Questions tagged [mathematics]
For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns
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Who was the first to give a proof of the cubic character of 2?
I am writing a paper on the cubic character of 2, and I am interested in the history of how the character of 2 developed. I am aware that Euler was the first to conjecture the form $p=C^{2}+27D^{2}$ ...
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Can you recommend a good book written on the history of Geometry?
Could you recommend a good book written on the history of Geometry? It would be even better if it were a comprehensive book covering from ancient Greek geometry to modern geometry.
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Who pioneered the use of the Fast Fourier Transform (FFT) for efficient multiplication?
The Fast Fourier Transform (FFT) is an efficient algorithm used in the computation of the discrete Fourier transform. While it's well-known for its applications in signal processing, it has also been ...
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Who was this scientist who saw his whole theory(ies) demolished by a publication
I once read somewhere that, in the beginning of the XXth century -if I'm not mistaken- a scientist saw his whole assumptions or theory utterly refuted by the publication of a book by a mathematician......
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Enriques' Principle of Degeneration
It is remarked here that Zariski's connectedness theorem is based / or vast generalizating & formalizating the so called "principle of degeneration" introduced by Federigo Enriques, ...
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Where did Russell eulogize mathematics as follows?
A colleague told me that Bertrand Russell expressed:
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to ...
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Motivation and history of Fubini's theorem
I saw the double integral version of Fubini's theorem on Wikipedia.
It was introduced by Guido Fubini in 1907. It states that if a function is Lebesgue integrable on a rectangle ${\displaystyle X\...
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Gauss and recursion – would defining factorial recursively have been quite surprising to him?
I understand that factorial, as the simplest example of a function that can be defined recursively, was fairly new in Gauss' time. The exclam notation was early 19th century, I believe.
I think Gauss ...
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A modern reinterpretation of Vandermonde's mathematical achievements
I already posted a question on the Mathematics Stack Exchange about a related topic, but after posting it, I realized that it is more appropriate for this site, so I am posting it again in this site.
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How did Jost Bürgi's logarithms work?
According to what I have gathered from the internet Jost Bürgi came up with the idea of logarithms (as he called Progress Tabulen) after learning a correspondence between arithmetic and geometric ...
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What are some examples of elegant solutions?
There are various problems in history such as the Basel problem which was solved by Euler using the Taylor expansion of the sine, then later by Cauchy by bounding the partial sum, both solutions were ...
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What is the historical origin of the concept of calculating area by multiplying length and width?
As per M. Schemmel, Ed., Spatial thinking and external representation: towards a historical epistemology of space. in Studies / Max Planck Research Library for the History and Development of Knowledge,...
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What is the history of the Scheme theory before Grothendieck?
If you read here, you will be able to read paragraphs like this:
Grothendieck created a synthesis out of these ideas, based in essence on the conceptual presentation of Zariski-Chevalley-Nagata. ...
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Egyptian origin of Euclid's axiomatisation of geometry
I recently watch this recording (in French) of a talk (La mathématique expérimentale) given by the mathematician Vladimir Arnold. There are some rather surprising claims about math history. One of ...
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Why are the categories of category theory called "category"?
The category-theoretical concept called "category" seems quite dissimilar to what we consider a "category" in everyday life or colloquial speech and even other fields of science, ...
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What's a Heine reference for the "Andréief-Heine identity"
The "Andréief identity" or "Andréief-Heine identity", which can be interpreted as a continuous analogue of the Cauchy-Binet formula, comes up a lot in the context of random matrix ...
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How was Laplace able to propose the Laplace expansion?
I read Sylvester's 1850 paper, which is on file here. If you look at page 147 of this file, you will see the following sentence:
Imagine any determinant set out under the form of a square array of
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History of Invertible linear transformations
Who studied invertible linear transformations for the first time? I would guess these linear transformations weren't studied for the sake of studying invertible linear transformations, they probably ...
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Regula Pigri: How far does it date back?
Regula pigri, or rule of the lazy, is a method of multiplication of single-digit numbers. If one is to multiply 6 by 8, one would start by bending one's fingers like so:
B B B B S B B S S S
...
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Did Grothendieck have any thoughts on foundations of mathematics? [closed]
I remember reading that Grothendieck didn't care much about foundational issues and didn't want to be 'stuck all the way down there'.
Does anybody know if he ever actually said this? Did he have any ...
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Does Henry Rice's doctoral dissertation exist online?
Henry Gordon Rice is perhaps best known for Rice's theorem, which states that any non-trivial semantic property of Turing machines is undecidable. In a footnote to his Trans. Amer. Math. Soc. article (...
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Origin of Multi-linear map
Multi-linear map is used to define the determinant. However, since the multi-linear map itself does not have linearity, I feel a sense of heterogeneity when I compare this concept with the contents ...
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Folk stories and notions in mathematics that are likely false, inaccurate, apocryphal, or poorly founded?
There are numerous popular folklore stories in mathematics, and it is an interesting question to understand the accuracy of these folk stories.
Folklore stories, and urban legends are subborn things, ...
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Historically are there any documented attempts at finding algorithms that are asymptotically faster than the FFT for the Discrete Fourier Transform?
I found out some bounds on the Discrete Fourier Transform calculation on certain models of computation but nothing on attempts at finding algorithms asymptotically faster than the Cooley-Tukey FFT on ...
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Does the paper "W.F. Eberlein, Axiomatic charge conjugation, J. Math. Phys. (to appear)" exist?
I found the reference
Axiomatic charge conjugation, J. Math. Phys. (to appear)
in W. F. Eberlein, Models of space-time, Bull. Amer. Math. Soc. 71 (1965), 731-736, (pdf) however, I don't find the ...
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Role of Alessandro Padoa in the development of modern mathematics
Here is an excerpt from ESSAI D’UNE THÉORIE ALGÉBRIQUE DES NOMBRES ENTIERS, PRÉCÉDÉ D’UNE INTRODUCTION LOGIQUE A UNE THÉORIE DÉDUCTIVE QUELCONQUE from Alessandro Padoa (as can be found here):
nous ...
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Were there any criticisms of his first FTA proof during Gauss's lifetime?
According to several papers related to Gauss' FTA proof, in the first proof he said, “It seems to be well demonstrated that an algebraic curve neither ends abruptly (as it happens in the ...
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When was the ‘mathematics department’ first established in universities?
It seems that 'mathematics' was within the category of 'philosophy', at least in universities, until 1799, when Gauss received a doctorate in 'philosophy' rather than a doctorate in 'mathematics'. So, ...
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Who first came up with the idea of a scheme in algebraic geometry? [duplicate]
At first, I thought that Alexander Grothendieck was the first to come up with the idea of the scheme and established it, but when I found out that the idea of the scheme existed even before ...
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Did Gauss ever explicitly claim ordinary least squares as his own?
I have seen Gauss claim in certain literature that he had been using the principle of least squares even before Legendre defined it. (It was probably a document calculating the orbit of the asteroid ...
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Was it after Riemann's death that Weierstrass gave a counterexample to Riemann's mapping theorem?
Since the period when Weierstrass pointed out the flaw in the proof of Riemann's mapping theorem is reported differently in different documents, I have doubts about the exact timing. When exactly did ...
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Did Riemann take for granted the existence of a function that achieves the minimum in the ‘Dirichlet principle’?
Or did Riemann take for granted the existence of a function that achieves the minimum value under the special assumption that used the Dirichlet principle (the assumption of partial smoothness as ...
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From which university did Riemann acquired Ph.D?
Did Riemann get a Ph.D from the University of Berlin? Or did Riemann get his Ph.D from the University of Göttingen? I thought he had acquired it from the University of Berlin, but when I found out ...
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Why isn't Boethius's Thesis more commonly accepted in mathematics and logic?
Why isn't Boethius's Thesis, that the negation of an implication is another implication where the consequent is negated, a commonly accepted axiom in mathematics and logic? It is an axiom of connexive ...
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Did Riemann leave any books?
As far as I know, Riemann never left any books,
but after accidentally discovering 'on the hypotheses which lie at the bases of geometry' registered as Riemann's book on Google,
I began to wonder. Did ...
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Was Riemann's research style closer to the 'collaborative' style of Grothendieck and von Neumann?
Or was he more of an 'independent' style like his teacher Gauss?
If you can give an objectively correct answer to this, what is the basis for it?
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Is it true that Aryabhata explicitly understood or stated the irrationality of $\pi$?
It is well known that Aryabhata, the prominent Indian mathematician and astronomer of the 5th century CE, made significant contributions to mathematics, including approximations of $\pi$ (pi). In his ...
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Who first introduced semantic and syntactic consequence
The relations $A \vdash B$, read "$A$ proves $B$'', and $A\vDash B$, read if $A$ is true then $B$ is true, are referred to as syntactic and semantic consequence, respectively.
In the history of ...
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How does the science community decide which scientist to credit for a particular discovery?
In the science community there are lots of cases where two or more scientists work on the same ideas or theories.
How is it decided which scientist to give credit for a particular discovery? What are ...
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History of representation theory
I read the book 'The Genesis of the Abstract Group Concept'. If you see page 91 of this book,
I wish to comment on the last two sections of Cauchy's paper. Both sections deal with a kind of ...
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Why Isaac Newton published his discoveries so much later than he discovered them?
Principia was completed in 1686 and published in 1687, but he discovered calculus, gravity and laws of motion long before (1665-1666 "Year of Wonders").Is this correct?
He wrote book Method ...
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Why is Einstein summation named after Einstein?
Why is Einstein summation of tensors (summation of repeated indices) named after Einstein?
"Einstein rule" in the Encyclopedia of Mathematics only says:
This rule was proposed by A. ...
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Grothendieck's Fine Topology in Esquisse d’un programme
I would like to clarify a couple points in the following excerpt from these notes (page 3) discussing Grothendieck's seminal Esquisse d’un programme pointing out the importance to reformalize the ...
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Source of Galileo quote on curves
In George Simmons' Calculus Gems there is an interesting quote, supposedly from Galileo, pertaining to whether one can compare curved and straight lines (in length, for instance):
Who is so blind as ...
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Does Lagrange's FTA proof meet rigorous requirements even by modern standards?
I know that Gauss pointed out flaws in Euler and d'Alembert's FTA proof when he submitted the FTA proof as a doctoral thesis in 1799, but I don't think I've ever seen any mention of Lagrange, so I'm ...
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Why did Grothendieck think that Deligne was more talented than him? [closed]
Was it just a sign of humility? Or was his idea of ‘talent’ a bit different from the general realm? And did Grothendieck regret that he could not solve the last part of the Weil conjecture?
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Why Did Riemann Venture into Number Theory for the Riemann Hypothesis?
I’m exploring the history behind the Riemann Hypothesis and I found something interesting. We know that Bernhard Riemann was mainly focused on complex analysis, but he also wrote a very important ...
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Where does the term "reflection" come from?
Earlier today, I was asked why a motion of the plane that fixes a line of points is called a reflection and I was stumped for an answer.
The best explanation I can think of is that the image of a ...
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What is the origin (and perhaps original) of this quote by André Weil
I found this quote by André Weil in a few places online:
As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, ...
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How did Fourier know an infinite number of frequencies were required to solve the heat equation?
If we look at the 1D heat equation on a conducting rod with non-insulated ends, we get the standard Heat Equation from which the Fourier series formula is derived. I know that the heat equation had ...
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