Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics

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History of the Fourier transform

Does anyone know a good book or article on the History of the Fourier transform? It's first appearance (of the transform) and use in particular? Or at least some source with some historical ...
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2answers
516 views

When is the degree of this number 3?

I am helping a friend of mine, that works in history of mathematics. She is studying the story of the solution of the cubic equation by Cardano. Sometimes she asks me some mathematical questions, that ...
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1answer
178 views

Historical question about MacMahon theorem, Wronski relation etc…

Seemingly the same fact goes under several names: MacMahon master theorem, Wronski relation, unnamed fact about symmetric functions - I wonder what is history and what should be ``correct name'' ? ...
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3answers
577 views

Who came up with the Euler-Lagrange equation?

Which man came up with the solution to the basic Calculus of Variations problem first? http://en.wikipedia.org/wiki/Euler-Lagrange Makes it sound like Lagrange got it first in 1755, then sent it to ...
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3answers
669 views

Serre's theorem about regularity and homological dimension

One of the nicest results I know of is (Auslander-Buchsbaum-)Serre's theorem asserting that a (commutative!) local ring is regular iff it has finite global dimensional. I'd like to ask a somewhat ...
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0answers
259 views

What is the history of the notion of subdivision of categories?

A recent answer by Peter May prompts me to ask a question which I have been considering to ask for several months. (The reason why I have not asked it before is that it is not directly related to my ...
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2answers
630 views

Did Hermite really prove “Hermite's Theorem” on number field discriminants?

Hermite's theorem, as it is typically called, is that there are only finitely many number fields of bounded (equivalently, fixed) discriminant. The usual proof (see Neukirch's Algebraic Number Theory ...
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1answer
424 views

What is the origin of the term magma?

Wikipedia credits Bourbaki with coining it, but doesn't provide a source. Does anyone happen to know the motivation for using this term?
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2answers
456 views

Who discovered the asymptotic formula for the number of partitions of n into distinct parts?

Who was the first to develop the asymptotic formulae for the distinct parts version of $p(n)?$
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253 views

Who proved that the plane partition generating function is valid?

I know Major Macmahon conjectured the formula $$ \prod_{m=1}^\infty \frac{1}{(1-q^m)^m}=1 + \sum_{n=1}^\infty PL(n)q^n$$ but who was the first to prove it?
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1answer
184 views

About the term “tangential derivation” on a free Lie algebra.

Let $\mathcal{lie}_n$ be the free Lie algebra generated by $n$ elements $x_1,\ldots, x_n$. A derivation $u\in \text{Der}(\mathcal{lie}_n)$ is called tangential if there exist $a_i\in \mathcal{lie}_n, ...
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19answers
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History Question: AUTObiography of Mathematicians

According to Wikipedia, an autobiography is an account of the life of a person, written by that person sometimes with a collaborator. An autobiography offers the author the ability to recreate ...
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360 views

Historical question: fiber bundles

I am sorry if this question is too trivial but I couldn't find the answer. Who did first classify topological principal $G$-bundles for some topological group $G$? So, I mean that equivalence ...
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2answers
316 views

Have derivatives of determinants along 1-psg's ever been 'coherently' computed via Jacobi's formula?

Suppose $\mathfrak{p}$ denotes all the symmetric matrices in $\mathfrak{sl}_{2n} \mathbb{R}$. Then for each parameterized 1-dimensional linear subspace $\xi=\xi(t)$ of $\mathfrak{p}$ we get a ...
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0answers
401 views

sine and Archimedes' derivation of the area of the circle

The elementary "opposite over hypotenuse" definition of the sine function defines the sine of an angle, not a real number. As discussed in the article "A Circular Argument" [Fred Richman, The College ...
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2answers
442 views

Why limit of discrete series representation?

In what sense is the limit of discrete series representation of $SL(2, \mathbb{R})$ a limit of discrete series representations? Where does the name origin from?
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5answers
926 views

What is the “ray” in ray class group?

I have never seen any algebraic number theory book discuss the origin of the term "ray class group." Does anyone know where the word "ray" comes from in this context? I always thought it might be a ...
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65answers
7k views

Fiction books about mathematicians? [closed]

What are some fiction books about mathematicians? It seems to me rather difficult for writers to create good books on this subject. Some years ago I thought there were no such books at all. There ...
6
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1answer
398 views

Who introduced the concept of Primitive recursive functions?

I have thought that Gödel introduced the concept of Primitive recursive functions in his seminal paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme" (I hope I ...
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2answers
946 views

Heuristics for the Hodge Conjecture

W. V. D. Hodge is famous for his Hodge conjecture, one of the Millennium prize problems. Hodge might have had some rough heuristics or ideas that led him to the formulation of the conjecture. I am ...
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6answers
797 views

Proof by `universal receiver'

Anyone following the news knows about the major breakthoughs that have taken place recently in $3$-manifold topology. These have come via a route whose big-picture I find to be conceptually ...
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6answers
2k views

When has pure mathematics been influenced by the social context of mathematicians?

I recently learned that the Moscow school of descriptive set theory (Egorov, Lusin, etc.) was deeply influenced by the religious movement of Name Worshiping in Russia, as recounted in Graham and ...
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0answers
210 views

First Table of Random Numbers

What was the first table of random numbers of any sort? The best I can do is Tippett and Pearson's Random Sampling Numbers of 1927. Can anybody identify an earlier table? Thanks for any ...
4
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1answer
190 views

History of provably total functions of a theory

Provably total functions of an arithmetical theory is one of the tools used in proof theoretic analysis of theories. I am looking for early history of its development. In particular, Where was ...
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1answer
836 views

Raoul Bott's quote on Morse Theory cited by Bestvina and Kahle: where is it from?

I wanted to properly cite the following awesome quote: Every mathematician has a secret weapon. Mine is Morse theory. - Raoul Bott Now this has been attributed to Bott in precisely two places ...
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3answers
907 views

Sum of the sum-of-divisors function

I was looking at the abstract of a paper [1] which claims that [2] and [3] prove $$ \sum_{n\le x}\sigma(n)-\frac{\pi^2}{12}x^2=\Omega(x\log\log x). $$ But I cannot find the above—or indeed, ...
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1answer
1k views

Why is this theorem attributed to Serre?

Page $117$ of Atiyah, MacDonald's Introduction to Commutative Algebra text has the following theorem. Let $P(M,t)$ denote the Poincare- series of $M$. $\textbf{Theorem.}$ ...
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3answers
2k views

Contacting an eminent mathematician

I have recently started a PhD. and am researching an area that two now eminent mathematicians devoted considerable time to in the 1980s. However, there appears to have been fairly moderate focus on ...
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1answer
525 views

Klein's Protocols: A window into our mathematical past

Klein's Protocols in over 8,000 pages recording seminars organized from 1872 to 1913 by Felix Klein and given by Klein, his colleagues, students and other invited speakers, including luminaries such ...
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0answers
771 views

Origins of the Nerve Theorem

Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question: Who was the first to prove the Nerve Theorem?
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1answer
2k views

FFT and Butterfly Diagram

Wikipedia presents butterfly as "a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into ...
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2answers
1k views

How the Fast Fourier Transform got its name

In 1971, T.S. Huang published a paper in IEEE Computer, May-June, pp.15, called How the Fast Fourier Transform Got its Name, available here. At the bottom of the paper, he wrotes: "The Chinese ...
12
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1answer
495 views

In search of an early picture of Max Dehn

I am trying to find a copy of a picture "Mathematische Gesellschaft: Group Portrait, Faculty, University of Göttingen (1899)." This picture was published by Springer-Verlag as a poster in 1985, but ...
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1answer
664 views

Steinmetz, Laplace and Fourier Transforms

I am looking for references on Steinmetz Transform and its relation with Laplace and Fourier Transforms. There is an Italian Wikipedia page about this topic but with no references.
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Mathematician, Graciano Ricalde

Does anyone understand more precisely how to explain the 5th degree equation and elliptic functions accomplishments of Mathematician Graciano Ricalde? I am his great grand-daughter and trying to ...
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11answers
2k views

Approachable French Masters

It has been my general desire for a few years to acquire the basics in other European languages for the purpose of reading some of the classics in their original language, in a similar vein to this ...
3
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1answer
492 views

What does the 'V' in 'V-manifold' stand for?

The story of how the name 'orbifold' came about is pretty well-documented, but I can't find any explanation as to why Satake originally named orbifolds 'V-manifolds'. The 'manifold' part is clear ...
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6answers
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In “splendid isolation”

While browsing the Net for some articles related to the history of the Whittaker-Shannon sampling theorem, so important to our digital world today, I came across this passage by H. D. Luke in The ...
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3answers
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How to Tackle the Smooth Poincare Conjecture

The last remaining problem in this whole "everything is a sphere" business, is the Smooth Poincare Conjecture in dimension 4: If $X\simeq_\text{homo.eq.} S^4$ then $X\approx_\text{diffeo} S^4$. ...
3
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1answer
562 views

Fourier and Bessel

Oliver Heaviside, on page 387 of Electrical Papers, Vol. I, Macmillan and Co., 1892, available here, writes $$v = 1 - \frac{n^2r^2}{2^2} + \frac{n^4r^4}{2^2 4^2} - \frac{n^6r^6}{2^24^26^2} + \ldots ...
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353 views

Official names for specific compound sentences

This question is, admittedly, a little less mathematical than what I normal ask. I seemed to remember that the compound sentence $A\wedge \neg A$ has an official name (maybe even "contradiction" but ...
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3answers
772 views

History of the Sampling Theorem

In January, 1949, Shannon publishes the paper Communication in the Presence of Noise, Proc. IRE, Vol. 37, no. 1, pp. 10-21, available here, which establishes the Information Theory. In this paper, the ...
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2answers
547 views

References for the Poincaré-Cartan forms

Hello, everybody. I'm looking for some reference about the Poincaré-Cartan form, I do not know how it is defined, I just know that it is used in Lagrangian mechanics but I have not found any ...
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5answers
6k views

New arXiv procedures?

Recently I encountered a new phenomenon when I tried to submit a paper to arXiv. The paper was an erratum to another, already published, paper and will be published separately. I got a message from ...
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9answers
5k views

Have we ever lost any mathematics?

The history of mathematics over the last 200 years has many occasions when the fundamental assumptions of an area have been shown to be flawed, or even wrong. Yet I cannot think of any examples where, ...
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17answers
3k views

Examples of conjectures that were widely believed to be true but later proved false

It seems to me that almost all conjectures (hypotheses) that were widely believed by mathematicians to be true were proved true later, if they ever got proved. Are there any notable exceptions?
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Gauss's views on pure mathematics

According to Wikipedia's entry on Gauss: "Though Gauss had been up to that point supported by the stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure ...
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919 views

History surrounding Gauss Theorema Egregium and differential geometry

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Gauss Theorema Egregium, that is the Gaussian ...
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2answers
909 views

Who was the first to formulate the inverse function theorem?

Let $U\subset \mathbb{R}^n$ and let $F:U\to \mathbb{R}^n$. The 'classical' inverse function theorem gives a sufficient condition for the existence and differentiability of the inverse function of $F$. ...
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542 views

Are k-spaces named for Kelley?

On page 58 of Mark Hovey's book Model Categories, he states the following definitions: "A subset $U$ of a space $X$ is compactly open if for every continuous $f:K\rightarrow X$ where $K$ is ...