proved the so-called "mean ergodic theorem". He wrote it up and sent it to the Proceedings of the National Academy of Sciences. It was reviewed by one of the editors of the Proceedings, senior mathematician G. D. Birkhoff. In due course, Birkhoff recommended ...


8

Thoralf Skolem could perhaps be counted as a quasi example of that. He did not enroll as a PhD candidate before becoming a docent and a member of the Norwegian Academy of Science and Letters, and it seems that he still needed some convincing from his colleagues in order to actually submit a thesis, several years later. When he finally defended it, his formal ...


8

As I was uncertain about the premise of this question—i.e., it looks as if there are fewer Spanish and Portuguese mathematicians than others—but without the numbers to prove it, I went in for some research on the OP's Cambridge website. In short, while there is some basis for the claims, I don't think the situation is as dire as claimed. Below is a table I ...


8

Unlike North Africa and the Near East, the Iberian Peninsula missed out on the Hellenic influence that dominated classical mathematics; hence the lack of an Iberian Euclid. Compared to the Greeks, the Romans produced very little mathematics. During the medieval period, there were in fact a fair number of internationally significant Iberian mathematicians: ...


8

First, "foundations" are not what they once used to be. The idea of "one true logic" and "one true mathematics" justifiable from self-evident truths does not have much currency these days. So interest in real foundations, and belief in their existence or necessity, has been consistently waning, see Azzouni, Is there still a ...


7

The quote appears to be from: Stuart Dreyfus, (2002) Richard Bellman on the Birth of Dynamic Programming. Operations Research 50(1):48-51. https://doi.org/10.1287/opre.50.1.48.17791. In context, it's clear Bellman is talking about DoD spending on basic math/research specifically, not math in general. As to why the DoD was cutting spending, Eisenhower ...


7

Is the Fast Fourier Transform a mathematical result? The point might be debated but its history has been well researched (e.g. Heideman et al., (1984). Gauss and the history of the fast FFT . IEEE ASSP Magazine). In 1987 One of the modern (re)discoverers also wrote on the topic. The method and the general idea of an FFT was popularized by a publication of ...


7

One of the most famous examples is the Gauss's diary which was discovered in 1897.


7

You can find the quote (or something similar) in multiple places in the Théorie analytique de la chaleur, for example in Chapter I, paragraph (article) 14: "L'examen de cette condition fait connaître que l'on peut développer en séries convergentes, ou exprimer par des intégrales définies, les fonctions qui ne sont point assujéties à une loi constante, ...


6

For Ramanujan's background see How did Ramanujan learn to do mathematics? According to Hardy himself, he did not teach him any topics, only the idea and perhaps some methods of proof, see his lecture Indian Mathematician Ramanujan. Ramanujan did pick up sporadic bits and pieces of modern mathematics from various sources that Hardy is not too sure about, ...


5

Jean-Robert Argand published his geometrical interpretation of the complex numbers as points of the plane in 1806. It become a standard way of dealing with these numbers and now sometimes the complex plane is called the Argand plane. However, the same idea had been published in 1799 by Caspar Wessel, a norwegian surveyor, and it was forgotten. Wessel's paper ...


5

Bayes' Theorem, fundamental in Bayesian statistics, was considered unremarkable by Thomas Bayes and so not published. After Bayes' death, Richard Price edited Bayes' manuscript for reading at the Royal Society for which he was elected a Fellow.


4

simplicio's answer certainly provides the correct historical context. Adding to his answer, the quote is also found in Bellman's autobiography, p.159 - which seems to be the original source. Immediately after the sentences you quoted, Bellman continues: [...] hatred of the word research. I'm not using the term lightly; I'm using it precisely. His face would ...


4

The Greek word "theorem" has a precise meaning "a statement for which a mathematical proof exists". As far as we know these notions were invented only once: in ancient Greece in 6 century BC. More precisely in the Greek city of Miletus on the territory of modern Turkey. This is what the Greek tradition says. From what we know, this ...


4

Leonard James Rogers (1862 - 1933) obtained degrees in Mathematics, Classics and Music from Oxford. During 1888-1919 he was Professor of Mathematics at Yorkshire College, before returning to his Alma mater. In 1894 he published the paper 'On the expansion of some infinite products'. This contains the Rogers-Ramanujan identities, so called because they were ...


3

This incident is recounted in Mac Lane's autobiography, in chapter 6, starting on page 56. It was not Königsberg, but rather Weimar, and he saw Hitler at a performance of a Wagner opera on Wagner's birthday. It's only mentioned in a single paragraph: Once I actually saw Hitler. While in Göttingen it suddenly occurred to me that I had never visited Weimar, ...


3

All these assessments about "cradle of civilization" are based on the archeological records that reached us and on surviving texts. The oldest surviving samples of writing come from Mesopotamia (Sumer) and Egypt. There was a long discussion whether writing was invented in these regions independently or there was some transmission. As I understand, ...


2

Yes, this database is called "Math Genealogy", genealogy.math.ndsu.nodak.edu. Its value and reliability has been much discussed, but on my opinion, it is useful and entertaining. AMS is probably of the same opinion: it includes links to it in MathScinet. Some points of criticism are the following: the notions of PhD degree and PhD adviser is ...


2

A famous case from this time period concerns priority dispute between Hilbert and Einstein over the deriving the field equations of general relativity. Hilbert completed the general theory field equations "at least 5 days before" Einstein submitted his final paper in 1915, Einstein accused Hilbert of "nostrifying" him. The word is interesting, "...


2

I wouldn't trust Hardys assessment; he after all said: he had been carrying an impossible handicap, a poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe... It was impossible to teach him systematically, but he gradually absorbed new points of view. Given that Ramanujan, by his own admission, had learnt mathematics from ...


1

It's because of Diracs use of it in QM. After QM was a revolutionary new theory of physics and so had immense visibility because of this. This is very similar to how Einstein popularised the study of non-Euclidean geometry by his use of such in his revolutionary theory of space and time. After all, non-Euclidean geometry had been known since Gauss's time but ...


1

No. The question is badly conceived and phrased. You cannot 'steal' a result and proving the theft is unconvincing. There is a sensible difference between a priority dispute and crime. It was not the Facebook Age and people were more interested in valid results and not in the person behind them. Objective validity is impersonal and, except for taking out ...


1

I think the conclusion here is that there is no proof that the claimed Fourier quote is an actual Fourier quote (in any language). However, (1) Absence of proof is not proof of absence. (2) Although Fourier may have not communicated the quote in substance, he did arguably communicate the quote in essence. Possibly what happened was that someone wrote a ...


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