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

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Why is “h” used for entropy?

Why is the letter "h" (or "H") used to denote entropy in information theory, ergodic theory, and physics (and possibly other places)? Edit: I'm looking for an explanation of the original use of "H". ...
4
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3answers
2k views

On the Origin and Precise Definition of the Term 'Surd'

So, in the course of last week's class work, I ran across the Maple function surd() that takes the real part of an nth root. However, conversation with my professor ...
14
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1answer
443 views

History of Commutative Algebra

There are books of the history of Algebraic Geometry, there are also papers about it (All had done by J.Dieudonné). But I could not find any book or paper about the history of Commutative Algebra. ...
5
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1answer
1k views

What applications of the Residue Theorem to real integration have had the biggest impact outside of pure math?

A typical undergraduate student (at least in North America) learns about integration of real-valued functions of one real variable, and learns some of its applications to science and probability, e.g. ...
12
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3answers
416 views

Is there any difference between a math invention and a math discovery? [closed]

From wikipekia: The calculus controversy was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates – ...
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2answers
2k views

Development of the Idea of the Determinant

While I basically understand what a determinant is, I wonder how this idea was developed? What was the principal idea behind its origination? I would like to know this so that I can have a better ...
17
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2answers
1k views

Who are some forgotten mathematicians? [closed]

In Thomas' Calculus, he presents ''Nicole Oresme's Theorem'': $$ \sum_{n=1}^\infty {n\over 2^{n-1}}=4. $$ My first reaction was "who is this person?''. As it turns out, he was a Frenchman from the ...
27
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3answers
1k views

When did Fubini's name get applied to the theorem without measures?

Fubini's theorem, from 1907, expresses integration with respect to a product measure in terms of iterated integrals. The simpler version of this theorem for multiple Riemann integrals was used long ...
2
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0answers
174 views

A full math history encyclopedia. Is there one?

Is there a book or a site or a periodic or a encyclopedia or something like this that's a complete reference in math history, talking about all known mathematicians and their achievements, not ...
11
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4answers
1k views

What was the notation for functions before Euler?

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical ...
13
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1answer
541 views

Polarization: etymology question

The polarization identity expresses a symmetric bilinear form on a vector space in terms of its associated quadratic form: $$ \langle v,w\rangle = \frac{1}{2}(Q(v+w) - Q(v) - Q(w)), $$ where $Q(v) ...
0
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1answer
163 views

Where does the % symbol originate from? [duplicate]

Possible Duplicate: What is mathematical basis for the percent symbol (%)? Where does the % symbol originate from?
7
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3answers
276 views

The Hopfian property for groups

Let $G$ be a group, which for my purposes would be abelian. To say that $G$ has the Hopf property is to say that every epimorphism of $G$ is an automorphism. Does anyone happen to recall the context ...
10
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3answers
768 views

Who introduced the notation $x^2$?

In the book 'Problem Solving and Number Theory' I read The law of quadratic reciprocity was discovered for the first time, in a complex form, by L. Euler who published it in his paper ...
10
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1answer
352 views

Is Hilbert's second problem about the real numbers or the natural numbers?

In his famous "23 problems" speech, Hilbert gave his second problem as follows: The axioms of arithmetic are essentially nothing else than the known rules of calculation, with the addition of the ...
2
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0answers
973 views

History of mathematical symbols, especially the symbol for right angle

Yesterday a child asked me, why (historically) a right angle is denoted by an arc and a dot like in this picture: I dont't know it, but I am interested in it too, so I post this question to this ...
0
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1answer
806 views

History of solving linear equations with matrices

I'm solving linear equations with matrices right now and I wonder, how did it start. Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or ...
14
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2answers
2k views

Curious about math and Soviet Union

Why so many very good books were written by authors with Russian surnames?
11
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1answer
638 views

Why is $i$ called “imaginary”?

I was reading this question, and, after reading the responses, I felt like I had a much better understanding about how they're just another type of number definition. Why, then, are they called ...
18
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1answer
674 views

Did Leonardo of Pisa prove $n=4$ case of FLT?

Reputable on-line sources agree that Leonard 'Fibonacci' proved the nonexistence of positive-integer solutions to $c^4 - b^4 = a^2$ . Yet my change to Wikipedia to reflect this was reverted. I hope ...
7
votes
2answers
209 views

Which is the primary source of the Conway base 13 function?

I have been looking for the first appearance of the Conway base 13 function in the literature, but the only thing I have found is the wikipedia article whose unique element in the bibliography I ...
4
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2answers
262 views

Rota's “lure of the algorithm”?

Quoting Gian-Carlo Rota (from the Foreword to Richard Stanley's Enumerative Combinatorics Volume I), "In mathematics, however, the burden of choice faced by the writer is so heavy as to turn off all ...
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2answers
1k views

Origins of the modern definition of topology

The modern definition of topology is 'a family of subsets of a set $X$ containing the empty set and $X$, closed under unions and finite intersections'. In Grundzüge der Mengenlehre (1914) Hausdorff ...
3
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1answer
779 views

Why are variables lowercased?

While contemplating the existence of math, I came across an interesting problem: Why are variables often lowercased? There may not be a reason, but if there is, I would like to find out. Maybe it's ...
0
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1answer
185 views

When - during the study and development of- - and how were complex numbers introduced in the study of [real-valued] power series (expansions)?

Follow-up to: Mathematical reason for the validity of the equation: $S=1+x^2S$ and General question on relation between infinite series and complex numbers (This question seems broad at this stage, ...
1
vote
2answers
335 views

What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; ...
1
vote
1answer
374 views

Why is the zero factorial one i.e ($0!=1$)? [duplicate]

Possible Duplicate: Prove $0! = 1$ from first principles Why does 0! = 1? I was wondering why, $0! = 1$ Can anyone please help me understand it. Thanks.
3
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0answers
214 views

What's the origin of the terminology “Normalization” in commutative algebra?

Since the terminology "normal", "normalized", etc has different meanings in mathematics (some geometric in flavor, like when referring to perpendicularity) and I just read in Eisenbud's book on ...
18
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2answers
943 views

Once and for all - “Rational numbers” - because of ratio, or because they make sense?

This is a question I'm sure was asked before but I can't find it. There are many sources claiming that the term "rational number" for the elements of $\mathbb{Q}$ comes from the word "ratio", since a ...
7
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2answers
693 views

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 ...
6
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2answers
161 views

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, ...
1
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1answer
235 views

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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3answers
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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”?
3
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1answer
124 views

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) ...
4
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2answers
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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 ...
27
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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 ...
5
votes
1answer
507 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 ...
1
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1answer
2k views

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 ...
101
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1answer
9k views

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.
14
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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 $$\int_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, can ...
8
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1answer
480 views

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. ...
3
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2answers
494 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
835 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?
27
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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 ...
13
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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 ...
10
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2answers
390 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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334 views

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
4k views

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 ...