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For questions about terms, definitions and related concepts used in science and mathematics.

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187 views

Why statistical moments are called moments?

According to the Jeff Miller's Earliest Known Uses of the Words of Mathematics "Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
2
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1answer
95 views

History of group theory character tables (as used in physics and chemistry)

Does anyone know who started using the symbols A, B, E, T (First column, left) for showing irreducible representations of symmetry groups? In older maths books I see capital gamma. Herein A= totally ...
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1answer
134 views

Etymology of Some Terms Used in Ratio and Proportion in Old Algebra Textbooks

In older algebra textbooks for high school (mainly 19th century) four properties of ratio and proportions were used. The properties were Invertendo, Alternendo, Componendo, and Dividendo. This ...
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1answer
100 views

Where does the letter S in “$S$-units” and in localization $S^{-1} R$ come from?

In number theory, we may encounter the notion of $S$-unit, $S$-integer, etc. where $S$ is a finite set of prime numbers (for simplicity). For instance, if $S = \{2,3\}$ then the $S$-integers are the ...
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1answer
74 views

First appearance of the term sinus cardinalis

Who introduced the term sinus cardinalis? I do not mean the abbreviation sinc, which was introduced 1952 by Woodward.
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2answers
321 views

How influential was the Kerala school to European development in Calculus?

Did it influence the work of Newton or Leibniz, i have often heard that Europeans "stole" calculus from the Kerala school, these are views often parroted by Indian nationalists, but how accurate is it?...
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2answers
69 views

Who coined the term “uniform” as in “uniform distribution”?

During the late 16th century and early 17th century, published work about probability theory (e.g. Liber de ludo aleae by J. Cardan published in 1663 but writen around 1564) studied dice games using ...
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1answer
112 views

Riemann's moduli and Dedekind's modules: any connection?

The concept of a moduli space goes back to Riemann's count of $3g-3$ (or $3p-3$, in older notation) coordinates to describe Riemann surfaces of genus $g$ when $g > 1$. See the bottom of p. 33 here, ...
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1answer
56 views

Why are microcanonical, canonical and macrocanonical ensembles called that way?

In statistical mechanics, why microcanonical, canonical and macrocanonical ensemble are called that way? Is there any reason according to the size of the system they can describe properly ( I don't ...
7
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1answer
143 views

Indiana Pi Bill: Other attempts to establish mathematical truth by legislative fiat?

Wiki: The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative ...
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2answers
323 views

Who coined the term ''Born's rule''?

Who assigned the term ''Born's rule'' to the statement that the measurement of a quantum observable is one of its eigenvalues, with a probability given by the square of the coefficient in the spectral ...
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1answer
135 views

Earliest known usage of letter gamma “Γ” for reducible representation in group theory

Does any know the earliest known usage of the Greek letter gamma for showing a reducible representation of a group? This symbolism is commonly used in character tables in chemical applications of ...
2
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1answer
71 views

References about the the development of the concept of mechanical work

I'm looking for references about how the concept of mechanical work ("$\boldsymbol{F}\cdot\mathrm{d}\boldsymbol{r}$") or the concept of mechanical power ("$\boldsymbol{F}\cdot\boldsymbol{v}$") came ...
1
vote
1answer
79 views

Who invented the term “Kuhn loss”?

This term has been discussed on this forum, e.g. under Examples of Kuhn loss?, and has been attributed to Kuhn himself. The term refers to the loss of explanations and predictions of the prior ...
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0answers
129 views

Who was the first to use the “does not exist” sign ∄?

Who was the first to use the "does not exist" sign ∄? I'm aware that Giuseppe Peano originated serifed ∃ and, moreover that Whitehead and Russell repurposed Peano's serifed ∃; I'm also aware that ...
3
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1answer
51 views

Who coined the term “degenerate star”?

I'm trying to find a good source for the definition of degenerate matter to differentiate it from Fermi gases. For my research a good section on history would be nice. This question is more ...
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2answers
205 views

Why is kinetic energy denoted by the letter $T$ in quantum mechanics?

I think the question is self-explanatory but stackexchange requires me to write something here.
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2answers
157 views

Why is the azimuthal quantum number so named?

The name "azimuthal quantum number" is often used for the total orbital angular momentum quantum number $\ell$ in an atom. What is the origin of this name? It makes no sense to me, since the usual ...
2
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1answer
34 views

Doctrine of the sterilazio magna

What was the "doctrine of sterilazio magna"? Example from 1912 article about the variability of drug effectiveness: "Although the doctrine of the sterilazio magna has only been urged against the ...
2
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1answer
319 views

Who Invented The Number Line?

Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?
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1answer
334 views

Who coined the term “iff” for “if and only if”?

The OED's entry for "iff" lists this as the earliest usage: 1955 J. L. Kelley Gen. Topol. vii. 232: "F is equicontinuous at x iff there is a neighborhood of x whose image under every member of ...
3
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2answers
79 views

What was the significance of Eisenstein's discovery of invariants?

I am trying to decipher a portion of James Joseph Sylvester's 1869 address entitled "The Study That Knows Nothing of Observation", which, among other things, surveys the landscape of 19th century ...
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3answers
110 views

Who are “analysts” and “synthesists” in mathematics?

What is the difference between the terms "analysis" and "synthesis" used in a mathematical context? For example, Hawkins's Emergence of the Theory of Lie Groups p. 3 says that Klein and Lie were ...
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2answers
92 views

Who assigned the name “work” to the quantity $\int F\,{\rm d}r$?

I am looking into the historical perspective of how the concept of work and energy came about: who coined the terms "mechanical work" and "energy", and how the concept evolved over time. I know that ...
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0answers
56 views

Gentzen and computer science

This is a cross-post from mathstack: https://math.stackexchange.com/questions/2584003/gentzen-and-computer-science?noredirect=1#comment5333947_2584003 I would like to learn a bit about the ...
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0answers
125 views

What is the name given to the principle that guides mathematical conventions like the product of two negative numbers is positive

I recall that I read---in a book by Constance Reid---of a named principle that guided the arithmetic conventions that applied to operations on newly discovered mathematical objects. For example, when ...
2
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2answers
180 views

Why is an inch (in the English Imperial system of measure) as long as it is?

My question is about the length of the inch which is a subunit of the Imperial foot. Is there any connection whatsoever between the Imperial system for units of measure and the dimensions of the ...
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0answers
60 views

History of mesoscopic physics

Mesoscopic physics is a topic of major research as nanotechnology becomes an important hot topic. There doesn't seem to be a major writing about the history of mesoscopic physics. I know a little ...
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0answers
91 views

Timeline of mathematical foundation?

As it is globally known that set theory as a foundation of mathematics, although in the beginning we didn't call it "Set" rather group of elements. For example - set of [1(banana) + 2(apple)+1(cow)] =>...
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4answers
203 views

Who was the first individual that used the word “torus” to refer to $\mathbb{S}^{1} \times \mathbb{S}^{1}$?

Further, I believe that the idea to call it thus had to do with its resemblance to the "torus" in the base of some Greek columns of old: What do you think of this hypothesis of mine? Thanks in ...
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0answers
77 views

Who was the first to use the term field in physics?

Faraday, after drawing his lines of force in 19th century, is normally credited as the first to use the term field in physics. But... ... was not the term field used in the context of gravitational ...
4
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2answers
126 views

Origin of the terminology “trace operator” related to boundary-value problems for PDEs

Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator (not to be confused with the trace from linear algebra) essentially ...
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1answer
161 views

Why is it called the butterfly effect?

The pop-sci answer is that Lorenz characterised chaotic atmospheric dynamics with the hypothetical example of a butterfly's flapping wings changing whether a tornado results. However, since butterfly-...
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0answers
184 views

origin of the terms “domain” and “range”?

A 1929 paper of Chittenden contains the following sentence (about the derived set operator on a space $P$): “Thus the relation $E' = K(E)$ defines a single-valued set-valued set-function, whose ...
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0answers
54 views

Why is $\eta$ used in $\eta$-conversion?

In lambda calculus there are three types of reduction, $\alpha$-renaming $\beta$-reduction $\eta$-conversion The use of $\eta$ in $\eta$-conversion seems rather strange to me. Since they already ...
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1answer
37 views

First use of the term/name “curved exponential family”?

Question: What was the first recorded use of someone calling exponential families (in probability/statistics) for which the dimension of the natural parameter space is strictly less than the dimension ...
3
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1answer
183 views

Name of the Gamma function

The Gamma function for positive arguments can be defined with the integral $$ \Gamma(\alpha) = \int_0^\infty x^{\alpha-1} e^{-x}\,dx $$ The function $ x^{\alpha-1} e^{-x} $ is called the Gamma ...
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0answers
156 views

Set Theory, onto and into their relation to spoken language definitions

Does anyone know how the definitions for onto and into map to the spoken language definitions of the words? I compared the Bourbaki definitions to these words and have a suspicion that the German ...
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273 views

Whence “homomorphism”, “homomorphic”?

The kernel question leads to another : Today, homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen? “Homomorphic” ...
3
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1answer
97 views

What is the origin of the term “involution” used in Hamiltonian mechanics

We say that two dynamical variables $f$ and $g$ are in involution if their Poisson bracket vanishes, i.e., $\{f,g\}=0$. Why is it called involution?
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1answer
175 views

What is the name of this numeral system?

In a XVth century french manuscript on arithmetic and astrology, there is a description of a numeral system as follows (it starts here in the manuscript). Numbers between 1 and 9 are depicted by a ...
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1answer
156 views

What are early examples of the rare notational convention to make the sign of the real number represented by a letter depend on the typography?

Question. What early published or citably attested examples (preferably in the mathematical literature) can you give of the following convention? Let $\mathbb{S}$ denote some nonempty subset of some ...
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1answer
211 views

Who was the first to prove that $\pi$ was a real number? [closed]

Recently, there were many topics in sci.math discussed by so many (mathematicians, logicians, physicians, cranks and anti-cranks,..etc) the old definition of $\pi$ that is still considered valid up to ...
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1answer
110 views

Was the word “function” used in mathematics prior to Leibniz?

Most sources attribute the first use of "function" in the context of mathematics to Leibniz. But D'Alembert, Lacroix and Dini claim the following: D'Alembert in Encyclopédie 1757: les anciens ...
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2answers
146 views

Where does the name “geometric sequence” come from?

On this and other Stack Exchange website, there have been question about the so-called geometric series, and where its name comes from. My problem is that most answers follow one of two different ...
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4answers
299 views

Why is the letter $\vec{r}$ used for position?

I'm sorry if this is a dumb question but I've never heard a convincing explanation for why seemingly all of physics names the position vector "$\vec{r}$". I've tried translating it into just about ...
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1answer
119 views

Where does the habit of calling the elements of a projective Hilbert space “rays” originate from?

When describing the projective Hilbert space as the state space in quantum mechanics, physicists habitually refer to its elements as "rays in Hilbert space", while the mathematical literature seems to ...
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Etymology of 'qubit'; is there any relation to cubits?

Whilst several not-very-authoritative sources e.g. Wikipedia state that the word qubit was derived, partially, as a play on the word cubit (obviously it also stands for 'quantum bit'), is there any ...
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1answer
171 views

Why and who was the first to denote the square root operation in fractional form as $1/2$

Basically, the square root operation was discovered and proved rigorously from the Pythagorean theorem, it was denoted by square root of a rational number say $n$ as $\sqrt{n}$, but at a later stage, ...
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838 views

Who first considered the $f$ in $f(x)$ as an object in itself, and who decided to call it a function?

The question is in the title, but allow me to provide some background. I’m aware that Leibniz introduced the word “function” into mathematics (around 1673) and that Johann Bernoulli or Euler ...