# Tag Info

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The letter Ш (sha) of the Cyrillic alphabet is widely accepted in theoretical computer science as the symbol for the shuffle product, which gives the shuffle algebra. The same letter is also used to denote the Tate-Shafarevich group, but I'm not sure if it's really a standard (the letter was introduced by Cassels only in 1990 in 1962 instead of TS, see below ...

11

It is sometimes asserted that $\varnothing$ for the empty set was introduced by Bourbaki using a Danish and Norwegian letter. EDIT: The source is the Weil autobiography, cited in Jeff Miller's collection of the origins of mathematical expressions: André Weil (1906-1998) says in his autobiography that he was responsible for the symbol: Wisely, we had ...

10

There are several non-alphabetic symbols, the best known is the integral sign $\int$ and the Weierstrass $P$-function $\wp$. To be sure their origins are letters of Latin alphabet, but they are special stylized symbols, and as far as I know there is no computer code for them in the standard sets of computer characters. Strictly speaking they do not belong to ...

8

As best as I can tell, the term Potenzbegriff (powerclass, later variation Potenzmenge, powerset) was introduced by Bernstein in the late 1890s (Cantor did not use it in his papers). In his Habilitation dissertation Untersuchungen aus der Mengenlehre (1901, published 1905) he states in the introduction (my translation): "The introduction of the concept of ...

8

There were several layers of craft technology now partly superseded by pdflatex and friends. There were author's instructions for marking up manuscripts with type font indications, there were technical typists adept at using special math symbol shapes with their modified typewriters, there were Monotype operators who ran typesetting machines from the marked ...

8

Gauss also came up with the more discrete $n/\ln (n)$- in volume 10 of his collected works appears a short (5-6 pages) fragment entitled "asymptotic laws of arithmetics", which is dated to the year 1791. In [1] of this fragment Gauss states this approximation of the primes counting function, as well as additional conjecture on the asymptotics of k-prime ...

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

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 ...

7

If Euler introduced the term and did not explain his reasoning we can only speculate as to what he had in mind. Euler himself was followed on many notational and terminological choices simply because he put them together in well structured and comprehensive books. But Euler likely followed the precedent with the "moment of force". According to Worthington'...

7

The modern concept of magnetic monopole (as a real isolated charge) is due to Dirac in 1931, although Curie speculated about the possibility earlier. Even electric charges, as in particles, only appeared in 19th century, see Wikipedia's Discovery of two kinds of charges. Before that electricity and magnetism were mostly viewed as produced by fluids, one or ...

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

Here is a list of "Mathematicians who were awarded Nobel prize" taken from this paper 1902 Lorentz (Physics) 1904 Rayleigh (Physics) 1911 Wien (Physics) 1918 Planck (Physics) 1921 Einstein (Physics) 1922 Bohr (Physics) 1929 de Broglie (Physics) 1932 Heisenberg (Physics) 1933 Schroedinger (Physics) 1933 Dirac (Physics) 1945 Pauli (Physics) 1950 ...

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 ...

6

Yes, it seems that there are linguistic reasons1 why positive definite works better than positively definite. 1BTW, for that reason, I think that it was a mistake to migrate this question from the English Language and Usage (EL&U) StackExchange to the History of Science and Mathematics (HSM) StackExchange. It seems that when we are picking adjectives ...

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

The germ theory dates to late middle ages, and was favored by Avicenna among others, although it did not gain much currency in Europe until the mid 19th century. But it was not needed to discover the success of inoculations, which long predate Jenner, and which were later developed into more elaborate vaccinations. That much was established empirically, see ...

5

No, they did not. Several methods were proposed but they do not give "correct" distances. Of course, all depends on the exact meaning of the word "measure" and "correct". But their estimates were orders of magnitude away from the true numbers. Some details are given here: Historical knowledge of Distance of Earth from Sun and also here the related ...

5

There is a heap of answers to this question, and they cover a wide range of aspects of the early computer industry. As has been pointed out, the very first machines were hand built lab experiments. It was not at all obvious how to build a digital computer that would work. Remember Babbage's Analytical Engine had foundered on the challenge of actually ...

5

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) ...

5

With all due credit to Gauß, see the other answer, it seems to have been Adrien-Marie Legendre who first published this conjecturally. More precisely, on the last page of the introduction (p. 19) of the first edition of his Essai sur la théorie des nombres (1798), he says in a footnote: Au reste, il est vraisemblable que la formule rigoureouse qui donne ...

5

The book came out in 1977, not 1995; look at the year at the end of the Foreword that Marcus wrote. My copy has a copyright from 1977 too. LaTex or even TeX was not an option in 1977 since that was the year before the original version of TeX was released. The typesetting in the original version of Marcus was clearly done on a typewriter. I agree it is ...

5

The main calculation in practical astronomy is solving a spherical triangle, from three elements one wants to find the rest, using formulas of spherical trigonometry. This calculation is always performed when for example one transfers between the coordinate systems. Positions of celestial bodies are usually described in ecliptic coordinates, while ...

5

In 1795 lower case abbreviations were proposed for the prefixes myria, kilo, hecto, deca, deci, centi, milli: m, k, h, d, d, c, m. They were rarely used until after 1840, when the temporary mesures usuelles were replaced by the original unit names of the metric system. By then capitals were often, but not always, used for the multiples (myria, kilo, hecto, ...

4

My theoretical physics papers and thesis were written by hand, then typed on an IBM "golf ball" typewriter. The golf ball was so called because the type head was about the same size as a golf ball. The type heads were interchangeable with different fonts and symbols. Corrections were made using tippex. 40 years later, I'm still amazed at the skill of the ...

4

The cyrillic letter Ш (sha)is -- for obvious reasons when looking at the graph) also used to denote the "function" (well, it is a distribution if you want to be picky) given by the sum of integral displacements of the Dirac-delta function, see https://en.wikipedia.org/wiki/Dirac_comb

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

First machines were one-off affairs, custom built (often for a very narrow purpose). There just weren't enough of those around to make standarization of anything surrounding them worthwhile. Thomas Watson (IBM president at the time) accurately estimated a demand of half a dozen computers worldwide in that timeframe. Remember the idea behind the Multics ...

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