Questions tagged [terminology]
For questions about terms, definitions and related concepts used in science and mathematics.
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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 ...
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Why do we say "Matrices" and "Vertices", but "Complexes" rather than "Complices"?
I had a professor point out that it is odd we refer to more than one chain complex as "complexes." It seems that in most other definitions in math we stick to the typical latin plural, i.e. we say ...
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Is "de" in "de Morgan" supposed to be capitalized or not?
I am currently writing about the "de Morgan's laws" and have seen both "de Morgan" and "De Morgan."
Which of these is correct?
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Where did the term "set-builder notation" come from?
In math stack exchange I often see notations like $\{x\in\mathbb Q:x^2<2\}$ being called instances of set builder notation. When I went to school we (that is, I, my fellow students, my teachers, ...
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What is the origin of "root" as a solution to an equation?
I was curious to know more on the history of the term "root", in the sense of "a value that results in a true statement, when substituted into an equation" (e.g., the roots of $2x^...
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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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History of "independent and dependent variables"
I have a lot of questions that can be summed up by "whats the history of independent and dependent variables?" Here is a list of those questions:
Where does our conception of independent and ...
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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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Why did Linnaeus equate the phoenix, the mythical bird, with Phoenix, a palm genus?
I've been reading about the "paradoxa" section of Carl Linnaeus's Systema Naturae, where he debunk some of the more far fetched ideas about animals.
Wikipedia includes this translation of what ...
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What is the origin of "normal" in normal coordinates and normal modes?
I am trying to understand why vibrational modes of polyatomic molecules are called "normal" mode of vibrations and with corresponding normal coordinates. What is the origin of the term normal here? I ...
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What is the origin of "ortho-," "meta-," "para-," in chemistry?
The prefix "ortho-" means straight or right; "meta-" means beyond or after; "para-" means beside or along. How, then, did ortho-, meta- and para- come to refer to the carbon positions one, two, and ...
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Definition of ordinal multiplication
The ordinal multiplication $\cdot$ can be defined recursively via ordinal addition $+$ for any ordinal $\alpha$ as follows:
$\alpha\cdot 0=0$.
$\alpha\cdot (\beta+1)=\alpha\cdot \beta+\alpha$ for any ...
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Why did Euclid define "a unit" instead of "the unit"?
I know Euclid's Definition VII.1 of a unit only from English and German translations:
A unit is (that) according to which each existing (thing) is said (to
be) one. [translation by Fitzpatrick]
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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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Who came up with the link between the spectrum of an operator and the poles of a meromorphic function?
From Dieudonné's "History of Functional Analysis" I learned that Picard in 1893 gave a characterization of an eigenvalue of the Laplacian as the simple pole of a meromorphic function.
Is there an ...
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When was the function 1 + cos(x), aka the vercosine, given a name?
Nowadays, when one searches for little-known trigonometric functions, one usually finds a list containing the versine, coversine, vercosine, and covercosine. When using this list, $1+\cos(x)$ is given ...
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Is $\Gamma^i_{jk}$ the Christoffel symbol or the Christoffel symbols?
For years, I have been perplexed that the expression $\Gamma^i_{jk}$ is often referred to in the plural as "the Christoffel symbols", although sometimes it is referred to in the singular as "the ...
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When and why did people stopped using "natural philosophy" term and started using "science"?
Previously what is called now "natural sciences" was called "natural philosophy". I'm interested in details, what was so wrong with the name "philosophy" so the name "science" became preferred?
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Why are 'speed' and 'velocity' not given the same name?
Position is a vector. Distance/length is a name of its magnitude.
Velocity is a vector. Speed is a name of its magnitude.
Acceleration is a name of a vector and its magnitude.
Force is a name of a ...
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Origins and history of branched covering
During my research on branched coverings of the projective plane, I am interested to know the origins and history of branched coverings of the projective plane and the projective line, together with ...
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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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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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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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When did non-SI double prefixes go out of use?
In old physics and engineering publications from the 1950s or so, it's common to see non-SI "double prefixes", such as a "millimicrosecond pulse", or a "10 micromicrofarad" capacitor.
These units are ...
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Why is the meaning of "linear" different in school and college use?
Is the map $y=2x+3$ linear?
"Of course it is." -- a high school teacher will answer.
"Nope; it's affine, but not linear." -- a college student will contradict.
This difference terminology that ...
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What is the origin of the term "Ordinary Differential Equation"?
Who first used the term "Ordinary Differential Equation (ODE)"? Is it known why the word "ordinary" is used here? What makes an ODE "ordinary"?
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What is the origin of the use of "g" for a Riemannian metric?
I am asking about the reason for the use of this letter, if known, as well as the initial occasion of its use. Ideas that have been suggested concerning the former include:
That it stands for ...
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Origin of the "law of quadratic reciprocity"
Today, "reciprocity" is the standard mathematical word used for quadratic reciprocity and its generalizations.
I found that the name dates back to no later than 1832, when a paper of Dirichlet (...
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How did the use of the word "origin" become commonplace in geometry?
My understanding is that in Cartesian geometry, all coordinate axes of an n-dimensional space may intersect at one point. I would like to know how that point--whether (0, 0), (0,0,0), ... -- came to ...
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What is the etymology of "phase space" of a dynamical system?
The state space of a dynamical system is often called a "phase space". What is the etymology of this?
(Note that I'm not asking about the history of the concept, but rather about the history of the ...
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Who coined the term “machine learning”?
A lot of sources attribute the definition to Arthur Samuel (1959), "the field of study that gives computers the ability to learn without being explicitly programmed", but none of these sources ...
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When was the term "union" first used?
I found out that the symbol for union, ∪, was created in 1895 by Giuseppe Peano in his Formulario Mathematico but of course the use of the word "union" in mathematics was older. Do you have a ...
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Origin of "dust" in cosmology?
In cosmology, "dust" refers to a pressureless perfect fluid, which essentially means a continuum of nonrelativistic material particles, such as galaxies. This is a picturesque and unusual piece of ...
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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 ...
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Who in history coined the term "character" of a group and why is it called so?
I first read the term in an introduction of Fourier transform on locally compact groups. In this article on Character of a group from Encyclopedia of Mathematics, a character of a group is defined as ...
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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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Why is the thermoelectric figure of merit denoted by $ZT$?
Why is the thermoelectric figure of merit denoted by $Z T$? Does $Z T$ come from the abbreviation of words in some language?
Update: So far, $T$ has been figured out — it is the temperature, to make ...
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Who coined kernel in mathematics?
I'm convinced that there is no such a mathematician whose name is "kernel". The wiki article about kernel doesn't include history in its content.
So I wonder, who is the first mathematician to use ...
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What was the evolution of "basis" and "generating set" in algebra?
Today, I've heard someone speak of a basis (of an ideal), meaning a generating set. All the time, I was fine with the term Gröbner-basis, but when it comes without the prefix, it's a bit funny, since ...
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Could a "field" have non-commutative multiplication originally?
Today, when the term "field" is defined in algebra, it is almost always stipulated that all fields are commutative. However, the author of these lectures says that this has not always been ...
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Modern usage of alchemical symbols
As far as I know, not many (if any) alchemical symbols have survived in modern nomenclature of science, either in chemistry or any other. I think $\LaTeX$ doesn't even support most of them! I know ...
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What's the origin and meaning of the adjective "free" in mathematics?
It's pretty common to call a group, ring or module free when it has a 'basis', but unlike other mathematical definitions whose names can be easily related to the concept they describe (e.g. the ...
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Who coined the term: "Directed Graph"?
I found that the term "Digraph" was coined in 1955 by Frank Harary in "The number of linear, directed, rooted, and connected graphs", and that it was a term actually suggested by ...
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Where is the first reference to the "Z combinator", a call-by-value fix-point combinator?
I'd like to know the earliest reference to the Z-combinator. This could be either where the name was first coined, or even the first discussion of a need for an applicative-order Y combinator. I didn'...
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Origin of the expression “Fundamental theorem of Algebra”
Who was the first person to use the expression “Fundamental theorem of Algebra”? It is well-known that Gauss called it “Fundamental theorem of algebraic equations”. Grattan-Guiness, in his The Rainbow ...
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Origin of the Hankel contour?
Who was the first to publish a Hankel contour integral?
See notes in my answer to the MO-Q How does one motivate the analytic continuation of the Riemann zeta function?.
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Why is one meter as long as it is?
The metre is defined as the length of the path travelled by light in
a vacuum in 1/299 792 458 of a second
Why is this so? Who decided that 1/299,792,458 of a ...
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Was the word 'gravity' an invention of Newton?
Before Newton many phycisists try to understand nature and the rotations of planets. But Newton founded his laws of gravity. But was he the first who used the word gravity or when was it first used? ...
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What animals or plants were used to illustrate ideas of physics?
This crossed my mind today...
There is Schrödinger's cat and Newton's apple.
Are there any other famous animals/plants featured in physics in a similar way?
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Why is kinetic energy denoted by the letter $T$ in quantum mechanics?
Kinetic energy is often written as $K$, $KE$ or $E_k$. Where does $T$ come from in quantum mechanics? Why and how did it come to be different?
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