Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

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Historical basis and mathematical significance of Riemann surfaces

It is written in Riemann Surfaces (Oxford Graduate Texts in Mathematics) by Simon Donaldson, that: "[t]he theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination ...
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History of the vocabulary for group extensions

In regular everyday English if you say something like "A was extended by B to get C", to me it means that A was in existence, B was added onto it, and now there is a larger object C. For example, ...
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1answer
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Historical reason for calling $\nabla\cdot F$ divergence?

Consider the continuously differentiable vector field in ${\mathbb R}^3$: $$ F:{\mathbb R}^3\to{\mathbb R}^3,\qquad F(x,y,z)=(U,V,W) $$ where $$ U,V,W:{\mathbb R}^3\to{\mathbb R}. $$ According to ...
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Why is lambda calculus named after that specific Greek letter? Why not “rho calculus”, for example?

Where does the choice of the Greek letter $\lambda$ in the name of “lambda calculus” come from? Why isn't it, for example, “rho calculus”?
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1answer
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Counting bases to which numbers are pseudoprime

Let $n=p_1^{a_1}\cdots p_k^{a_k}$ be an odd composite. Then the number of bases $1\le b\le n-1$ for which n is a strong pseudoprime is $$ \left(1 + \frac{2^{k\nu}-1}{2^k-1}\right) ...
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What did Simon Norton do after 1985?

Simon Norton is a mathematician that worked on finite simple groups and co-authored the Atlas of Finite Groups. With John Conway they proved there is a connection with the Monster group and the ...
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3answers
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Where can I find the old papers of the Math Tripos?

Is there a repository on the Internet which has the old question papers of the tripos? I am specifically interested in the papers during the 1890-1910 era, which was the era before the reforms, ...
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4answers
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Origin of the dot and cross product?

Most questions usually just relate to what these can be used for, that's fairly obvious to me since I've been programming 3D games/simulations for a while, but I've never really understood the inner ...
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1answer
517 views

Is the Unicode designed assuming the Continuum Hypothesis?

The Unicode chart for "letterlike symbols" states that א 2135 ALEF SYMBOL = first transfinite cardinal (countable) ב 2136 BET SYMBOL = second transfinite cardinal (the continuum) I ...
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1answer
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Proofs of Hyperbolic Functions

I know that functions which are associated with the geometry of the conic section called a hyperbola are called hyperbolic functions. But where on earth did '$e$' come from? I really don't ...
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1answer
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Why are rings called rings?

I've done some search in Internet and other sources about this question. Why the name ring to this particular object? Just curiosity. Thanks.
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6answers
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Motivation of the Gaussian Integral

I read on Wikipedia that Laplace was the first to evaluate $$\int\nolimits_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, ...
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1answer
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What is the primary source of Hilbert's famous “man in the street” statement?

I read somewhere a long time ago that Hilbert once said words (no doubt in German) to the effect that any mathematician worth his salt ought to be able to explain his results to any man in the street. ...
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2answers
506 views

When was the last prime number discovered? [closed]

By last, I mean the most recently discovered prime number. What was the length of time between the discovery of the last two prime numbers?
17
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1answer
925 views

What was the last mathematical paper published in Latin?

From an answer to a previous question I learned that Peano published in Latin as long as 1889. What was the last mathematical paper/book of recognized importance published in Latin?
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5answers
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Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?

I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the ...
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2answers
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Hardy / Wright's intro to number theory is highly praised but has no exercises

"An introduction to the theory of numbers, G.H Hardy, E.M. Wright, revised by D.R. Heath-Brown, J.H. Silverman. Originally published 1938. Sixth edition 2008 with a foreword by Andrew Wiles" is AFAIK ...
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2answers
406 views

What's the history of the result that $p_{n+1} < p_n^2$, and how difficult is the proof?

In Edsger Dijkstra's monograph "Notes on Structured Programming", he describes a simple imperative program for generating an array of the first $n$ primes. For each prime $p_n$, it finds the next ...
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3answers
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Provenance of Hilbert quote on table, chair, beer mug

All over the web one can find statements to the effect that: "One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs" There are many ...
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What's the “geometry” in “geometric multiplicity”?

The geometric multiplicity of an eigenvalue is defined as the dimension of the associated eigenspace, i.e. number of linearly independent eigenvectors with that eigenvalue. Here are my questions: ...
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1answer
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Was Grothendieck familiar with Stone's work on Boolean algebras?

In short, my question is: Was Grothendieck familiar with Stone's work on Boolean algebras? Background: In an answer to Pierre-Yves Gaillard's question Did Zariski really define the Zariski ...
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0answers
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Irrationality of $e$

I have a question about the irrationality of $e$: In proving the irrationality of $e$, one can prove the irrationality of $e^{-1}$ by using the series $$e^x = 1+x+\frac{x^2}{2!} + \cdots + ...
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2answers
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Did Zariski really define the Zariski topology on the prime spectrum of a ring?

The question is not: “Did Zariski really define the Zariski topology?” It is: “Did Zariski really define the Zariski topology on the prime spectrum of a ring?” Here is the motivation. --- On page ...
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1answer
451 views

who first defined a tangent to a circle as a line meeting it only once?

From googling, it seems commonly believed that Euclid did this, but it seems nowhere in Euclid does he even state this property of a tangent line explicitly. Rather Euclid gives 4 other equivalent ...
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1answer
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About a paper of Zermelo

This about the famous article Zermelo, E., Beweis, daß jede Menge wohlgeordnet werden kann, Math. Ann. 59 (4), 514–516 (1904), available here. Edit: Springer link to the ...
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10answers
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Why do people use “it is easy to prove”?

Math is not generally what I am doing, but I have to read some literature and articles in dynamic systems and complexity theory. What I noticed is that authors tend to use (quite frequently) the ...
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0answers
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notation for ramification index and inertial degree

For a prime $Q$ lying over a prime $P$, I have seen the ramification index of $Q$ over $P$ denoted by $e(Q|P)$ and the inertial degree of $Q$ over $P$ by $f(Q|P)$. What is the origin of the ...
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What is the origin of the expression “Yoneda Lemma”?

Thank you very much in advance for telling where the expression “Yoneda Lemma” comes from. EDIT 1. On page -14 of Reprints in Theory and Applications of Categories, No. 3, 2003. Abelian Categories, ...
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3answers
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Understanding of the Mean Value Theorem in PDE

I learned the following theorem in Folland's Introduction to Partial Differential Equations(p.69 Chapter 2): Suppose $u$ is harmonic on an open set $\Omega\subset{\mathbb R}^n$. If $x\in\Omega$ ...
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2answers
347 views

Models of hyperbolic geometry

Wikipedia states the following: [The Poincaré half-plane model of hyperbolic geometry] is named after Henri Poincaré, but originated with Eugenio Beltrami, who used it, along with the Klein model ...
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1answer
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Proof of Euler's Theorem without abstract algebra?

Every proof I've seen of Euler's Theorem (that $\gcd(a,m) = 1 \implies a^{\phi(m)} \equiv 1 \pmod m$) involves the fact that the units of $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. ...
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3answers
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Article or book about the history of spherical geometry?

I teach a course on non-Euclidean geometry to high schoolers. I'm looking for an article or book that gives a thorough and interesting history of spherical geometry and trigonometry. I'm looking for ...
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3answers
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Are there numerical algorithms for Roman numerals?

In positional number systems there are algorithms for performing certain operations, like long division, to name one of the simplest. This works for positional systems, whatever base. I realize in ...
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2answers
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Motivation for Napier's Logarithms

In the wikipedia article on logarithms, I am clueless about the approach and motivation for the following computations done by Napier (and the mysterious appearance of Euler's number) in this section. ...
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2answers
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Fermat's Last Theorem: implications (there is no new proof)

I am not experienced in Number Theory but what I know is that some results of this filed are applicable in other areas, e.g. algebra. For sure FLT made (and makes) people be interested in Number ...
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8answers
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Reference request: is mathematics discovered or created?

I have to write a short monograph as an assignment for a course on the philosophy of science. Being a math student, of course I want to opt for something math-related. After some initial ideas which ...
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3answers
976 views

Where is the name “coset” in group theory from?

One of the most important application of "coset", I think, is to prove the Lagrange's theorem, which was not originally stated in the group theoretic terms. In some textbooks I have read about ...
10
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2answers
515 views

Origin of the name 'test functions'

This is a very simple question really: where did the name 'test functions', used nowadays when speaking of infinitely differentiable and compactly supported functions, come from? More to the point: is ...
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1answer
260 views

Who invented linearization of exponential datasets to find their approximating functions?

I just learned how to find the exponential function that approximates a dataset by taking the logarithm of the data points, doing a linear regression on that data, then working out the exponential ...
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6answers
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What kind of “symmetry” is the symmetric group about?

There are two concepts which are very similar literally in abstract algebra: symmetric group and symmetry group. By definition, the symmetric group on a set is the group consisting of all bijections ...
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4answers
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Angle brackets for tuples

I've recently noticed that use of angle brackets for writing tuples, e.g. $\langle x, y \rangle$ instead of the usual round brackets in a few books I've been reading — Lawvere's Sets for Mathematics, ...
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3answers
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where does the term “integral domain” come from?

Self-explanatory title really! A student today asked me why they were called integral domains -- and I realised that the word "integral" seems to be being used in a way totally unlike any other way I ...
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5answers
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Results that were widely believed to be false but were later shown to be true

What are some results which were widely believed to be false, but were later to be shown to be true, or vice-versa?
5
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0answers
172 views

History Question - Branch Cut

My professor began discussing branch cuts in class today and mentioned that he did not know the origin of the term. Does anyone know the origin of the term and perhaps a source that talks about it?
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5answers
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Where did mathematicians learn how to do truth tables?

I'm trying to find out who invented truth-tables. Here is what I have so far. Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 ...
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7answers
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History of zero?

I learn't as a kid from my teachers that zero was discovered/invented in india and if you ask anybody here in india, the answer is simple yes it was invented in india. Now we have something to say ...
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1answer
498 views

Fibonacci, compositions, history

There are three basic families of restricted compositions (ordered partitions) that are enumerated by the Fibonacci numbers (with offsets): a) compositions with parts from the set {1,2} (e.g., 2+2 = ...
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1answer
254 views

“Hilbert foresaw the possibility of negative solutions to some mathematical problems”

In My Collaboration with JULIA ROBINSON it is said Hilbert foresaw the possibility of negative solutions to some mathematical problems What evidence is there that Hilbert knew (around the time ...
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342 views

Etymology of the name “deck transformation”

What does the word "deck" mean in "deck transformation"? What's the idea behind this name?
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Zeta functions in Chebychev's Prime Number theory

In two papers from 1848 and 1850, the Russian mathematician Pafnuty L'vovich Chebyshev attempted to prove the asymptotic law of distribution of prime numbers. His work is notable for the use of the ...