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

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History of elliptic curves

In one sense elliptic curves are a rather modern object as some of its properties have been studied only in the last century or so. But in another sense there are a very classical object for studying ...
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1answer
100 views

When was the significance of $i$ first noticed?

Complex analysis is an entire field of mathematics that focuses on the use of the complex constant $i$. When was the significance of $i$, an imaginary number, first noticed? If I did not know some ...
13
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3answers
773 views

Journals of math history?

In a related question to this one, in what journals do math historians publish their article in? Brian M. Scott provided a link to Judy Grabiner's, who is a math historian, home page and it seems that ...
20
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2answers
967 views

History of Modern Mathematics Available on the Internet

I have been meaning to ask this question for some time, and have been spurred to do so by Georges Elencwajg's fantastic answer to this question and the link contained therein. In my free time I ...
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2answers
1k views

Who is a Math Historian?

In the context of classes, it is very often that discussion on the history of mathematics arises, whether it'd be on who should a lemma be attributed to or a certain event that occurred during the ...
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2answers
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Why is the topological pressure called pressure?

Let us consider a compact topological space $X$, and a continuous function $f$ acting on $X$. One of the most important quantities related to such a topological dynamical system is the entropy. For ...
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1answer
156 views

History of Double Coset Enumeration.

I must know how and when it began. I can't seem to find anything historical on this. All I know up to this point is that Todd-Coxeter method was created in 1936. And, "words"? How did they even arise ...
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6answers
3k views

Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...
6
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1answer
283 views

What are “Lazard” sheaves?

Early in Categories, Allegories, by Freyd and Scedrov (p.12, in the section on basic examples) there appears the following example: Let $\mathcal{LH}$ be the category whose objects are topological ...
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1answer
90 views

“fluent” functions

In an old mathematics book (Ritt, 1948, p.5) I have come across the notion of "monogenic analytic" and "fluent" functions. These are complex valued functions. Has anyone heard of these terms before? ...
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0answers
128 views

Reference: Wittgenstein teaching mathematics

Can anyone give me any reference concerning L.Wittgenstein teaching school kids mathematics? I have been wondering what kind of mathematics he taught and how he lectured the material.
27
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4answers
2k views

Examples of mathematicians who lost interest in Math and got interested again?

I am looking for some examples, and hopefully some short biographies on mathematicians who lost interest in Math along the way, and somehow got rejuvenated again. (Better still, who managed to do ...
4
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2answers
113 views

Where/What are good sources to learn about the history of computation?

I'm writing a giant paper containing the history of computation, and unfortunately, I'm far from being an expert on this. So far I have only a few sentences; I traced computation back to 3000BC, ...
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4answers
1k views

The contributions of James Sylvester to linear algebra.

The claim is James Sylvester and Arthur Cayley are the fathers of Linear Algebra. I can find the various parts that Cayley contributed to Linear Algebra, but there is not much on the contributions ...
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1answer
164 views

Which automata recognise the algebraic numbers?

I am reading historical stuff on the algebraic and transcendental numbers. Descartes, in his Geometry, excluded all curves not expressible as algebraic equations. Later, Leibniz called such curves ...
20
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1answer
2k views

What was Ramanujan's solution?

The wikipedia entry on Ramanujan contains the following passage: One of his remarkable capabilities was the rapid solution for problems. He was sharing a room with P. C. Mahalanobis who had a ...
19
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2answers
644 views

Approximation for $\pi$

I just stumbled upon $$ \pi \approx \sqrt{ \frac{9}{5} } + \frac{9}{5} = 3.141640786 $$ which is $\delta = 0.0000481330$ different from $\pi$. Although this is a rather crude approximation I ...
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0answers
114 views

Opinions attributed to Gauss

In this article, Armand Borel writes the following: [...] In fact, during the next quarter century, we experienced a tremendous development of pure mathematics, bringing solutions of one ...
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2answers
2k views

Can somebody simply explain Wilson's theorem (for a 13 year old)

I am Rohan Kapur. This is my first time posting on the Mathematics site, although I am quite active on StackOverflow, the programming site. I am doing a Islamic Maths assignment at the moment for ...
15
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3answers
1k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...
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4answers
754 views

Why are there isosceles triangles? [closed]

Why are isosceles triangles called that — or called anything? Why is their class given a name? Why did they find their way into the Elements and every single elementary geometry text and course ...
4
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3answers
1k views

Are questions of convergence important in real life?

In the real world, do we ever need to worry about convergence and what not? I am not talking about whether recursive functions and such terminate, but convergence in analysis. It seems like the ...
10
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1answer
783 views

Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in ...
9
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1answer
556 views

Original author of an exponential generating function for the Bernoulli numbers?

The Bernoulli numbers were being used long before Bernoulli wrote about them, but according to Wikipedia, "The Swiss mathematician Jakob Bernoulli (1654–1705) was the first to realize the existence of ...
10
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1answer
829 views

History behind Exact Sequences.

I am very much interested in listening to the history behind the exact sequence. We know that the exact sequence is sequence of objects with morphisms such that image of one morphism equals to the ...
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0answers
155 views

What was Cayley's formula for the number of invariants? (Lost Formula!?)

I need to find Cayley's formula for the number of linearly independent invariants of homogenous polynomials. This is a combinatorial formula. He is believed to have discovered it in 1854. ...
11
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1answer
805 views

Riemann's thinking on symmetrizing the zeta functional equation

In the translated version of Riemann's classic On the Number of Prime Numbers less than a Given Quantity, he quickly derives the zeta functional equation through contour integration essentially as ...
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1answer
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ancient concepts and modern concepts

Is there an extant published expository account, comprehensible to all mathematicians, of the conceptual differences between ancient Greek mathematical concepts and modern ones? I have in mind things ...
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6answers
11k views

Why is a full turn of the circle 360°? Why not any other number?

I was just wondering why we have 90° degrees for a perpendicular angle. Why not 100° or any other number? What is the significance of 90° for the perpendicular or 360° for a circle? I didn't ever ...
4
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2answers
207 views

A typo in a formula of Ramanujan?

In Mathworld's article Gamma function, in line (96), we find the formula, $\sum_{k=0}^\infty (8k+1)\left(\frac{\Gamma(k+\frac{1}{4})}{k!\;\Gamma(\frac{1}{4})}\right)^4 = ...
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0answers
173 views

When did mathematicians think of axiomatically building or defining operations etc?

Edited question: In response to Qiaochu Yuan's comment asking me to narrow down the question,the edited question is as follows: When did mathematicians first think of axiomatically building set ...
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1answer
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Why are imaginary numbers called imaginary numbers

Why do we call imaginary numbers "imaginary numbers"? As far as I can tell, there's nothing really imaginary about them. They exist. They're used all the time. What makes them so "imaginary"?
5
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2answers
293 views

When the Impossible becomes Possible again

Many times mathematicians draw proofs about the impossibility of something. As an example, take the Abel–Ruffini theorem, which states no generic formula exists for quintic equations (I know the proof ...
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3answers
2k views

What did Gauss think about infinity?

I have someone who is begging for a conversation with me about infinity. He thinks that Cantor got it wrong, and suggested to me that Gauss did not really believe in infinity, and would not have ...
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2answers
729 views

What has been the first theorem discovered in the history of mathematics? [closed]

I know there are many ancient theorems like the Euclid's theoems concerning geomentry. The Pithagorean theorem is also very old, maybe known by Sumerians. Does someone knows what has been the first ...
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0answers
387 views

History of line integral.

I'm looking for some information about how the line integral was discovered, since I've been looking for a long time for this. I found that Riemann could integer discontinuity functions, then Poisson ...
174
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19answers
12k views

In the history of mathematics, has there ever been a mistake?

I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of ...
23
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5answers
1k views

Importance of rigor

I always have a hard time explaining the importance of rigor to my friends who are not mathematically minded. A lot of past mathematicians develop the foundations of today's mathematics without going ...
5
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2answers
266 views

Analytic versus Analytical Sets

Browsing MathOverflow I came across a question about analytical sets. Through the discussion following a comment made by our very own Asaf, I learned that bold face $\mathbf{\Sigma^1_1}$ and light ...
12
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2answers
241 views

Lie and Weierstrass' visualization of complex functions

I am reading Whittaker and Watson's A Course of Modern Analysis. In the third chapter where they discuss different ways to visualize functions that map the complex plane to the complex plane, they ...
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5answers
4k views

Why do we consider prime numbers important, and what are their applications other than number theory in pure math?

Why do we consider prime numbers important, and what are their applications other than number theory in pure math? I know that Number theory is devoted to studying prime numbers, but there must be ...
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4answers
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History of $f \circ g$

$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what ...
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4answers
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Why is the axiom of choice separated from the other axioms?

I don't know much about set theory or foundational mathematics, this question arose just out of curiosity. As far as I know, the widely accepted axioms of set theory is the Zermelo-Fraenkel axioms ...
0
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2answers
48 views

how to factor terms?

as i'm reading a paper a paper "An Underdetermined Linear System for GPS" By Dan Kalman and solving an equation ,and as i'm not good in math i missed there ,in factoring of the following equation: ...
4
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1answer
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History of Mathematics: Sophie Germain and Fermat's Last Theorem

Sophie Germain's greatest contribution to mathematics was in number theory. She discovered a special case of Fermat's Last Theorem which we now call the Germain Theorem. Stated precisely: The ...
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1answer
785 views

Reference request for “Weierstrass equation” and “Weierstrass normal form”

I would like to know more about the history of the widely used terms "Weierstrass equation" and "Weierstrass normal form", as they appear in the theory of elliptic curves. When were these terms first ...
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1answer
185 views

Expanding squares and simplification of equations

as i'm reading a paper "An Underdetermined Linear System for GPS" By Dan Kalman i understand the paper but when i traced the equations there's something i don't understand ,may be my mathematics is ...
2
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1answer
123 views

Chebyshev/Tchebycheff's results concerning $\phi(x)$.

The book "A SOURCE BOOK IN MATHEMATICS" has a great collection of mathematical papers. On of the is Chebyshev's Memoir on "The Totality of Primes Less Than a Given Number." The book states that ...
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1answer
418 views

Was the definition of $\mathrm{erf}$ changed at some point?

I have seen two competing definitions of the error function. When I was an undergrad, Spiegel's Mathematical Handbook of formulas and tables (mine is the 1968 edition) was the definitive authority, ...
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0answers
154 views

Do mathmatician ever prove that a theorem could not generalize into a much general theorem? Is there a historic mile stone example?

Do mathmatician ever prove that a theorem could not generalize into a much general theorem? Is there a historic mile-stone example refer to the above question?