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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3
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1answer
100 views

Did Fourier use heated metal rings as experimental evidence to justify his mathematical discoveries?

In his answer to a previous question Alexandre Eremenko pointed out that Joseph Fourier in his book Analytic Theory of Heat gave all kinds of arguments in favor of the following mathematical ...
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1answer
181 views

Did Euler produce any Russian text?

Wikipedia says that Euler (1707 - 1783) "mastered Russian and settled into life in Saint Petersburg" in 1727. Did he produce any Russian text, mathematical or personal? I can only find Latin,...
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Is there any English translation of this Gergonne paper?

This is the paper: “Variétés. Essai de dialectique rationnelle”. Annales de Mathématiques pures et appliquées, tome 7 (1816-1817), p. 189-228 (“Varieties. Essay about rational dialectic”, By J.D. ...
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Who invented the integers?

I know that Kronecker claimed it was God's doing, and that even prehistoric humans used some ways of counting. But I am curious where the idea of a sequence of numbers stretching out into infinity ...
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36 views

Did anyone ever propose the distinction between “divergent to infinity” as opposed to “divergent but with finite average”?

There are different regularization methods that allow us to ascribe finite values to divergent integrals, series or sequences. Still, in my view there is fundamental difference between divergent ...
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34 views

How did Roger Cotes come up with logarithm form of Euler formula?

I have been trying to get my head around how Roger Cotes first discovered Euler Formula. I knew how Euler did it, but I wanted a new perspective, especially from someone who discovered it earlier. ...
8
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1answer
159 views

When and where did scientific publications become the norm in mathematics?

In other words, how old is the practice of submitting mathematical work for peer review to specialized magazines? When/where it started to become the norm? My question is oriented toward the ...
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212 views

When did it become a norm for mathematicians not to read proofs of all the results they use? [closed]

Please include evidence in your answer. This question is not opinion-based. I've heard that mathematicians sometimes don't read proofs. The following is a quote from mathoverflow. ... I think a vast ...
2
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1answer
162 views

Why did the existential and universal quantifiers in logic took so long to become formalized into symbols after the invention of boolean algebra?

Was there a specific reason that prevented researchers in boolean algebra to invent such quantifiers in the flexible format that are known today earlier? Since the compact symbols for multiplication ...
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1answer
73 views

Did anyone ever propose a hypercomplex numbers system with more than one anisotropic axis?

The real number axis is asymmetric against zero: for instance, multiplication of two negative or two positive numbers will produce a positive number, a square root of a negative number is not real, ...
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1answer
61 views

Mathematical research institutes similar to Banff and Oberwolfach [closed]

What other institutes such as these two exist for a visit by a scientist for an undisturbed period of short research? Ideally with a good landscape. Dagstuhl is another one I found.
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Beltrami's Essay on the Interpretation of non-Euclidean Geometry

I am reading the Essay of the title written by Beltrami in Italian and I found a specific point of the essay which in my opinion could be fully clarified only if compared with its translations. At the ...
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211 views

Origin of Tensor Product

When and why did Mathematicians saw a need to define Tensor Products? I want to know the historical development of the idea "Tensor Product"?
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230 views

How did Yao come up with his minimum spanning tree algorithm?

I recently stumbled upon this text about Yao's algorithm for the minimum spanning tree (MST) and I was wondering if there are some preceding algorithms (other than Sollin's algorithm) that were ...
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109 views

Origins of Stone duality

My question is a mix of mathematical and historical, if you consider my question will be better answered in the mathematics community, please tell me. I want to know the historical roots of Stone's ...
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1answer
120 views

The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
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1answer
230 views

What is the origin of “banana brackets”?

"Banana" brackets are used to denote catamorphisms: Another notation found in the literature is . These symbols are very similar to the composition of a $($ and a $|$, is this similarity ...
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1answer
122 views

Why do we still use degrees and cycles if we all implicitly use radians in trigonometric functions?

For various reasons already discussed in other stackexchange posts, we implicitly use radians in trigonometric functions by convention. For example, one period of $sin(x)$ lies in $0 \leq x < 2\pi$,...
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2answers
306 views

A branch of mathematics which refused to be rigorous?

I'm currently in a class on formal mathematics/formal logic/axiomatic set theory. Someone asked, "At the end of the day, as mathematicians, why do we care about rigor?" My professor gave an ...
2
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1answer
111 views

First time the real numbers were axiomatized as the “unique complete ordered field”

(originally asked at M.SE: https://math.stackexchange.com/questions/4094361/first-time-the-reals-were-axiomatized-as-the-unique-complete-ordered-field) I'm looking for historical references on the ...
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5k views

On Einstein's proof of the so-called Pythagorean theorem

Part I In E. Maor's book [2, p. 117] we read that, somewhere in his Autobiographical Notes, Einstein wrote this: An uncle told me about the Pythagorean theorem before the holy geometry booklet had ...
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0answers
55 views

What is the middle name of George A. Grätzer?

What is the middle name of George A. Grätzer?
3
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1answer
118 views

What was the influence of Gauss on the understanding of the importance of non-Euclidean geometry?

As is known, Gauss came to similar conclusions as Lobachevskii in the problem of fifth postulate, but I don't know whether Gauss had any impact to the contemporaries in that story. Can anybody ...
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0answers
59 views

Appearance of the Dirac delta operator in Laplace's work

I found a reference to the following article ; O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat. Issled. Vyp. 20 (1975), 303-308, 381. I don't ...
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1answer
72 views

Origin of “Inverse Pythagorean Theorem”

There is a lot of information on the history of the Pythagorean theorem, but not much on its closely related cousin; the Inverse Pythagorean Theorem. Would appreciate any resources on the the history ...
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Equations in right-to-left languages

Is there an historical tradition in languages read right-to-left (Arabic, Hebrew, Urdu, etc.) to display mathematical equations in some right-to-left form? So, instead of $$x = \frac{-b \pm \sqrt{b^2 -...
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1answer
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Is there a 'lost calculus'?

Are there any 'lost' theorems of calculus that could be used to 'simplify' it? For example, are there ways to calculate derivatives without using limits, maybe by some forgotten methods in calculus?
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4answers
10k views

Who first used the word “calculus”, and what did it describe?

This comment cites Wikipedia in stating that, before the development of the modern-day subject of calculus (i.e. analysis), the term "calculus" referred to general mathematics. Who first used the ...
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2answers
302 views

I am searching for a book of this form and content, is there any?

I would like to know is there a book that is both a history of mathematics and a collection of open problems? I know that there exist many books that cover either larger or smaller periods of the ...
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1answer
91 views

In what sense was it thought (at one point) that every lattice was distributive?

Blyth writes in his 2006 book Lattices (p. 65): It is a curious historical fact that it was originally thought that every lattice was distributive! That this is not so is shown by the following ...
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1answer
638 views

Meaning of passages by Gauss on the “convergence of expansions (in infinite series) of the (elliptical) equation of the center”?

Yesterday I took my time to look again into Schlesinger's essay on Gauss's contributions to analysis, and I found something new I didn't know about (so it caught my eye) in the last subsection of the ...
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1answer
75 views

Stories about the consequences of statistical simplification?

I am currently preparing a presentation about the value of more complex (specically: non-Gaussian) statistical inference. I thought it might be interesting to start the presentation with a small real-...
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1answer
216 views

Did Gosper or the Borweins first prove Ramanujans formula?

This is a copy of my question on MSE (https://math.stackexchange.com/questions/3372432) because this forum seems better suited for historical questions: In 1985, Gosper used the not-yet-proven formula ...
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1answer
147 views

($\varepsilon$, $\delta$)-definition of limit by Weierstrass

I am looking for the original ($\varepsilon$, $\delta$)-definition of limit by Weierstrass, but I cannot find an exact quote or a reference. I saw that somewhere it was claimed that this definition ...
2
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1answer
97 views

Yuktibhāṣā, 16th century, first modern proof of $\frac{\pi}4=\int_0^1 \frac{dt}{1+t^2}=\sum_{n\ge 0} \frac{(-1)^n}{2n+1}$

It is an Indian (Kerala) text, it would be the first modern proof (based on earlier knowledge) of $$\frac{\pi}4=\int_0^1 \frac{dt}{1+t^2}=\sum_{n\ge 0} \frac{(-1)^n}{2n+1}$$ The integral would be a ...
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1answer
62 views

History of primality testing

Consider a uniform random variable $n$ which is an integer in the interval $2^{1023} < n < 2^{1024}$. What is the oldest algorithm capable of determining whether or not $p$ is a probable prime ...
2
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1answer
74 views

How did the idea of a formal derivation emerge?

Infinitesimal calculus and the introduction of derivatives is often linked to Newton and Leibniz. I was wondering, when and why the idea of studying formal derivatives (e.g., of a formal polynomial) ...
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5answers
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What was the appeal of numerical analysis before computers?

I'm currently doing a numerical analysis course, and it seems many of the techniques were developed by mathematicians, such as Euler and Newton, who lived before the age of the computer. Why were ...
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3answers
215 views

Any book on the timeline of progress of mathematical concepts and applications?

I was wondering if there is any book that chronicles the progress of Math over the centuries and also mentions about how/when applications of various theories were discovered/invented. I have been ...
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3answers
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What led to the fall of Göttingen?

Göttingen was the place in which many important mathematicians such as Riemann worked. It was also one of the main locations for the development of quantum theory in the twenties (e.g. Heisenberg, ...
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2answers
229 views

For many years, were Emmy Noether and Helene Braun the only female mathematicians to obtain habilitation at Göttingen University?

Emmy Noether was the first woman in Germany to obtain habilitation in 1919. But I remember to have heard in the debate concerning the situation of women in academic mathematics that took place on the ...
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1answer
268 views

Fraenkel's appointment at Göttingen

Abraham Fraenkel grandpère writes on page 127 of his book recently translated into English: My professional career began in March 1919 with... an invitation to Göttingen to Privy Counselor Felix ...
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3answers
2k views

Source for Hilbert's famous quote “Mathematics in Göttingen? There really is none anymore”

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
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5answers
1k views

What led to the rise of Göttingen?

this is a counter part to my other question: What led to the fall of Göttingen?. Göttingen was a major university in which many famous physicists and mathematicians lived. It was located in ...
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4answers
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Why are étale morphisms called “étale”?

Alexander Grothendieck developed the theory of "locally trivial coverings spaces for rings/schemes" in SGAI as an analog to the theory of covering spaces in algebraic topology. He called such ...
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1answer
152 views

How did the Vietnamese manage set up the Vietnamese Mathematical Society during the Vietnam War?

The Vietnamese Mathematical Society was set up in 1965 by Le Van Thiem and Hoang Tuy. Both had studied in Europe, the former in Paris and Germany and the latter in Moscow. By 1965, the Vietnam War, ...
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4answers
5k views

Writing Mathematical Symbols in 20th century

As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
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95 views

Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
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72 views

Where can I find the complete papers of abstracts published by P. G. Tait in Proc. Roy. Soc. Edinburgh in 1880?

I am interested in looking up P. G. Tait's flawed proof of the four-colour theorem, published in 1880. The citation that I have seen is: P. G. Tait, On the colouring of maps, Proc. Roy. Soc. ...
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1answer
115 views

Who was Paul Gerwien?

The famed Wallace–Bolyai–Gerwien theorem has got its name from three mathematicians who proved it independently. More precisely speaking Farkas Bolyai first formulated the question. Gerwien proved ...

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