Questions tagged [terminology]
For questions about terms, definitions and related concepts used in science and mathematics.
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Who introduced the terminology “nondecreasing” for weakly increasing (i.e. x≤y ⇒ f(x)≤f(y)), and when/why?
Arguably one of the most hated parts of English mathematical terminology is the word “nondecreasing”, referring to a function such that $x\leq y \;\Rightarrow\; f(x)\leq f(y)$ (what other conventions ...
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Who first introduced the term "necessary condition" in mathematical language?
I recently delved into a discussion about a statement attributed to the renowned mathematician and philosopher, Benjamin Peirce. In this statement, he refers to mathematics as "the science that ...
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Who was the first to use bijections?
I know that Bourbaki were the first who used the word 'bijection', but one-to one functions were for sure used before them. So do you aware of the earliest examples of one-to-one correspondences?
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How did the concept of local field emerge and develop in mathematics?
When I was studying class field theory, I saw local class field theory. However, I suddenly became curious about local fields, not local class field theory. As far as I know, the local field is the ...
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Dissemination of Calculus in China
Much has already been written about the dissemination of Euclidean geometry into China: https://www.maa.org/press/periodicals/convergence/mathematical-treasure-euclid-in-china, https://academic.oup....
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Origin of $V_a$ (median) notation
My question about median of a triangle.
The English equivalent of the Turkish word "kenarortay" is "median". In English-language geometry sources (like books or web pages), the ...
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What is the origin of the "red, green, yellow" quark color convention?
In physics, quarks come in one of three color states, usually chosen to be called, "red", "green", and "blue". However, because these are just labels, there are other ...
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Who first called $\mathrm e$ "Euler's number"?
Euler is usually credited with denoting this number with the letter $\mathrm e$. But
It seems unlikely that Euler chose the letter because it is the initial of his own name, as occasionally been ...
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Light propagated instantaneously rather than gradually
In the following paper from I. Bernard Cohen, "Roemer and the First Determination of the Velocity of Light (1676)" published on Isis (1940):
Can be read:
explaining that the delay would ...
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In a survey of historical science has anyone studied the propensity of other departments to co-opt scientific terminology to further their own ideas?
For example, Albert Einstein complained that sociology departments across the quad were using his theory of relativity to advance the idea of "relativistic morality."
The meaning of ...
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What is the etymology of the term space-time?
I'm looking for the earliest references to the word space-time (in the modern sense), in any language.
The first references would likely be in German, as Raum-Zeit or Raumzeit.
Of course, H. Minkowski ...
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Who coined the term Orthonormal?
Does anyone know who coined the term orthonormal to refer to a basis that is orthogonal and normal?
In such a poorly named mathematical world (looking at you, conditionally convergent series) I think ...
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When did Macaulay rings become Cohen-Macaulay rings?
In his book on commutative rings (published 1970), Kaplansky talks about Macaulay rings. In the mid 1970's, I learned some commutative algebra from a student of his, who referred to these rings as ...
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Use of the verb "induct" in proofs by mathematical induction
Occasionally, in a proof by mathematical induction, the writer will say something like, "We induct on $n$" or "We induct on the number of vertices." This usage of the verb induct ...
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The etymology of "radio waves"
The word "radio" originates from "radius", which in turn came from "ray". That's why "radius" means any line from a central focal point to any directions.
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Poisson's laws for adiabatic processes
I've been reading about Thermodynamics lately. The set of equations satisfied in an adiabatic process (and also more generally in polytropic ones) is:
$$p_1V_1^\gamma = p_2V_2^\gamma$$
$$T_1V_1^{\...
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When did the error function get its modern definition?
I am currently writing an essay on the error function and after researching its historical origin, I found out who first defined it: J.W.L. Glaisher. But his definition is different from today's form. ...
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Terminology associated with mathematical induction
In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...
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Katz's symbol 兄 for Gauss-Manin connections
In his famous 1970 paper [1], Nicholas Katz used the character 兄 for the Gauss-Manin connection. I have always been curious about the history behind this symbol.
Question: What motivated Katz to use ...
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The origin and use of the term "equianharmonic" (elliptic function)
In Weierstrass notation, the principal elliptic function $\wp$ is a solution of the differential equation
$$ (\wp')^2= 4\wp^3 -g_2\wp -g_3. $$
The case when $g_3=0$ is called lemniscatic (it ...
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Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?
In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum').
Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
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The symbol h for class numbers
We use $h_K$ conventionally to denote the class numbers of number fields $K$.
But I have never thought why the letter $h$ was used for it.
Why and who used $h$ for the class number?
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Weyl's gauge theory and railroad tracks
There is a claim I occasionally read that the origin of the word "gauge" refers to a track gauge used in railroad tracks (the distance between two rails). It's a claim I have seen here, here,...
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Who coined the term "sulphuretted hydrogen"?
Hydrogen sulfide was previously named "sulphuretted hydrogen" but I can't find the person who named/coined it. Although Carl Wilhelm Scheele is credited to have discovered and isolated the ...
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What's the difference between Galileo's "impeto" and "momento"?
In Galileo's Two New Sciences, he describes an experiment demonstrating pendulum motion and how the pendulum will rise to the same height from where it started its fall. This discussion can be found ...
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Definition and Name Change of the Oscillation Function
I have two related questions:
Who first defined the oscillation function (perhaps under a different name)?
When did the switch from the phrase "saltus function"(*) to "oscillation ...
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Usage of "sphere" as ball's surface vs as ball itself
In everyday English, "sphere" means a round object. People will think of the insides as part of the sphere.
In Mathematics it specifically means the surface of the ball.
How did the ...
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Who coined the name "cosmological constant"?
I am aware that Albert Einstein first added the $\Lambda$-term to his field equations in his 1917 paper "Cosmological considerations in the general theory of relativity" (german: "...
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When was Lipschitz equivalence first attributed to Lipschitz or did Lipschitz formulate it himself?
In his book Introduction to Metric and Topological Spaces, author Wilson A Sutherland in explaining the equivalence of metrics invoked the definition:
Two metrics $d_1, d_2$ on a set $X$ will be ...
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When was the term "Sparingly soluble" first introduced in chemistry?
This question is inspired from: Why do we call salts such as AgCl sparingly soluble?
The extent of solubility can be expressed as descriptive terms. U.S. Pharmacopoeia has made the following ...
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What is the origin of the negation ( ¬ ) operator from logic?
I'm curious as to what the rationale was, and who the idea occurred to, for the ¬ symbol. I'll grant that more common mathematical symbols like +, −, × and ÷ are also likely unknown, but they seem to ...
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Did Kronecker's "ganzen Zahlen" refer to whole numbers as natural numbers or integers?
Maybe this is a question better for German language Stack Exchange, but in the quote attributed to Kronecker:
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
So "...
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Origin of the term "affixe"/"affix" in the geometric treatment of complex numbers
In current French mathematical tradition, when introducing complex numbers, it is common to hear about "complex plane of Argand-Cauchy".
What is particular in French treatment, it is the ...
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At what point did "Archean" go from meaning the entire Precambrian to just the middle part?
I can't find the exact date when the Archean began to mean "the middle of the Precambrian", as opposed to the beginning or the whole thing. It is some time after 1925 and before 1972.
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Why is $T_{\mu\nu}$ the Standard Notation for the Stress-Energy-Momentum Tensor
My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)...
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First use of "Spur" (trace) for linear maps / matrices
Every student of linear algebra learns about the trace of a linear map. Its easiest (albeit not most conceptual) definition is: write the map as matrix, then the trace is the sum of the diagonal ...
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Why is the letter $b$ used to represent the y-intercept in the equation of straight line?
The slope-intercept form of a non-vertical line is $y=mx+b$. I have been told that the slope is called $m$ because it is the first letter of the French word for mountain. But why is there the letter $...
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Why is thermodynamics called thermodynamics?
Thermodynamics is derived from two Greek words
Therme, which means heat
Dynamis, which means power
We know that 'thermodynamics' encapsulates many concepts like energy, temperature, entropy, exergy, ...
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Who proclaimed separation of science from philosophy?
Historically (since 2500 years ago), philosophy - "love of wisdom" in Greek - encompassed all intellectual endeavors, and natural philosophy was seen as its part. However, these days the ...
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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?
The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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First example of regularization
Background:
I like to think of L'Hospital as one of the earliest authors of least-squares regression.
L'Hospital, G. (1696). L'analyse des infiniment petits pour l'intelligence des lignes
courbes.
I'm ...
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Formal logic as a synonym to syllogistic logic, or as a name for the study of logic?
On page 443, section 1.1 Expanding to Contradiction, in José Ferreirós' A Road To Modern Logic - An Interpretation, the following is written:
Philosophical conceptions of logic have been complex and ...
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Context of the discovery of ultraproducts
Łoś's theorem is a fundamental theorem in model theory (a branch of mathematical logic).
Historical question: What was Łoś's original motivation to define ultraproducts and prove Łoś's theorem? Which ...
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Who, between Cayley and Hamilton, first worked on the theorem that bears their name?
I know that Frobenius is the one who proved the Cayley-Hamilton theorem in all its generality. However, between Cayley and Hamilton, who did first work on the subject?
In English: Cayley–Hamilton ...
user16484
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What or who is Peloritan in the name "Accademia Peloritana dei Pericolanti"?
The University of Messina has a scientific organization and publication "Accademia Peloritana dei Pericolanti", see 1. What is the origin and meaning of the word "peloritana"?
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The term "constant" in "integration by parts" ("partielle Integration")
In Riemann's "Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe", Riemann mentions taking a factor as "constant" in "partial integration", which ...
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Early uses of the word "operator" in mathematics
I'm looking for early uses of the word "operator" in mathematics and how it evolved to become a synonym for the modern "function" in certain areas. Jeff Miller's page only has an ...
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Why some calculations noted as "sym^2" and "sym", while others noted as "symA" and "symB", where "symB" is the square root of "symA"?
Today I learnt that the standard deviation is calculated as square root of the mean of the squares of the deviations from the arithmetic mean of the distribution. The mean of the squares of the ...
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Classification of "Epitaph of Diophantus" problem
The well-known riddle of the Epitaph of Diophantus, attributed to Metrodorus, is one of the style of simple problem in algebra whose pattern when expressed in contemporary algebraic notation is:
$$x = ...
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Is it known who coined the term Episteme?
I thought that such old terms wouldnt be known who "created" them, but terms of the same time like Natural Philosophy and Philosophy are said to be created by Aristotle, and believed to be ...
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