Questions tagged [mathematicians]

For questions about those who do mathematics.

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4
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1answer
258 views

Who influenced Gauss in his abstract approach to mathematics?

I have studied that Gauss was one of the firsts mathematicians to defend this idea, about the Abstract Math and the conception of number, claiming that "What is calculated (in the sense of things ...
4
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1answer
289 views

Was Hilbert ambivalent about set theory?

There is the well-known quote of Hilbert: "No one shall drive us from the paradise which Cantor has created for us." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (...
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1answer
1k views

Who Invented The Number Line?

Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?
2
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1answer
127 views

What is the work of al-Khwārizmī for algorithms?

The word algorithm comes from al-Khwārizmī. From Wikipedia, I can read that he did a great work on algebra, but I could not find any algorithm attributed to him. Has he actually made any algorithm?
3
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2answers
894 views

What is the international standing of Italian mathematics?

Being Italian, I have a biased view on my homeland's mathematical impact in the world, so I would like to get some impartial opinion on the topic. I would measure the mathematical relevance in terms, ...
3
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2answers
144 views

What was the significance of Eisenstein's discovery of invariants?

I am trying to decipher a portion of James Joseph Sylvester's 1869 address entitled "The Study That Knows Nothing of Observation", which, among other things, surveys the landscape of 19th century ...
5
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1answer
300 views

Source of cartoon lampooning Felix Klein

There is an interesting cartoon in the book Lillian Hoddeson, Ernst Braun, Jurgen Teichmann, Spencer Weart (Eds.) Out of the Crystal Maze: Chapters from The History of Solid State Physics. Oxford ...
2
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1answer
127 views

Nomizu's structural approach to differential geometry

In this article in Wikipedia about Katsumi Nomizu https://en.wikipedia.org/wiki/Katsumi_Nomizu it is written that "Over the course of his career, Katsumi Nomizu was influential in determining the ...
9
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2answers
419 views

What did Fermat do as a lawyer?

Fermat is easily one of the best known mathematicians of all time. We all know about Fermat's Last Theorem, Fermat's Little Theorem, his quadrature rule, his invention of probability theory, etc. ...
5
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0answers
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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3answers
501 views

When were the concepts of pure and applied Mathematics introduced?

I know that there are no standard definitions for pure and applied mathematics however I would like to know who first considered them as two separate entities, I have seen people mention it was around ...
3
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1answer
186 views

Does Lakatos' argument in favour of 'informal mathematics' hold up in most cases?

Lakatos, in his Proofs and Refutations, rejects the Euclidean methodology and exposition of mathematics: where axioms and definitions precede the proofs. In other words, a Euclidean mathematician ...
6
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2answers
772 views

What is the correct statement of Cauchy’s erroneous theorem on continuity?

I read recently that Cours includes a famous, or perhaps infamous, error in that Cauchy states and proves a false result concerning sequences of continuous functions. (Here, obviously, continuous ...
5
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2answers
229 views

Are there any records that show how Hilbert came to “invent” or “discover” Hilbert spaces?

I think it's fuzzy as to whether or not this question is appropriate to ask on this site. The reason I ask it that the characteristics of Hilbert spaces are very much used in expressing quantum ...
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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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179 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)] =>...
5
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1answer
783 views

What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
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0answers
133 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 ...
11
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6answers
2k views

Why was modern science and mathematics a European phenomenon?

Of course much of this can be debated on what you mean by the word “modern” But most of us would agree that the Arabic World and places like India were the leading mathematical and ...
2
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1answer
226 views

Did someone refer to a “plague of indices” in tensor calculus?

I do not mean the "debauch of indices" discussed at Debauches of indices: Translation request I have a memory of someone talking about a "plague" of indices, or perhaps of tensors. Maybe I am just ...
3
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0answers
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 ...
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3answers
929 views

How did Newton & Raphson's version of the N-R method differ?

To quote Wikipedia, Raphson's most notable work... contains a method, now known as the Newton–Raphson method... Newton had developed a very similar formula in his Method of Fluxions, written in ...
2
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1answer
148 views

Did Kepler influence Fermat?

On page 347 in his "Mathematical Thought, volume 1", Morris Kline writes: "The work on the third class of problems, finding the maxima and minima of functions, may be said to begin with an ...
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2answers
552 views

What did Farcas Bolyai write to his son?

There are famous quotes about what Farcas Bolyai wrote to his son Janos to persuade him not to study the "theory of parallels " or what is now known as hyperbolic geometry But not all translation of ...
4
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1answer
99 views

Name of a XIXth-century German scientist from the University of Berlin

In December 1892, the french mathematician Charles Hermite had a jubilee celebration. He received a number of letters and telegrams. One of them is from the members of the University of Berlin, see ...
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1answer
1k views

Paul Erdos' quote “Mathematics is not yet ready for such problems”

It is believed, and often cited, that in relation to the Collatz conjecture Paul Erdos once said "Mathematics is not yet ready for such problems". However, I have not found any credible reference for ...
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164 views

Time for big results to become widely recognized in the scientific community

What are some examples of big results in mathematics and or physics that took a long time to be considered groundbreaking? What was the length of time from the original publication to the recognition? ...
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1answer
355 views

Who was the first to prove that $\pi$ was a real number? [closed]

Recently, there were many topics in sci.math discussed by so many (mathematicians, logicians, physicians, cranks and anti-cranks,..etc) the old definition of $\pi$ that is still considered valid up to ...
23
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1answer
19k views

Story of Grothendieck's Prime Number

There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which goes roughly as follows (cf. this wikipedia article): In a mathematical conversation, someone suggested to ...
2
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1answer
154 views

Did Cantor knew the work of Paul du Bois-Reymond (the original inventor of the diagonal argument proof method in mathematics)? [duplicate]

In the wikipedia page about Cantor's diagonal argument, it says: Historically, the diagonal argument first appeared in the work of Paul du Bois-Reymond in 1875. However, the diagonal argument is ...
5
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1answer
340 views

Who classified plane isometries first?

There are only four types of plane isometries: translations, rotations, reflections, and glide reflections. My question is: who was the first person who proved this? I asked this question personally ...
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0answers
223 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 ...
4
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1answer
244 views

Why and who was the first to denote the square root operation in fractional form as $1/2$

Basically, the square root operation was discovered and proved rigorously from the Pythagorean theorem, it was denoted by square root of a rational number say $n$ as $\sqrt{n}$, but at a later stage, ...
2
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1answer
207 views

Fields of Study Introduced by Leonhard Euler

Leonhard Euler is called the Father of Graph Theory. He also started off the studies of Calculus of Variations. Which all are the other mathematical/science disciplines that evolved as an ...
2
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1answer
438 views

History of the origins and development of problems of finding maximum and minimum values of quantities

I am aware that perhaps the earliest source concerning problems of maximum and minimum values occurs in Euclid's Elements. After Euclid, Archimedes of Syracuse and Apollonius of Perga seem to consider ...
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146 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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1answer
187 views

Who was Puppe of the Puppe sequence?

I have had difficulty locating the full name and story of the mathematician Puppe whose name adorns the beloved underlying long-exact sequence algebraic topology is built on. Does anyone know who they ...
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1answer
109 views

Who said that theory of probability was not mathematics?

I seem to remember that as late as in the XIX century there was a prominent mathematician who denied that the theory of probability was part of mathematics, since it does not deal with certainty. Do ...
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0answers
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 ...
5
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3answers
775 views

Are there well-known mathematicians who shared Arnold's view about mathematics as natural science?

V. I. Arnold asserted that mathematics is a natural science: Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where ...
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1answer
53 views

Lobachevsky and the University of Kazan

When I read about Nikolai Lobachevsky  it is said that the university and Kazan itself was not very important or well known but also when I check Kazan in the 1800 's it was in the top 10 of the ...
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2answers
1k views

Who first considered the $f$ in $f(x)$ as an object in itself, and who decided to call it a function?

The question is in the title, but allow me to provide some background. I’m aware that Leibniz introduced the word “function” into mathematics (around 1673) and that Johann Bernoulli or Euler ...
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2answers
142 views

Books on recent developments of abstract mathematics

I've read Marcus Du Sautoy's "The Music of Primes" recently and, although I'm not so much interested in number theory, I really liked it for the global perspective on the subject, though at an "...
4
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1answer
340 views

Grothendieck and the Gaussian integral

This article goes something like this: In a discussion with Grothendieck, Messing mentioned the formula expressing the integral of $\exp(-x^2)$ in terms of $\pi$, which is proved in every calculus ...
6
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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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5answers
642 views

Are there any famous mathematicians who did regular physical workouts?

Because regular physical exercise is in theory linked to better brain function and is also recommended in another question here on stack exchange, I wonder if there are any famous mathematicians who ...
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2answers
324 views

Jakob or Jacob Bernoulli?

What is the correct spelling of the name of the brother to the Swiss mathematician Johann Bernoulli? I've seen it spelt both ways, which one is the correct one?
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1answer
156 views

Why did Einstein get a better hearing in Goettingen than Berlin?

Jeremy Gray in his 2008 book writes matter-of-factly that Albert Einstein "found he got a better hearing from Hilbert and Klein in Goettingen than he did from his colleagues in Berlin" (page 326). ...
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3answers
315 views

Evaluating the Mehrtens hypothesis concerning Felix Klein

Historian H. Mehrtens hypothesized an opposition between moderns and countermoderns in early 20th century mathematics, with the former led by Hilbert and the latter by Klein. Hilbert's lecture at the ...
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125 views

Why did Nikolai Luzin almost commit suicide?

I tried accesing the original article without much success. Can someone fill in the details ?

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