Questions tagged [mathematicians]

For questions about those who do mathematics.

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17
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695 views

Did Kontsevich start a lecture with “one I will not define, the other nobody knows how to define, and we will be proving that they are equivalent”?

The story was circulating in early 2000s, so presumably it happened in 1990s. Kontsevich, it goes, opened a lecture course on mirror symmetry with:"This course is about two categories. One I will not ...
12
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261 views

Who was that forgetful mathematician?

Who was the (Japanese?) mathematician who said in a lecture that a certain conjecture still remained to be proved, and one of the students present told him that he (the mathematician) had already ...
12
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268 views

What was the typical format of a 16th century mathematical debate?

In The Equation that Couldn't be Solved, Mario Livio writes of academia in 16th century Bologna. Apparently, mathematicians would take part in public debates, sometimes involving solving problems. ...
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201 views

Did John Von Neumann hate pure mathematics that became too abstract?

John von Neumann wrote the following in his essay The Mathematician: As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only ...
7
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557 views

About the LOR of John Nash, was there any relationship between Richard Duffin and Solomon Lefschetz?

In Academia SE, there is a question about the credibility of Prof. Richard Duffin, who wrote the notorious letter of recommendation for John Nash, who later received the Nobel Memorial Prize in ...
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480 views

What was Gödel's proof that errors in U.S. constitution could allow the U.S. to become a fascist dictatorship?

According to this document, Kurt Gödel had discovered logical inconsistiencies in the U.S. constitution that could theoretically allow it to become a dictatorship. Morgenstern told him not to bring it ...
5
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125 views

Photo of Wilhelm Ackermann

I am writing a text on the Theory of Computation. I am looking for a photo of the mathematician Wilhelm Ackermann. He is well-known in the field, was a student of one of the most famous ...
5
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90 views

Is there any historical evidence of this quote E.T. Bell attributed to C.G.J. Jacobi?

I read Men of Mathematics by E.T. Bell long ago, and this quote he attributed to Jacobi stuck with me: Certainly I have sometimes endangered my health from overwork, but what of it? Only cabbages ...
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99 views

What was Littlewood's quip about Hardy and plagiarism?

I'm searching for a quote by Littlewood about Hardy not giving proper credit. The story (as I remember it) is that Littlewood claimed uncredited authorship of something Hardy wrote, Hardy claimed it ...
5
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93 views

Nature of Fermat's friend Lalouvère's activities as censor?

Fermat had a friend at Toulouse named Lalouvère. Lalouvère was censor, jesuit, and mathematician (in alphabetical order). Antonella Romano writes on page 512 of her book La Contre-Réforme ...
5
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221 views

Who gave you infinitesimal epsilon?

As someone reputed among certain historians to have given you the epsilon Cauchy startled me by using $\varepsilon$ to denote an infinitely small number in his 1826 text on differential geometry; see ...
5
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527 views

Why isn't Aryabhata more famous than Pythagoras?

You saw the question right. Why isn't it so? Aryabhata had done more things than him. Is it because of the 400 or 500 years of difference between their existence? Pythagoras is famous most for his ...
5
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176 views

Reflections in the 18th century

It is well known that the theory of reflections was considerably developed during the 19th century with the development of group theory (e.g. Klein) and the theory of transformations. However, I'm ...
4
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173 views

Is there a biography of Robert Risch?

The Risch algorithm for computing symbolic integrals was developed by Robert Risch in the 1968-70 time frame. Based on the German Wikipedia article, I know that Risch was awarded a Ph.D. by U.C. ...
4
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163 views

How old might Emmy Noether be in this picture?

I have not found bibliographic data to show what age Noether was in this picture: And I cannot estimate well either by her clothes or her face. Can anyone here help me? In the past I have known ...
4
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202 views

Symbolism in illustration for a book by Riccati

Wikipedia has a jpeg of the front cover of the book Opere (1761) by Jacopo Riccati, author of the celebrated Riccati equation. What is the symbolism incorporated in this illustration? See discussion ...
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128 views

A Lecture by Polya on Symmetric Algebraic Equations with an Unexpected Conclusion

Sometime in 1980 George Polya gave a lecture at the University of Minnesota about solutions of algebraic equations that have symmetry in the appearance of the variables in the equation (any ...
4
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1answer
134 views

Who formalized integer numbers?

I'm currently working on a thesis about Zermelo's axioms. In my first chapter I'm giving an introduction to the numerical treatment that Cantor gave to infinity. When I was writing something about ...
3
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128 views

How did Euler obtain this formula from a paper/work in 1748?

I am reading this book on trigonometric series, "Тригонометрические ряды от Эйлера до Лебега" (Trigonometric series from Euler to Lebesgue) , it is in Russian, and my Russian is abysmal. But ...
3
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1answer
92 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 ...
3
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84 views

How did Kolmogorov came up with his formalization of intuitionistic logic?

According to this article Kolmogorov published a paper in 1925 in which he attempted to formalize Brouwer’s intuitionistic mathematics. In that paper there are the following logical formulas: \begin{...
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63 views

How much ground was prepared for Riemann so that he could conjecture Riemann hypothesis?

Although I do not doubt in Riemann˙s originality, I would like to know how much complex analysis was developed up to the day when Riemann conjectured what is today called Riemann hypothesis and how ...
3
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53 views

Asymptotically Periodic Potentials

Who came up with the idea of solving elliptic equations with periodic potentials and from there solving elliptic equations with asymptotically periodic potentials? I heard it was Pierre Louis Lions, ...
3
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126 views

Textbooks used by Oliver Heaviside

Oliver Heaviside achieved a very high level in mathematics and physics by self-study, starting from a modest school-level math, and working alone in his room, without a tutor. Is it known what ...
3
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92 views

Who first “depressed” the cubic equation?

In his Ars Magna Cardano specifies procedures to "depress" a cubic - a means to convert an equation such as $x^3+6x^2=100$ to $y^3=84+12y$, eliminating the $x^2$ term. Was he the one who discovered ...
3
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104 views

Courant (1943) and History of Finite Element Method

I am interested in the history of Finite Element Methods and Methods of Weighted Residuals (MWR), especially reduced quadrature and collocation methods. I have a paper coming out called “Orthogonal ...
3
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77 views

A portrait of Bombelli

Is there any known portrait of Rafael Bombelli? I don't think so, but if you visit his MacTutor biography, you will see there this picture: It is clear to me that this cannot possibly be a picture of ...
3
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124 views

How many active mathematicians were there in Euler's time?

It seems that when you play around with the Math Genealogy Project, starting at some contemporary mathematician and going backwards through their advisor, advisor's advisor, etc., you tend to arrive ...
3
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221 views

Priority on lemniscate of Gerono?

The Lemniscate of Gerono is a special case of the Lissajous curves. The dates for the two mathematicians are fairly close: Gerono (1799-1891) and Lissajous (1822-1880). Historically who has priority ...
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80 views

What motivated Green to develop his theorem in order to calculate work for a non conservative vector field?

I am somewhat amazed at the depth of the theorem but I believe it involved his work with electricity and magnetism. Additionally I don't think he had a formal education. I have not found much on this ...
3
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92 views

Who is the first to give the proof of insolvability of quintic functions using Galois theory?

The first correct proof of the insolvability of the quintic is due to Abel. But my question is who gave the proof of insolvability of the quintic using Galois theory? Does Abel know about Galois ...
2
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124 views

What was Newton's road to his discovery of “Puiseux series” and “Newton polygon”?

In my opinion, one of Isaac Newton's greatest achievements in the "purer" aspects of mathematics was his discovery of Puiseux series; power series with fractional exponents. According to p.6 ...
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162 views

What was Havil's source for the statement that G.H. Hardy would offer his Savillian chair to whoever could prove $\gamma$ irrational?

In Havil's 2003 book Gamma he states that Hardy offered up his chair in Oxford to whoever could prove that the Euler-Mascheroni constant $\gamma$ is irrational. I'm almost positive I had heard a ...
2
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258 views

Grothendieck and Gaussian integral

http://www.jmilne.org/math/apocrypha.html This article goes something like this: "In a discussion with Grothendieck, Messing mentioned the formula expressing the integral of exp(-x2) in terms of pi,...
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165 views

Works of mathematician François Viète

I'm searching for a book or an online copy of complete works of the mathematician François Viète, preferably in English. Any help will be appreciated. Thanks.
2
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2k views

Kakutani's Lemma

I read this story a while ago, and I'm wondering whether there's any proof that it is true or whether it's just made up? One day Shizuo Kakutani…was teaching a class at Yale. He wrote down a ...
2
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104 views

Are there any memorial of Marcel Riesz in Lund?

Marcel Riesz spent most of his career in Lund (Sweden). Are there any memorial of Marcel Riesz in Lund? A plaque or a sculpture? I was looking for information about it, but I didn't find any. I ...
2
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100 views

Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
2
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159 views

The intersection of history, mathematics, and geography

I was looking for some material on the history of fractional calculus and googled Pincherle Amaldi to find a source. Up popped a map of the environs of the University of Rome and there was the ...
2
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1answer
172 views

Are there any mathematicians who expressed non-obvious sets of rules on how to do research?

I recently saw a paper where there are presented some rules on how to learn mathematics (and do research) which were firstly articulated by Lagrange. Are there any similar rules that were expressed ...
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29 views

Timeline for the earliest work on Frobenius problems

If $a, b$ are positive and coprime integers, then the set of linear combinations of $a$ and $b$ with nonnegative coefficients is all integers past $(a - 1)(b - 1)$; i.e. $\{ \lambda_1 a + \lambda_2 b :...
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56 views

Which mathematical objects retained the names given by their discoverer(s)?

Many mathematical objects and even theories are named after people, and most of the people with mathematical things named after them did not name said things after themselves. There is the famous ...
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41 views

Where did the Delannoy numbers make their first appearance?

I am writing a short exposition on the central Delannoy numbers and would like to find the year which Henri Delannoy first introduced them in a formal setting. I believe Delannoy's initial ...
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84 views

Who came up with a formula expressing the sign function in terms of the absolute value?

I read here and here that Karl Weierstrass used "| |" to indicate absolute value in 1841. The same sources indicate that Leopold Kronecker wrote of the sign function in 1878. Here it is indicated that ...
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99 views

Looking for Cantor's correspondence

I am trying to collect all available letters written or received by Cantor or written between his colleagues about Cantor. I have searched already the literature given below. But I would like to ...
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117 views

How did Euler stumble on this proof?

Euler proved $n=641$ divides $2^{32}+1$ by noting $n=5^4+2^4=5\times 2^7+1$ so $$2^{32}\equiv-5^4\times 2^{28}=-(5\times 2^7)^4\equiv-1\,(\text{mod}\, n).$$How did he happen upon this realisation? One ...
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176 views

Timeline of mathematical foundation?

As it is globally known that set theory as a foundation of mathematics, although in the beginning we didn't call it "Set" rather group of elements. For example - set of [1(banana) + 2(apple)+1(cow)] =>...
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132 views

18th and 19th century skeptics of imaginary numbers?

Complex numbers were used in as early as the 16th century to solve cubic equations, but they didn't gain wide acceptance until the late 18th and early 19th century. What is the reason for the 200 year ...
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145 views

Which mathematician first proved the laws of arithmetic?

Specifically, the associative, distributive, and commutative laws of addition and multiplication. Was it Peano?
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134 views

Was Newton aware of a nascent inverse function theorem?

More specifically, was Newton aware that given an inverse pair of functions $f$ and $h$ such that $$f(h(x)) = x = h(f(x))$$ about the origin that, for $$(x,y)=(h(y),f(x)),$$ the derivatives satisfy ...