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25

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 ...


20

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 (...


19

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 ...


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 ...


16

This Wikipedia page, 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 for use in the ...


15

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”, ...


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

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 ...


13

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 ...


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 ...


12

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 ...


12

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 ...


12

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 ...


12

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

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

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 qui ne monte ni ...


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

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 ...


11

Some reflections of J. Michael Steele (cf. The Cauchy-Schwarz Master Class. Cambridge University Press, 2004, pp. 10-12) on this matter: THE PACE OF SCIENCE -- THE DEVELOPMENT OF EXTENSIONS Augustin-Louis Cauchy (1789-1857) published his famous inequality in 1821 in the second of two notes on the theory of inequalities that formed the final part of ...


11

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 ...


10

From the article "Astrology", by Sheila J. Rabin, in Encyclopedia of the Scientific Revolution from Copernicus to Newton, p.77: In fact, astrology was part of the mathematics curriculum of every Western university from their founding in the twelfth century to the seventeenth century, and mathematicus was a synonym for astrologer Lynn Thorndike's ...


10

See Earliest Known Uses of Some of the Words of Mathematics, sub voce : Field : The term Zahlenkörper (body of numbers) is due to Richard Dedekind (1831-1916) (Kline, page 1146). Dedekind used the term in his lectures of 1858 but the term did not come into general use until the early 1890s. Eliakim Hastings Moore (1862-1932) was apparently the first ...


10

Maybe it is interesting to note that the term "l’inégalité de Schwarz" was coined by Poincaré in an 1896 paper in Acta Mathematica 20, p. 73, and was used in the French and German literature for the integral inequality until well into the 20th century. https://archive.org/stream/actamathematica20upps#page/73/mode/1up The term "Cauchy-Schwarz inequality" was ...


10

I wonder why the insistence on the (English) word rule, especially as German wikipedia translates / redirects it to interpretation. Isn’t it enough for your purposes to see it stated, named and credited as Born’s Deutung (Jordan 1927, p. 811), assumption (Dirac 1927, p. 257), Interpretation (Hilbert et al. 1928, p. 29), or Auffassung (Schrödinger 1927, p. ...


9

August Horstmann first introduced the concept of gram-molecular weight in the sense of today’s mole concept in 1881. In 1865 Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83 × 10$^{18}$, and in 1889 Than first determined the gram-molecular volume of gases under normal conditions as 22,330 cm$^3$....


9

Cantor 1895 is predated at least by Dedekind in §2 of Was sind und was sollen die Zahlen? (1888) (translation): 21. Erklärung *). Unter einer Abbildung $\varphi$ eines Systems $S$ wird ein Gesetz verstanden, nach welchem zu jedem bestimmten Element $s$ von $S$ ein bestimmtes Ding gehört, welches das Bild von $s$ heißt und mit $\varphi(s)$ bezeichnet wird; ...


9

As Francois Ziegler notes, Kelley attributes it to Halmos. In the past (before Halmos), definitions might be given in the form A group is called abelian if $xy=yx$ for all $x,y$. ...and every mathematics student would need to be told "since this is a definition, if means if and only if." I was one of the students told this: in the 1960s many ...


9

"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 τέμνωσιν ἀλλήλας, τὰς πρὸς τῇ ...


8

The connection between (2) and (3) is one of the surprising curiosities in the history of mathematics and physics. Hilbert worked on integral equations mostly from 1903 to 1910. Here's what Constance Reid has to say about this in her biography: The Courant-Hilbert book on mathematical methods of physics, which had appeared at the end of 1924, before both ...


8

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: ...


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