Questions tagged [terminology]

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

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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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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 ...
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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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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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364 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” ...
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224 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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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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242 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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200 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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354 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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149 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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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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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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184 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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243 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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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 ...
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290 views

When was a partition of unity discovered?

A partition of unity is a mathematical concept in geometry. I want to know when and in what context this concept appeared.
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What is the origin of the terminology 'spin up/down'?

In my research area one seminal reference is H. Bethe, ''Zur Theorie der Metalle'', Z. Phys. 71 205 (1931), see also the English translation by T. C. Dorlas (2009). On page 206 of the original ...
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336 views

What is the first usage of the term “Adjoint” and why was this word chosen?

The term "Adjoint" appears in many different mathematical areas and for sometimes seemingly different kinds of things. Wikipedia says -- "In mathematics, the term adjoint applies in several ...
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108 views

Why isn't the ${\gamma}^5$ matrix not called ${\gamma}^4$?

This is not really a physical question, but it relates to notation in QED. The ${\gamma}^5$ matrix is defined as $${\gamma}^5=i{\gamma}^0 {\gamma}^1{\gamma}^2{\gamma}^3$$ Wouldn't it be more ...
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Why is the term “kernel” used in algebra? [duplicate]

What was the motivation to use the word "kernel" in algebra to denote the set of all arguments which are mapped to the idendity element (by a homomorphism)? Who introduced it?
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Why are étale morphisms called “étale”?

Alexander Grothendieck developed the theory of "locally trivial coverings spaces for rings/schemes" in SGAI as an analog to the theory of covering spaces in algebraic topology. He called such ...
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What is the history of why electrical circuit diagrams list positive as the direction of electron flow?

In the study of electrical engineering circuit diagrams it is usually the norm to show the + ( positive ) polarity as the direction of motion. However in reality the electron is the elementary ...
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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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Why is the SI prefix k- lower case?

In the SI unit prefixes, there's a general pattern of using uppercase prefixes for multipliers larger than 1 and lower case for prefixes that are smaller than one. However, this is not a universal ...
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1answer
154 views

How is “soul” meant to be understood in the context of the “Soul Theorem”

My mathematics are still quite rudimentary, but am I correct in assuming this is a reference to the "finite" state of closed manifolds as opposed to a potential, "infinite" state of the non-compacted ...
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578 views

What is the etymology of lower case p as the operator for the negative of the common logarithm?

In high school we were taught that the formula for pH is the negative of the common logarithm of hydrogen ion concentration: pH = -log[H+]. It wasn't until I took organic chemistry that the "acid ...
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292 views

First use of litte $o_p$ (little $o$ in probability) notation?

I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this ...
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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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152 views

Why are rings called rings?

I copied the question from https://math.stackexchange.com/q/61497/378968 because I think it is more suitable for this site and I think an answer to this question here could do better than: Hilbert ...
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Why are canonical coordinates canonical?

Canonical coordinates are coordinates $q_i$ and $p_i$ in phase space that are used in the Hamiltonian formalism. The canonical coordinates satisfy the fundamental Poisson bracket relations: \...
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Analysis vs Synthesis in Greek Mathematics

I am trying to understand the difference in "analysis" and "synthesis" as used by the ancient Greek mathematicians. Most sources characterize synthesis as working from givens to a desired conclusion, ...
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What is the connection between Lamarck's Mediterranean mussel and the province of Gallia?

The scientific name of the Mediterranean Mytilus is Mytilus galloprovincialis, with Lamarck being reported as the creator. I wonder where this name comes from, in particular what is the (supposed) ...
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124 views

Coordinate axis - Why the name “axis”?

In "natural life" "axis" is often used in terms of an axis of rotation. But in the mathematical sense, it's more used like a ruler. One could say an axis in "natural life" sense has something to do ...
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source of “logistic growth”?

I've been trying to find the source of the name of the DE modelling population growth known as logistic growth, for some time: why "Logistic" ? So far all my attempts to research it have hit dead ends ...
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Who originated the biological senses of palindrome and pseudopalindrome?

One would think that when DNA biology uses the word palindrome it would mean approximately the same thing as palindrome in other contexts. As I understand it, this is not true. Whereas, a normal ...
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518 views

Grassmann Formula

I'm in my first year of Mathematics at the University. Recently, we've learnt about Grassmann Formula and when I was making a little research on the internet, I couldn't find a single reference ...
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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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Why do English volume units use base 2?

I would post this on Quora, since it is more of a "just wondering" sort of question, except that I much prefer StackExchange's platform: As weird as Imperial units generally are, English volume units ...
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1answer
108 views

Were integrals really called solution curves (or vice versa)?

For some reason I recall hearing that around the time Euler wrote his Calculus books (1768-1770), or even before then, what we call integrals now were called solution cuvres (or even possibly the ...
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What is the etymology behind sine, cosine, tangent, etc.?

I heard somewhere that it was actually a mistake in translation. What's the correct story?
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Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \triangleq ...
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First mention of Fundamental Theorem of Arithmetic

Without a Disquisitiones Arithmeticae at hand, I may ask... When the unique factorization theorem was first called the Fundamental Theorem of Arithmetic?
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When was the convention for the indefinite integral $\int\frac{1}{x}dx$ changed?

In Europe, in the 20th century, $\int\frac{1}{x}dx$ equalled $\ln{x}+C$. (I have references from Poland for 1930-1947 and the UK for the 1960s and 1970s). Now, if one mentions $\int\frac{1}{x}dx=\ln{...
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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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360 views

Introduction of $\imath$ and $\jmath$ notations for the imaginary unit

The imaginary unit is generally denoted $i$ or $\imath$. I have learned that the term imaginary ("imaginaires") was coined by R. Descartes in 1637, and the "i" notation was introduced by L. Euler (cf. ...
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Why is one of Maxwell's equations named after Ampère? Who first named it after Ampère?

Ampère never wrote down what is confusingly called "Ampère's circuital law," not even the form without the displacement current term, as Ampère never dealt with the field concept.* Maxwell derived $$\...
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Origin of “Spline” word

I was studying interpolation by Splines in numerical analysis and started to wonder the word's origin. I've found that it was a system used in technical drawings using weights but couldn't find why ...
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1answer
2k views

What is the origin of the term “ordinary differential equations”?

Who has first used the term "ordinary differential equation"? Is it known, why the term "ordinary" is used here? What makes an ODE "ordinary"?