# Tag Info

45

The short answer is that this is how he referred to himself. He was born Tyge Otteson Brahe but at the age of 15 (1561) changed 'Tyge' to Latinized 'Tycho', see Redd's biography of Tycho and Thoren's book Lord of Uraniborg. Johannes Müller, a well-known German astronomer, wrote under 'Regio Monte', which Melanchton, an educational authority at the Copenhagen ...

17

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 ...

16

The same person who introduced it, Cayley. Sylvester first used the term "matrix" (womb in Latin) for an array of numbers in 1848, but did not do much with it. Cayley started developing matrix algebra in 1855 and summarized his theory in A Memoir on the Theory of Matrices (1858). In the opening paragraphs he writes: "It will be, seen that matrices (...

12

This number has no significance. Its origin is historical. Originally meter was defined as 1/40,000,000 part of the Paris meridian. Based on the measurement of this meridian they made a standard rod in Paris. Since it is inconvenient to base the definition on something which is difficult to measure, meter was soon redefined simply as the length of this rod. ...

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 ...

10

The nickname appears to be a creation of the New Math movement, and spread from the math education literature. The notation itself in its modern form can be traced back to Lefschetz's Algebraic Topology (1942), and variants appear already in Principia (1910) and von Neumann's Zur Einführung der transfiniten Zahlen (1923). See Who first discovered the ...

9

When introducing the older terminology in the previous sentence, Peano describes it thus: ... signifie "il y a des a", "les a existent"... It seems likely this is the source of the inverted "E".

9

Such terms as “given in species” are defined in Euclid’s Data (Greek, English): III. Rectilineal figures are said to be given in species, which have each of their angles given, and the ratios of their sides given. (English version, R. Simpson, 1810, p. 367) [Species is the translation of eidos, shape or form; see LSJ, εἶδος, def. A.2.b.]

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 ...

7

Resolution 12 of the 11th Conférence Générale des Poids et Mesures (CGPM) adopted 12 SI prefixes in 1960, including pico- and nano-. Google Ngrams show steep decline in the use of millimicro- after 1964, and micromicro- after 1966. Some other double prefixes, like kilomega- and hectokilo- were also in use, decimilli- was even standardized in Frace until 1961....

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

One detailed account of the history of equivalence relations and associated terminology is Equivalence: An Attempt at a History of the Idea by Ashgari largely based on Fowler's posts on the Historia Mathematica forum. The terminology was a long time in the making, with "equivalence relation" appearing much earlier than "equivalence class"....

6

Here is a direct link to Nolte's Tangled Tale of Phase Space on Physics Today. Big takeaways: the name did not come from Liouville's oft-cited 1838 paper, and Boltzmann used "phase" without "space" in the right context back in 1872, and he is the one who fully developed the concept, with a big help from Jacobi's 1842-43 work. Nolte also ...

6

The real etymology is lost, I am afraid, but various speculations have been offered since antiquity and continue to this day. In Egypt the tree was known since at least 2600 BC. Egyptians already used the same name ('Bennu') for the bird and the date fruits. Bircher in The Date Palm A boon For Mankind speculates as to the reason: "This bird was found ...

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

It is helpful to separate concepts from words. The sharp separation between mathematical variables and physical quantities they represent is a modern phenomenon. Ancient Greeks had magnitudes, which included numbers and lines, areas, etc., without taking them as something abstract and separated from reality. They had the idea of "independent and ...

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

We often forget that even the minute is not an SI unit, only the second and its decimal multiples and fractions are. It is a leftover of the sexagesimal system (base 60), whose use predates the decimals by many centuries, and goes back to the ancient Babylon. So are the angular degrees. Heinrich Hertz was born in 1857, and the International Electrotechnical ...

5

The earliest reference appears to be: ... it is easy to see how a machine could be programmed so that it appeared to learn... whether it would in principle be possible to construct a generalized learning programme which would enable an operator, if he had sufficient patience, to 'teach' the machine any subject he chose... Can Machines Think?, M. V. ...

5

As @Dave L Renfro noticed, the distinction between series and sequence is not old, and it was possible for the same author to use the two terms with different meanings (also in the same article). Consider e.g. Gauss's Theoria Residuorum Biquadraticorum Commentatio Prima & Commentatio Secunda, we have some examples: article 5 cunctos numeros $1, 2, 3 \... 5 German was the language of chemistry, physics and mathematics until the 1940s. Just today, I had to request two German translated papers in chemistry from the library. Anyone interested in doing a PhD in sciences had to show a reading knowledge of German, French or Russian and this requirement was determined by the field of study in American, British or ... 5 In 1795 lower case abbreviations were proposed for the prefixes myria, kilo, hecto, deca, deci, centi, milli: m, k, h, d, d, c, m. They were rarely used until after 1840, when the temporary mesures usuelles were replaced by the original unit names of the metric system. By then capitals were often, but not always, used for the multiples (myria, kilo, hecto, ... 4 It depends on how the question is interpreted. Common notion 4, "things which coincide with one another equal one another", is not exactly a definition of congruent triangles or even of congruence generally. Likely due to Platonist strictures, Euclid deliberately avoids using congruence in his demonstrations. The idea of moving and superimposing ... 4 They did. A natural way to treat such matrices is to introduce an indefinite inner product on$\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)$, i.e. complex orthogonal matrices are isometries of this space. The "orthogonal"/"unitary" ... 4 The cyrillic letter Ш (sha)is -- for obvious reasons when looking at the graph) also used to denote the "function" (well, it is a distribution if you want to be picky) given by the sum of integral displacements of the Dirac-delta function, see https://en.wikipedia.org/wiki/Dirac_comb 4 With credit to @ConsigliereZARF for helpful comments and references. The earliest definition of group character ("Charakter") for Abelian groups is likely due to Weber (1881-2), and it was generalized to general groups by Frobenius (1896). According to Mackey's survey Harmonic analysis as the exploitation of symmetry: "In 1881 Weber defined a character of ... 4 Complex numbers were used long before Gauss. They appeared for the first time in 16th century when people found a formula for solving cubic equations. One problem with this formula is that even for simplest equations like$x^3-x=0\$ which have 3 real solutions, square roots of negative numbers occur in the formula (they cancel in the end, when you do ...

3

It's no more arbitrary than any other measurement unit, including the second. Nearly all modern values were chosed to try to avoid changing existing units' values while providing a source less subject to variation. The most well-known example is the kilogram. There's a standard cylinder platinum&iridium of which served as the original kilogram for ...

3

As far as I know, the first appearance of the concept of positive/negative definiteness (and of indefiniteness) is in the article 271 of Gauss' Disquisitiones Arithmeticae about ternary forms. Of course the Disquisitiones are written in Latin, but maybe the original context can help in clarify the terminology also in English. Gauss wrote Quaedam formae ...

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