17

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 ( interesting reading ) Much of his work was unpublished until much later (for reasons see the link), thus remaining largely unknown.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 ...


13

The Grothendieck Circle site suggests a more innocent explanation for the loss these letters. Having left Montpellier in 1984.... In May of that year [1985] a secretary informed him that his office on the fourth floor of the institute had been cleared out. Seeing this incident as an egregious example of the general decline of mores, an outraged ...


13

Kolmogorov was not exactly free to express his views considering the situation in the Soviet Union. Philosophical issues, even concerning mathematics, were ideologically sensitive, and everyone had to express allegiance, in one form or another, to the dialectical materialism of Marx and Engels. It went beyond that, as the only grand philosophy available it ...


9

Kolmogovov expressed his views in this paper: MR2278817 Kolmogorov, A. N. Modern debates on the nature of mathematics. (Russian). With a commentary by V. A. Uspenskiĭ. Reprinted from Nauchnoe Slovo 1929, no. 6, 41–54. Problemy Peredachi Informatsii 42 (2006), no. 4, 129–141; translation in Probl. Inf. Transm. 42 (2006), no. 4, 379–389. It is a reprint of ...


8

Sharing with other mathematicians is not how things were done in the 13th century Europe. The only other mathematician of note in Europe whose years of life overlap with Fibonacci's was Nemorarius (1225-1260), and he was not even born when Liber Abaci came out (1202). Nonetheless, Fibonacci was quite active in promoting mathematics both to the folk and to ...


8

Al-Khwarizmi was a ninth-century mathematician who created many of the most basic techniques for how we perform calculations. His greatest contributions were in the realm of developing formal, systematic ways of doing arithmetic and solving equations. His works mark the beginning of what we today understand as Algebra. One of his principal achievements in ...


7

Yes, he did, multiple times. Singular double integrals (1814) In Mémoire sur les intégrales définies (1814) Cauchy studied why switching the order of integration in a double integral can sometimes lead to different results. This led him to introduce the notion of "singular integral". For $K = \frac{z}{x^2 + z^2}$ he showed that $\int_0^1\int_0^1\frac{\...


7

It depends on what counts as working "on it". His prior work under Hilbert was related to this area of geometry. Bolyai (1832) and Gerwein (1833) proved that polygons of equal area are equidecomposable, and Gauss urged a 3D extension in letters to Gerling mentioned by Hilbert. It was in the works in 1890-s. In 1896 Bricard reproved Gerling's 1844 result that ...


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, ...


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.


6

A significant obstacle to doing an online search for Fritz Peter is that both Fritz and Peter are common as German first and last names. The German Wikipedia provides some basic pointers, such as his 1923 dissertation in Göttingen. Arne Schirrmacher, "Establishing Quantum Physics in Göttingen: David Hilbert, Max Born, and Peter Debye in Context, 1900-1926." ...


6

He was concerned with providing an abstract analog to the geometric notion of dimension for algebraic varieties given by polynomial rings. Zero-dimensional ideals are abstract algebraic analogs of discrete collections of points. The idea goes back to Hilbert's conversion of algebraic geometry into the language of rings and ideals, and Dedekind inspired ...


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

As mentioned in the comment by Confiold, it is very hard and subjective to assess a talent for anything. It may be true that Ada Lovelace did some basics mistakes and she had some typos or misuderstanding in her translations, however, this does not mean that she had no talent for mathematics. Very often people with gift for science and technology are poor ...


5

I first ran across this story at an exhibit in Los Angeles' Museum of Science and Industry some time before 1970, maybe as early as 1964. In the version I read there, a magistrate was involved, and the person questioning the baker's methods had some sort of civic power connection. When you suggest that no Frenchman might have taken a loaf of bread home and ...


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.


5

You have misinterpreted the article you refer to; nowhere does it say that "Cantor claimed that there would only be potential infinity, not actual infinity". In fact, it says the opposite: Furthermore, Cantor claimed that we could add and multiply infinity sets. Until that time, humans had followed Aristotle’s ideas about infinity. According to ...


4

Roger Cotes, a contemporary of Newton and best known for the Newton-Cotes quadrature rules in numerical integration, died of a fever aged only 33. Newton supposedly said of his death 'If he had lived we would have known something': this is extremely high praise given that Newton was generally not inclined to praise the work or intellect of others.


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 ...


4

There are several prominent mathematicians of the medieval era, most notably Leonardo of Pisa, or more commonly called "Fibonacci". He developed the Fibonacci sequence and he also introduced the Hindu - Arabic numeral system to Europe in the 13th century. As a result, the Roman numeral system was discarded in favor of the former. Link: https://www....


4

The following is taken from the book Walter K. Buhler, "Gauss: a biographical study." Springer Verlag, 1981. Only a very few characteristic and interesting facts are known from the childhood and youth of Gauss. Basically, we have to satisfy ourselves with the bare data of his biography and that kind of information which can be induced from a ...


4

There is probably nothing "flawless" in this world. But mathematicians and physicists indeed took part in the improvement of musical instruments. See, for example Wikipedia article Well temperament which mentions the invention of the musical scale for modern keyboard instruments. Many people, scientists and musicians participated in this ...


4

Leon Theremin, born in St. Petersburg, Russia in 1896, was a youthful enthusiast of both music and physics. As a young man working at the Physical Technical Institute in Petrograd, he noticed that something odd happened when he hooked up audio circuits to an electrical device called an oscillator in a certain configuration. The oscillator produced an ...


4

Isaac Barrow had given a series of lectures in 1664-65. These lectures dealt with the general concepts of space, time and motion. With Newton assisting in their preparation, these lectures were compiled and published in 1670 as Lectiones Geometricae. It is in the Lecture X, Proposition 11 of Lectiones Geometricae, that a geometrical theorem is mentioned, ...


3

Yes, he was, at least in a particular example. Near the end of his life, in 1808-09, Lagrange studied perturbative dynamics of a planet on an elliptic orbit, and derived what came to be called Hamiltonian equations for it in Second mémoire sur la théorie de la variation des constantes arbitraires dans les problèmes de mécanique, dans lequel on simplifie l'...


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