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

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-...


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 ...


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

It is hard to prove that answer is negative, but I suspect that that's the case. That sentence looks familiar. In fact, in his book Relativity: The Special & the General Theory, Einstein wrote “Without it the general theory of relativity […] would perhaps have got no farther than its long clothes.” But here Einstein is talking about ...


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

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 ...


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.


4

Yes, orthogonal matrices with complex entries appeared at least as early as 1900, in E. Cartan's classification of simple Lie algebras (and Lie groups). In many ways, the complex numbers could be replaced by any algebraically closed field of characteristic $0$. Thinking of complex orthogonal groups as real Lie groups ("forgetting" the complex structure) ...


4

They did. A natural way to treat such matrices is to introduce an indefinite inner product on $\mathbb{C}^n$, a non-degenerate bilinear form $(z,w):=z_1w_1+z_2w_2+\dots z_nw_n$, instead of the usual sesquilinear one. Then $A^T=A^{-1}$ is equivalent to $(Az,Aw)=(z,w)$, i.e. complex orthogonal matrices are isometries of this space. The "orthogonal"/"unitary" ...


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

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

"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

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

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 ...


2

I think I've found what you are remembering. There's a free epub available at google books, "Memoirs of the Royal Society" . Around page 386, I found: Or possibly this one, also free epub from google books. Perhaps they are multiple descriptions of the same thing -- I'll leave it up to you to research these two publications :-)


2

–– Note: this currently answers the first revision of the question. The current edit invalidates this answer. It seems to be a bit more indirect than how I read your question. But here are the relevant parts from one such reference: Propagandists echoed and magnified the hatred and suspicion sown by Habyarimana and officials around him. Under the cover ...


1

Here is a source from psu.edu in which Marc P quoted Einstein The problems that exist in the world today cannot be solved by the level of thinking that created them. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.4598


1

The 3-volume book by Thomas Muir The Theory of Determinants in the Historical Order of Development covers a narrower subject, but its first sections are very interesting to understand the early history of linear algebra. The notion of determinant predates other notions of linear algebra, and the book gives an exhaustive listing of all its early occurrences ...


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