# Tag Info

48

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 ...

34

Taking a look at her 1933 paper in Mathematische Annalen one sees: Similarly for a 1923 paper: From a glance at a few other papers, she (or all the journals) used "Noether" for her last name. Further, since the titles clearly indicate that the journals are quite happy with umlauts it is not by accident.

26

Jabir ibn Hayyan was the first to describe processes such as liquefaction, crystallisation, distillation, purification, oxidisation, evaporation and filtration. He also did an early classification of chemical elements around their properties which seems pertinent, and noted that "a certain quantity of acid is necessary in order to neutralize a given amount ...

22

I just want to comment that the agreement on letters, by which we write $\frac d{dt}\mathbf L=\mathbf M$ for the law of angular momentum, must have come very late -- after 1964. As evidence, note that it is still written $\frac d{dt}\mathfrak N=\mathfrak M$ by Sommerfeld in Mechanik (1943, p.63); $\frac d{dt}\mathbf M=\mathbf L$ by Sommerfeld in Mechanics (...

22

Lemaitre, who proposed the first version of "Big Bang" in 1927, called it Primeval Atom hypothesis since late 1930s, notably in the 1950 book of this name. However, it was rather different from the subsequently adopted version, and singularity cosmologies did not gain much traction until 1950s to get a common label. By then, when they came to be ...

21

This number has no significance. Its origin is historical. Originally the 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, the meter was soon redefined simply as the length of ...

20

There is a historical reason. But it was not a fluke of history, the underlying reason is that energy comes up in non-mechanical (thermal, electric) contexts whereas momentum does not. Derived alternative, newton-meter in SI, did not arise naturally in such contexts, and alternative units, like calories, were used prior to the discovery of the general energy ...

19

History of the metric system - Wikipedia says: In 1861, Charles Bright and Latimer Clark proposed the names of ohm, volt, and farad in honour of Georg Ohm, Alessandro Volta and Michael Faraday respectively for the practical units based on the centimetre-gramme-second absolute system. This was supported by Thomson (Lord Kelvin). These names were later scaled ...

18

There could not have been a $\pi$ day in 1592 regardless of calendar conventions for the simple reason that there was no such thing as $\pi$ back then. The symbol was introduced by William Jones in 1706 and did not come into common usage until after 1737, when Euler popularized it in his texts. This was similar to zero, which got a placeholder symbol long ...

18

From Milne's site: There are two different words in French, "étaler", which means spread out or displayed and is used in "éspace étalé", and "étale", which is rare except in poetry. According to Illusie, it is the second that Grothendieck chose for étale morphism. The Petit Larousse defines "mer étale" as "mer ...

17

Very few (if any) mathematicians before Cantor thought of the SET of integers. Certainly for Euclid it was completely evident that the sequence of integers extends without limit. (He actually has a famous theorem that the sequence of PRIMES extends without limit). Who discovered this we will never know because very few mathematical sources before Euclid ...

17

There was a related question on Math.SE, which Mauro Allegranza answered with reference to Cajori's classic History of Mathematical Notations (v.II, p.205). It is a great source and is freely available online. Surprisingly, it was not Leibniz, the notational lion of calculus, who introduced it. "A provisional, temporary notation $\Delta$ for differential ...

17

Victor Katz is not a linguist and a lot of what he says in the quoted extract is wrong: for example that “Arabic is written without vowels” and that the word in question is spelt “jb”. In fact it is written jyb جيب (as mobileink has pointed out). But the decisive error from the viewpoint of the history of science is his failure to remark that Sanskrit jyā ...

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

No, it is not widely accepted. The language of "crises" is rather obsolete and mostly reflects the attitudes of the early 20th century projected backwards. At that time, the contemporaries did indeed characterize the situation in mathematics (and physics) as a crisis. For example, Weyl's 1920 address was titled “The new foundational crisis in mathematics”, ...

15

For sinus, see : Victor Katz, A History of Mathematics (3rd edition, 2008), apge 253 : The English word “sine” comes from a series of mistranslations of the Sanskrit jya-ardha (chord-half). Aryabhata frequently abbreviated this term to jya or its synonym jiva. When some of the Hindu works were later translated into Arabic, the word was simply transcribed ...

15

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 (...

14

Actually when we say Integer today, we mean set of all positive whole numbers, negative whole numbers and zero. But this complete set was not discovered/invented in a day. People were working with integers from the very beginning. They might be using different names though(like Whole numbers, Natural numbers, ...). According to Wikipedia Negative ...

14

I'm going to try to answer the question you end with, "Why has atomic bomb instead of another better term become the predominant term?", rather than the question in your title, because that's the historical question. (The other might be interesting to debate, but unlikely to produce a satisfying final answer.) Let's start with the Google ngram, showing the ...

14

According to Carl B. Boyer, "The history of the calculus and its conceptual development", Dover Publications 1959, page 98, The improved notation led also to methods which were so much more facile in application than the cumbrous geometrical procedures of Archimedes, of which they were modifications, that these methods were eventually recognized as ...

13

This question is based on a misunderstanding. The statement that $\pi$ is constant has precise meaning: $\pi$ is a ratio of the length of circumference to the length of diameter. The statement that it is constant means that it is the same for all circles. (This statement is independent of the representation of this ratio with digits). Contrary to what many ...

13

Actually, it happened in the reverse order, algebras came first, and vector spaces only later. For the vector space story see When did people start viewing a matrix as a linear transformation between two vector spaces? Peano gave the modern axiomatization of them only in 1888, and he called them linear systems. But the use of "an algebra" in essentially ...

13

Such coordinates were called canonical because they are those in which equations of motion (or, of the hamiltonian flow of a function $H$) take the “canonical form” $$\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}, \qquad \frac{dp_i}{dt}=-\frac{\partial H}{\partial q_i}$$ first written by Poisson (1809, pp. 272, 313), Lagrange (1810, p. 350), and Hamilton ...

12

The theory of Linear Algebra, along with the associated concept of linear mapping, was named as "linear" by its creator, Hermann Graßmann, which he developed in his 1844 linear algebra manifesto, Die Lineale Ausdehnungslehre, ein neuer Zweig der Mathematik [The Theory of Linear Extension, a New Branch of Mathematics], and also later in Die Ausdehnungslehre: ...

12

Because unlike vertex, matrix or simplex, that came directly from Latin and have primarily mathematical uses, complex was borrowed through French around 1650s, with the meaning "a whole comprised of parts". By the time of entering mathematics as a noun it already had colloquially established plural in English, complexes. It is similar with apexes, annexes, ...

12

The $r$ is for "radius", and in particular, describes the radial vector from the origin to the location described by the vector. This is sensible because some sort of polar or spherical coordinates are the most common for many physical applications, where the forces described have some sort of spherical symmetry, and point radially outward.

11

"Corollary" is similar to the word "bonus": a little extra (i.e. an extra proposition coming from a demonstration). The term Euclid uses is πόρισμα "porism," which Liddell-Scott-Jones cite as akin to πορίζω in the sense of "to find (money)." For instance, after I.15: Πόρισμα ἐκ δὴ τούτου φανερὸν ὅτι, ἐὰν δύο εὐθεῖαι ...

11

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 ...

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 ...

11

“Goethe” is not an “anglicization” of “Göthe” or indeed of “Göte”; it is the way the poet spelt his own name. The overriding principle is that everyone is entitled to spell his or her name as he or she likes.

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