12

Poincare refers to the Lie's solution of the so-called problem of space, a.k.a. the Helmholtz , or Riemann-Helmholtz, or Helmholtz-Lie problem of space, which amounts to characterizing all manifolds (originally, only 3-dimensional) with free mobility of figures (roughly, homogeneity and isotropy). In modern terms, free mobility amounts to constant Riemannian ...


7

Going by Wikipedia's definition, a physical constant is a number "generally believed to be both universal in nature and have constant value in time". The significance of these constants began to be recognized in the late 19th century, partly as a result of the standardization of the measurement system. But their modern prominence is due to Eddington's semi-...


7

What motivated Euler was not any problem in particular, but rather the general need to solve differential equations approximately when an analytic solution could not be found. He explains the method in a general form in Section 2, chapter VII of volume I of Institutionum Calculi Integralis (Foundations of Integral Calculus, 1768), his textbook on integral ...


7

Elementarmathematik vom höheren Standpunkte aus, Bd.2 Was eine Kurve ist, glaubt jeder Mensch zu wissen, bis er so viel Mathematik gelernt hat, daß ihn die unzähligen möglichen Abnormitäten verwirrt gemacht haben. see also Quotations by Felix Klein for the English version.


7

The reference is probably to a treatise sent to Huygens on 5 October 1691, where Leibniz says (and illustrates with several examples) that "Whenever the subtangent [$=y/y'$, but it would also work for just the tangent $y'$] is a product of two quantities or formulas, of which one is given purely in terms of the abscissa $x$, and the other in terms of the ...


7

L. Aubry was a French mathematician (most likely a high school teacher) who published 56 papers in mathematical journals and 4 books in the period 1894-1933, (according to Zentralblatt database). The paper you mention is not in this database. Most of his papers are in elementary mathematics journals for school children and amateurs. Such journals are rarely ...


7

I am Camille Aubry, granddaughter of Léon Aubry (1882-1947), and I thank you for your interest in my great-grandfather. He was a wine grower, farmer, beekeeper, in Jouy-lès-Reims (51). He was also a self-taught mathematician and he was published in the journal Sphinx-Oedipe, in l’Intermédiaire des mathématiciens, l’Enseignement mathématique, by Gauthier-...


6

Contrary to what the name suggests, Fourier series were not invented/discovered by Fourier. They were considered by Euler and Bernoullis, in relation to the one dimensional wave equation, not the heat equation. This early story is described for example in the papers by Luzin in Amer. Math. Monthly: Luzin, N. Function. I. Amer. Math. Monthly 105 (1998), no. ...


6

§1.1 (+ supplement) of Bressoud’s A radical approach to real analysis, recommended here just recently, does pretty much exactly what you want.


6

This answers (with some explanation and references) the two questions, (a) Were any concrete corrections proposed (in the 1740s, to the law of gravitation)? and (b) Where can one read about it? (a) Clairaut (but not Euler or d'Alembert) proposed in 1747 a correction to the inverse-square law, that is, an additive term depending on a higher power of the ...


6

In: D.V. Anosov, M.I. Monastyrskii, M.A. Soloviev, Nas ostalos' tak malo... (So few of us remained...), Istoriko-Matematicheskie Issledovaniya 7 (2002), 166-189 (in Russian) (the periodical is available in many places, for example here), Ado is mentioned in passing. It is claimed that Chebotarev failed to create an algebraic school in Kazan' due to ...


6

It does not appear that Cambridge changed the policy for Ramanujan, although they did use a rather atypical degree they had for him (Bachelor of Arts by Research, not Bachelor of Science by Research). PhD in Mathematics was not traditional in Britain, and was only created after the First World War. Ramanujan was a beneficiary of the general conversion in ...


6

It is in the third book of La Géometrie: I could also add rules for equations of the fifth, sixth, and higher degrees, but I prefer to consider them all together and to state the following general rule : ...and, consequently, if it is of the third or fourth degree, the problem depending upon it is solid; if of the fifth or sixth, the ...


5

It is only a recent mistake. See : Anthony Lo Bello, Origins of mathematical words (John Hopkins UP, 2013), Septagon This vox nullius is a learned mistake for heptagon. People of some education make a certain type of error not committed by the multitude, and this word is an example of one such mistake, viz., the confusion of languages. Knowing that they ...


5

There is the one-page obituary mentioned by Keith Conrad. V. Gubarev and me have uploaded an English translation to the arXiv, see here. Furthermore I have tried to provide a more detailed English wikipedia page for Igor Dmitrievich Ado, see here. I am grateful to Yurii Neretin for providing me with information.


5

Not sure who Machamer and Silberstein had in mind specifically, but, in any case, they are mistaken. Simon published The axioms of Newtonian mechanics in 1947, Hermes Eine Axiomatisierung der allgemeine Mechanik in 1938, and Hamel Die Axiome der Mechanik in 1927. Von Neumann even axiomatized quantum mechanics back in 1932. In a follow-up note (1954) Simon ...


4

For the down to Earth geometry see Surveying Instruments of Greece and Rome by Lewis. For the astronomical measurements, which aside from the names mentioned would include Aristarchus, Ptolemy, see Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley by van Helden. The Mathematics of the Heavens and the Earth by van Brummelen focuses ...


4

The book Introduction to the Theory of Fourier's Series and Integrals by H. S. Carslaw answers your questions in the first chapter on the History of this subject. Many commonly held false beliefs are debunked in his first chapter, including the idea that Fourier failed to give a rigorous proof of convergence. Another common false belief is that Fourier ...


4

This is a supplement to the previous answer to the question, confirming what has been written above. Illustreret Nyhedsblad, where prof. Chr. Hansteen in 1862 first published some letters from Abel, is available online from the National Library of Norway. The relevant letter is the one Abel wrote on December 5th, 1825, which is quoted above, and which can ...


4

Sphinx-Œdipe was a publication edited by the French mathematician André Gérardin, as noted in this recent report: Maarten Bullynck, "From exploration to theory-driven tables (and back again). A History of Tables in Number Theory.": Between 1906 and 1928 Gérardin published a special journal, Sphinx-Oedipe, journal mensuel de la curiosité et de concours In ...


4

Johann Bernoulli explains the idea of a direction field quite explicitly (Modus generalis construendi omnes aequationes differentiales primi gradus, Acta Eruditorum, November 1694). He focusses on drawing isoclines rather than slope segments. There is no figure in that work but Bernoulli drew an example in his correspondence: Corresponding to: Dominique ...


4

Dominguez in History of the Convolution Operation poured through the original sources, and found many of Miller's and Gardner-Barnes's claims and citations to be inaccurate or erroneous. He devotes a separate section to main theorems associated with the convolution, where we read: "On the other hand, another important theorem related to the CCO is the so-...


4

"Qubits" were only named by Schumacher in 1995, and even early ideas about "quantum computing" do not appear until 1960-s. "Bloch sphere" refers to representing the pure states of a 2D quantum system (2 refers to complex dimension). What comes to be called "the Bloch sphere" is spelled out by Feynman, Vernon and Hellwarth in Geometrical Representation of the ...


4

It is easy to find fault with Descartes and Leibniz spent his life doing it (see Belaval Y., Lz critique de Desc., P.1960). Descartes knew that some problems of higher degrees are reductible and erroneously believed that it is the general case. The question here however concerns a paraphrase without reference and asks for a good match. such as e.g. La ...


3

Fortunately (and surprisingly) i found the answer very quickly - at the website of Springer they allow the readers to see the first 2 pages of each chapter, and to see the complete list of references for this book. Since the desired reference is reference 279, the relevant pages of Gauss's Nachlass are p.56-57 of volume X,1, which are entitled "Hauptmomente ...


3

This is a partial answer, offering references relevant to ancient observation methods for equinoxes and solstices. References below cover only the near and middle East (recognizing that the question would also cover early knowledge from any period or civilization). 'Preserved [ancient] texts' with descriptions of how to detect and measure the times of ...


3

Atomic weights, like much else in chemical science, were the result of a long sequence of developments and discoveries; but a convenient starting-point for the discussion is "A new system of chemical philosophy" (1808, 1810) by John Dalton (1766-1844)). In brief summary of the detail offered below, the H = 1 scale was originally an arbitrary (and rather ...


3

All of the self-help books out there belong into the dubious category. Whether it is about psychology, interpersonal skills, psychology, medicine or especially nutrition; and the biggest loser has to be economics. Many psychology research findings are in a replication crisis, not the least because they are based on findings in weird people. Yet, the '...


2

The prime example is psychoanalysis. Thousands of books were written, popular and not. But the general consensus today if that this is a very weak science. Other examples are homeopathy, astrology, and UFOlogy. Unlike psychoanalysis (which is a weak science) these are not sciences at all. Nevertheless an enormous amount of literature was written on each of ...


2

There were a number of pop-sci books written by non-mathematicians (physiciscs, chemists, etc.) where the notion was spread that $\aleph_1$ denotes the cardinal of the continuum. For example, George Gamow, One, Two, Three... Infinity


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