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Questions tagged [terminology]

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

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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 $$\...
Geremia's user avatar
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24 votes
2 answers
3k 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 ...
Michael Bächtold's user avatar
3 votes
2 answers
690 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. ...
Laurent Duval's user avatar
23 votes
2 answers
19k views

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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6 votes
2 answers
2k views

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?
rus9384's user avatar
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8 votes
2 answers
659 views

Historical roots of the justification for the rule for multiplication of negative numbers

As a follow up question with respect to : Who wrote down minus times minus is equal to plus? and to : Historically, how did people define multiplication for negative numbers?, it can be interesting to ...
Mauro ALLEGRANZA's user avatar
4 votes
3 answers
3k views

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 ...
Dylan Kerler's user avatar
21 votes
1 answer
8k views

Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
Floris's user avatar
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13 votes
2 answers
2k views

Etymology of "power" (math.)

Having done some searches on the internet, seems like the term "power" is a mistranslation. The Wikipedia article links to an article in the MacTutor History of Mathematics archive where it is written ...
მამუკა ჯიბლაძე's user avatar
12 votes
2 answers
888 views

Is it true that Leibniz introduced "constant," "variable," and "function"?

I read in a not always reliable source (David Foster Wallace's Everything and More, p.104), that Leibniz introduced the terms constant, variable, and function, the latter as an alternative to Newton's ...
Joseph O'Rourke's user avatar
8 votes
3 answers
337 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 ...
Geremia's user avatar
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8 votes
4 answers
267 views

What was the definition of a scientist and how did it evolve? When was science categorized?

I'm asking this question as I've noticed that scientists like Gauss, Newton, Euler, Lagrange etc developed theories in many scientific fields(these ones that I know of were mostly interested in math ...
UserX's user avatar
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7 votes
1 answer
241 views

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 "...
qwr's user avatar
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7 votes
2 answers
360 views

Why do we call it a "positive definite matrix" rather than a "positively definite matrix"?

The term positive definite matrix is a standard one used in mathematics, especially in linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called a positively ...
modnar's user avatar
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5 votes
1 answer
235 views

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 ...
Ben's user avatar
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3 votes
2 answers
772 views

Origin and use of the adjective "improper" in mathematics

Anybody with elementary mathematical education will have seen improper fractions to refer to fractions where the numerator is greater than or equal to the denominator. At a certain point in calculus ...
Easymode44's user avatar
2 votes
2 answers
2k views

Who wrote down minus times minus is equal to plus? [duplicate]

I am not here to ask why "minus times minus is plus", this is a basic arithmetic fact. The related question most people ask is: why does $-\times-=+$. Of, course there may be several explanations for ...
Kushal Bhuyan's user avatar
0 votes
3 answers
237 views

When did the term 'scientist, physicist, science, physicist' come in use?

Down to the eighteenth century physics was called philosophia naturalis. When were the terms Physics, Science and Scientist, introduced? By whom? When did they supplant the old ones?
user157860's user avatar
25 votes
1 answer
1k views

When did the names of scientists first become the names of scientific units?

Many scientific units are named after scientists, for example, Tesla for magnetic flux Farad for capacitance Newton for force. When did the tradition of naming scientific units begin?
user avatar
23 votes
4 answers
1k views

Did ancient/medieval non-European cultures have a concept of energy? If so, what are the similarities and differences to the modern concept?

For example, do we find something related to the modern energy concept in Ancient China, Ancient India, or the Islamic Golden Age? Among "similarities and differences", conservation is obviously ...
Michael Weiss's user avatar
23 votes
2 answers
5k views

Why is there no named unit for momentum but there is one for energy?

Momentum and energy play very similar roles in mechanics, each being changed by the application of force over a interval. For energy the interval is in space and for momentum it is in time. Both have ...
dmckee --- ex-moderator kitten's user avatar
11 votes
1 answer
2k views

Why is differentiation under the integral sign named the Leibniz rule?

The question here asked why differentiation under the integral sign is named "Feynman's trick". That is a comparatively recent name for the method. Aside from the name "differentiation under the ...
KCd's user avatar
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10 votes
1 answer
610 views

What caused the name change from "analysis situs" to "topology"?

J. Alexander's 1926 paper, Combinatorial Analysis Situs, doesn't refer to the field as combinatorial topology. He mentions that combinatorial analysis situs is concerned with topological invariants ...
Catherine Ray's user avatar
10 votes
1 answer
554 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 ...
BCLC's user avatar
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9 votes
2 answers
2k views

History of the definition of Injective & Surjective Function

I'm a college student, just beginning to study Elementary Set Theory. In studying about the definition of injective and surjective function, out of curiosity, it came to my mind a question about the ...
Gin99's user avatar
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9 votes
1 answer
1k views

Why is the Heaviside step function named after Heaviside?

The Heaviside step function is usually defined as $$ \theta(x)=\left\{\begin{array}{ll}0&\text{if }x<0\\\tfrac12&\text{if }x=0\\1&\text{if }x>0.\\\end{array}\right. $$ It is ...
Emilio Pisanty's user avatar
9 votes
1 answer
1k views

Why is the Sophie Germain Identity called thus?

Several authors (z.B.: Arthur Engel in his Problem-Solving Strategies, Alexander Bogomolny in this entry of the Cut the Knot website) refer to the following (straightforward) consequence of the ...
José Hdz. Stgo.'s user avatar
9 votes
1 answer
627 views

Who was first to differentiate between prime and irreducible elements?

I recently learned about irreducible and prime elements in a commutative ring. However, my professor was not quite sure who was the first to make this distinction, or give an example of an irreducible ...
David's user avatar
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9 votes
1 answer
2k views

When and by whom was the term 'momentum' introduced?

We know that up to 1726, when the third edition of the Principia was published, the name for $m\vec v$ was: quantitas motus. Do you know who substituted that with another Latin word: 'momentum'?
user avatar
8 votes
3 answers
1k views

Why do we call a linear mapping "linear mapping"?

According to P. M. Cohn's Classic Algebra, for historical reasons we call a linear mapping "linear mapping". What are the historical reasons that led to the adoption of the term "linear ...
Chilote's user avatar
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8 votes
2 answers
5k views

What is the status of the three crises in the history of mathematics?

I have seen a claim in some literature that there are three crises in the history of mathematics. The first is the discovery of $\sqrt2$ being irrational in Greek time which shook the belief that ...
Eugene Zhang's user avatar
7 votes
1 answer
3k views

How did the term "Michel electron" come about?

The Michel electron is what we call the electron produced from muon decay, and it's named after Louis Michel. I mention this in a paper I'm writing, and I was told that I need to cite it. I can't find ...
Luka's user avatar
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7 votes
2 answers
4k views

Why is magnetic flux density named after Nikola Tesla?

I have my respect for Mr Tesla, but it seems weird that "he" was chosen to be the units of magnetic flux density. I mean, he didn't contribute much to magnetic fields theory, nor did he work ...
Eminem's user avatar
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7 votes
4 answers
4k views

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: \...
Matta's user avatar
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6 votes
1 answer
2k views

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 ...
Kahovius's user avatar
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6 votes
1 answer
481 views

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 ...
Jan Peter Schäfermeyer's user avatar
6 votes
2 answers
474 views

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 ...
ACR's user avatar
  • 4,079
5 votes
1 answer
246 views

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 ...
user avatar
5 votes
1 answer
353 views

What changes in mathematics resulted in the change of the definition of primes and exclusion of 1?

Why 1 is not prime? I read in this article that G.H Hardy explicitly included 1 as a prime in the first 6 editions of "A Course in Pure Mathematics", published between 1908-1933. He updated ...
Saikat's user avatar
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4 votes
3 answers
13k views

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? ...
Marijn 's user avatar
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4 votes
1 answer
398 views

Where does "the grating equation" come from? Does it have a another name?

What we often refer to as Snell's law: $$n_1 \sin(\theta_1) - n_2 \sin(\theta_2) = 0$$ has quite a bit of history behind it. It can be demonstrated in several ways, one of which is by asserting that ...
uhoh's user avatar
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4 votes
2 answers
155 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 ...
user avatar
3 votes
1 answer
253 views

On early US patriotism to choose quark color charge labels

Sean Carroll has a video about gauge theory (2020) in his series about Greatest Ideas of the Universe, where he claims that early in the development of quantum chromodynamics, some physicists tried to ...
Mauricio's user avatar
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3 votes
2 answers
2k 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?
user 85795's user avatar
3 votes
3 answers
306 views

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?
André LFS Bacci's user avatar
3 votes
1 answer
315 views

Degenerate States in Quantum Mechanics

In his book on quantum mechanics in the chapter on perturbation theory Dirac says in a footnote: A system with only one stationary state belonging to each energy-level is often called non-...
blackholedynamite's user avatar
3 votes
2 answers
615 views

How did the early chemists make a connection between gram formula weight with 1 mole and Avogadro's number?

According to one historian Mustafa Sarikaya's article in Foundations of Chemistry DOI 10.1007/s10698-011-9128-7, the mole concept was introduced to chemistry earlier than Avogadro’s number. The mole ...
ACR's user avatar
  • 4,079
3 votes
1 answer
326 views

Jordan called isomorphisms (iso.) and homomorphisms "iso. holoedriques" and "iso. meriedriques" respectively; translation of holoe/meried-driques?

Stillwell mentions in his Elements of Algebra: The first to use the term "isomorphism" was Jordan, in his Traite des Substitutions [1870], the first textbook on group theory...Jordan used the word "...
bzm3r's user avatar
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2 votes
1 answer
119 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 ...
pglpm's user avatar
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2 votes
0 answers
203 views

The origin of $∂^2=0$ and $d^2=0$

I know that formula $∂^2=0$ and $d^2=0$ very important in the homology and cohomology theory. And I understand that this formula was generated from the process of finding a solution to the partial ...
pokssin's user avatar
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