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For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns

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During Gauss's lifetime, was there a 'living' mathematician more prestigious than Gauss?

I became curious about Cauchy after reading that he was more prestigious than Gauss during his lifetime. During Gauss's lifetime, was there a 'living' mathematician more prestigious than Gauss?
Mathhhhhhhhhh's user avatar
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Why didn't Alexander Grothendieck win the Wolf Prize and Abel Prize? [closed]

Although Grothendieck was clearly one of the greatest mathematicians of the 20th century and one of the greatest mathematicians of all time, it is hard to understand why he did not win Wolf Prize and ...
Lie's user avatar
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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 ...
kcrisman's user avatar
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30 views

Did Lagrange ever made mathematical mistakes in the books or papers he published? [closed]

What's interesting about Lagrange to me is that all the descriptions of him by his contemporaries, and even a century later, essentially make him seem perfect. has he ever made any mathematical ...
olipo's user avatar
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1 answer
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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 ...
Lag's user avatar
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1 answer
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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?
olipo's user avatar
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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 ...
Metehan Turan's user avatar
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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 ...
Numeral's user avatar
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2 votes
1 answer
166 views

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, ...
Lukas Heger's user avatar
4 votes
2 answers
151 views

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 ...
user21035's user avatar
1 vote
2 answers
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Who was the first to understand a derivative and integral as both giving rise to new functions?

NOTE: Even if not called "functions" surely someone understood that returning something other than a numerical value was significant? If I understand it correctly, Newton, for example, was ...
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5 votes
1 answer
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Why was FFT needed to detect Soviet nuclear tests?

On the Wikipedia page of Fast Fourier transform it mentions that [John] Tukey came up with the idea during a meeting of President Kennedy's Science Advisory Committee where a discussion topic ...
anonymous's user avatar
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The history of under-40 rule of Fields Medal: has it ever been seriously discussed, voted on to change or at least challenged in IMU/ICM?

From Wikipedia, the under-40 rule is based on Fields' desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further ...
No One's user avatar
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The Root of a Geometric Progression

Good people! I'm presently in the process of putting something together on Euler and Gauss and cyclotomy and modular arithmetic, and I noticed that when it comes to the terminology primitive root ...
StormyTeacup's user avatar
2 votes
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95 views

Who "made" Gauss?

I was looking at the math genealogy related to probabilities and there was pretty much a straight line going from Kolmogorov to Laplace. Then I got to Markov's sequence which gets a bit messy: Markov -...
student's user avatar
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1 answer
86 views

Equicardinality of $\mathbb{R}$ and $\mathbb{R}^2$ via interleaving decimal expansions

As Fernando Q. Gouvêa notes in his paper, Was Cantor Surprised? (Amer. Math. Monthly 118 (March 2011), 198–209) Cantor initially tried to prove that $(0,1]$ and $(0,1] \times (0,1]$ have the same ...
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When did people first thought of a purely symbolic logic?

In Euclid's Elements, the famous five planar geometry axioms are formulated in common language (ancient greek in this case) and use ambiguous terms. On the other hand, modern theories like ZFC or ...
Weier's user avatar
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Were Ten and One Hundred Thousand treated more like "special" numbers at one point than today?

Note: Not English specific but about any major system of recording or discussing numbers. I know some systems would not give 100 a special place. People today when discussing largish numbers tend to ...
releseabe's user avatar
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7 votes
5 answers
374 views

Math concepts introduced by physicists and made rigorous later

I am looking for mathematical concepts (*) which have been introduced by physicists in a non rigorous way (e.g. without a formal definition, without rigorous proofs of the results, etc.) and used to ...
Weier's user avatar
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3 votes
1 answer
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What is the origin of the method of undetermined coefficients?

This MSE post asked about a specific integration technique that appears to be attributed to Charles Hermite, per a comment. The OP's source calls the technique el método alemán, i.e. the German method....
user170231's user avatar
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Was Euler aware of the general form of the characterization of primes of the form $p=x^2+ny^2$ for arbitrary $n>0$?

If $n$ is a positive integer then there is a monic irreducible polynomial $f(x)$ such that if $p$ is an odd prime not dividing $n$ nor the discriminant of $f$ then $$ p=x^2+ny^2\iff \left(\frac{-n}{p}\...
Croqueta's user avatar
2 votes
0 answers
76 views

What did Gauss think about V. A. Lebesgue's proof of quadratic reciprocity?

The proof can be found here (pdf). It was published in 1838 and Gauss lived until 1855, so I would guess that he read it. Did Gauss say anything about it?
Croqueta's user avatar
4 votes
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192 views

How and why was catastrophe theory brought to its knees?

How applications of catastrophe theory outside mathematics stalled the theory, and why? I know that the theory had its fair share of popularity during the 1970s, with many distinguished mathematicians ...
Prelude's user avatar
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Are there alternatives functions for the gamma function that was used as generalisation for the factorials?

I asked this question on MSE here $$\Gamma(x)= \int_0^ \infty e^{-t}t^{x-1}dt \ \ \ \ \ x>0. $$ Bohr and Mollerup showed that the gamma function is the only positive function $f$ defined on $...
pie's user avatar
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0 answers
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Who discovered that the Lanczos method can only calculate extremal eigenvalues of large matrices?

The Lanczos tri-diagonalization process is widely or even routinely used today. It is said that it is useful for obtaining the extremal eigenvalues, but useless for medium eigenvalues. But who ...
poisson's user avatar
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1 answer
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Where does Oliver Heaviside fit in the ranks of physicists/mathematicians? [closed]

It seems to me that he was able to reformulate Maxwell's equations in a more understandable form and in fact come up with vector calculus without finishing high school would arguably cause him to be ...
releseabe's user avatar
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1 vote
1 answer
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F = ma -- How was did we come to understand that this compact form expressed what Newton said in words?

My understanding is, Newton in the 17th century did not use this formula but rather said, in words basically that if you apply a force it will cause a mass to accelerate in the direction of that force....
releseabe's user avatar
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6 votes
1 answer
1k views

How come there is no portrait of Legendre?

Besides the famous cartoon, of course, there seems to be no portrait of Legendre. Legendre is well regarded nowadays and he was also quite influential at his time, for example, Jacobi and Abel praised ...
Croqueta's user avatar
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37 views

Why did Kronecker say "the integers are the work of God, the rest is the work of man"? [duplicate]

To me, it seems no number is the work of God, they are all concepts of the mind. However, it seems negative numbers are more artificial than the rest of the numbers out there. So why did he describe ...
Demon's user avatar
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1 answer
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Is there a resource about integer constructions and motivations?

I have an assignment about the foundations of mathematics. I am trying to compile a list where I get common construction of integers and a small writing about the constructor and their explanation. ...
Fraser James's user avatar
1 vote
0 answers
47 views

Did Dedekind's construction of the integers and rational numbers become standard in mathematics textbooks?

I am referring to the construction using pairs of natural numbers in 1858. Since we use pretty much the same construction today in some analysis courses (Analysis 1, Terence Tao), except without the ...
Demon's user avatar
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3 votes
4 answers
150 views

Translated articles of Fatou and Julia

Is there any English translation of the 1918-1920 Memoirs of Fatou and Julia on the iteration of rational functions?
Prelude's user avatar
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1 vote
1 answer
152 views

When were negative numbers fully accepted into mathematics?

Dedekind gave a construction and explanation of integers and rational in 1858. This was as ordered pairs of natural numbers. I'm not sure if this was the standard view of these objects after this ...
Demon's user avatar
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3 votes
0 answers
55 views

What can I read to learn the history of multivariable calculus?

People have been doing calculus of several variables since well before the concepts of vectors, matrices, and linear algebra were formalized. Where can I learn about the development of multivariable ...
Dominic Stewart-Guido's user avatar
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0 answers
31 views

Did Heinrich Weber have a structural approach to mathematics similar to Dedekind?

So I was reading a History of Mathematics by Katz, and noticed that the first definition of a field came from Weber, who had previously done extensive joint work with Dedekind. His definition was used ...
Demon's user avatar
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1 vote
1 answer
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Did Dedekind's work directly influence the work of Hilbert?

I am wondering if Dedekind's theory about the structure of deductive science influenced the work of Hilbert. Hilbert obviously favored axioms at the beginnings of a deductive science, whereas Dedekind ...
Demon's user avatar
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4 votes
3 answers
281 views

Origin of modern definition of a function as a graph

In the past, I came across a very elegant direct definition (below) of a function, which is based on the fundamental concepts of triples, pairs, and sets. However, I find it difficult to search the ...
Kamil Kiełczewski's user avatar
4 votes
2 answers
773 views

When and why was the concept of "having a least upper bound" dubbed "completeness", as in Axiom of Completeness?

The Axiom of Completeness states that any non-empty set with an upper bound has a least upper bound. When and why was this concept of least upper bound dubbed "completeness"? It's true, of ...
SRobertJames's user avatar
1 vote
0 answers
71 views

What does Dedekind mean by "laws characteristic for the concepts"?

I’m slightly confused by what Dedekind means by “characteristic for the concepts they designate” in the quote below: "But [. . . ] these extensions of definitions no longer allow scope for ...
Jerry's user avatar
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0 answers
31 views

Notation for Propositional values in Church's "Simple Theory of Types"

In Alanzo Church's "A Formulation of the Simple Theory of Types" (The Journal of Symbolic Logic 5 no.2 (1940) 56--68, DOI:10.2307/2266170), he adopts the ...
Alex Nelson's user avatar
1 vote
0 answers
73 views

Did the principle of permanence have an influence on mathematicians like Dedekind and Cauchy?

Around the time when mathematics was becoming formal, the notion of detaching from attaching "contextual interpretation" to symbols in algebra, up to the point of avoiding inconsistency (...
Demon's user avatar
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4 votes
1 answer
366 views

What were Auguste Comte's contributions to mathematics (if any)?

Auguste Comte is often described (e.g., on Wikipedia) as a “mathematician” besides being a philosopher of science. I am aware that he taught mathematics (he was at various times a répétiteur and/or ...
Gro-Tsen's user avatar
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2 votes
0 answers
120 views

I would like to read about Euler's view on negative numbers

So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical ...
Demon's user avatar
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0 votes
1 answer
113 views

Why and how did the study of complex numbers progress despite the denial of negative numbers?

I am going over some history of the complex numbers, and two things baffle me (and they are not mathematics). From Cardano's time to around the 18th century, negative numbers were not accepted by all ...
James's user avatar
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0 answers
114 views

How did negative numbers “force themselves” onto Cardano, and was it analogous to how imaginary numbers were forced upon him?

I was reading “A brief history of numbers” by Corry, but I came across a part that confused me. Cardano accepted the law of signs for “subtractions” proposed by an older group of Italian ...
Fraser's user avatar
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2 votes
1 answer
169 views

Did Rafael Bombelli write any commentary about his rules for arithmetic involving negative numbers?

Rafael Bombelli was the first European mathematician to write about the laws of arithmetic for negative numbers. On Wikipedia I read that he wrote: “Minus 5 times minus 6 makes plus 30”. I also read ...
Fraser's user avatar
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3 votes
3 answers
259 views

History of cohomology theory

I saw this post. And I already posted it on Math stack exchange, but since someone recommended this site, I'm refining it and posting it again. And I understand that the mathematical object called ...
user1274233's user avatar
1 vote
0 answers
68 views

How exactly did Auguste Bravais come up with the regression line?

I am new to statistics and linear regression and I came across the face that auguste bravais discovered regression line but didn't realize it. Auguste Bravais (1811-1863), professor of astronomy and ...
Alexander Obidiegwu's user avatar
3 votes
1 answer
122 views

Mathematization of natural sciences

When was a mathematical formula (instead of just words) used for the 1st time in natural sciences to describe a natural phenomenon?
Sedat Olcer's user avatar
1 vote
1 answer
104 views

David Hilbert's paper: Substitution of the group of cyclotomic field

A question about a notation in David Hilberts's "Ein neuer Beweis des Kroneckerschen Fundamentalsatzes über Abelsche Zahlkörper" (here a german online available source, not sure if there ...
user267839's user avatar

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