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For questions about those who do mathematics.

3
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4answers
229 views

Failures in math

I would like to have help in producing examples of mathematicians that, in some sense I'll explain below,turned their career into failure. I am mainly interested in examples from XIX and XXth century. ...
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0answers
66 views

English translation of Lagrange's Théorie des fonctions analytiques?

I've done some looking around and came up with nothing. There apparently was a German translation done by August Leopold Crelle, but I couldn't find anything else. If anyone else knows of an English ...
4
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1answer
154 views

Can we identify Paul Benacerraf in these photos

This question is about Paul Benacerraf, who worked on the philosophy of mathematics, and wrote the 1965 essay What numbers could not be (see: Benacerraf's identification problem). He was at Princeton ...
3
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1answer
148 views

Do these trigonometric identities belong to Antonio Cagnoli?

I'm new to this stack community, please bear with me as I try to explain my question properly. Recently I came across with these trigonometric identities (where $ \omega + \phi + \psi = 180^\circ $): ...
2
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1answer
159 views

On the birthdate of Gotthold Eisenstein

The birthdate of Gotthold Eisenstein is Apr. 16, 1823 as is stated in the Wikipedia. But a letter(whose recipient is Gauss) of Encke on Oct. 11, 1852 clearly states that the birthdate of Eisenstein is ...
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4answers
574 views

Help translate from German a quote by Hermann Weyl in Space Time Matter

I would like to find an accurate translation to the following quote from Space Time Matter: Man muß gegen diese Orgien des Formalismus, mit dem man heute sogar die Techniker zu belästigen beginnt, ...
2
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1answer
81 views

Translation of Gauss' Disquisitiones Arithmeticae

Out of curiosity I was searching for an English translation of the Disquisitiones Arithmeticae, and I found out that there is indeed one. It was translated in English in 1965 by a certain Arthur A. ...
3
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0answers
93 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 ...
5
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1answer
98 views

Was Paul Cohen a student or assistant of Gödel?

In The Man Who Loved Only Numbers, a biography about Paul Erdős, by Paul Hoffman, the author claims that Paul Cohen was "Gödel's former assistant" (p 225). However, I can't find any other sources ...
4
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1answer
147 views

Poincaré and the baker: was the anecdote true?

There is a story featuring Henri Poincaré and an unscrupuolous baker. Every day Poincaré bought a piece of bread which should have weighted 1 kg. After an year, the mathematician brought the baker to ...
6
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4answers
219 views

Mathematics PhD dissertations that opened a new field of research

I propose this as a companion wiki page to the one about PhD dissertations which contain a solution to an open problem in the style of big-list questions, thinking ...
7
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2answers
191 views

How was the sum of squares formula discovered by Archimedes?

AFAIK, Archimedes is credited with discovering the following formula for computing the sum of squares: $1^2 + 2^2 + 3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}$ This seems to have come up in his quest for ...
7
votes
1answer
196 views

What was Euler's first language?

Mathematicians of the 18th century and the Swiss people are known to speak and write every language. Leonhard Euler belongs to both of these categories and wrote articles in any language, I am not ...
4
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1answer
144 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 ...
2
votes
1answer
100 views

Does an English translation of Bombelli's L'Algebra exist?

I'm looking for an English translation of Rafael Bombelli's L'Algebra. From what I can tell searching the usual corners of the web, it doesn't exist, but I'm asking here just in case. I'm ...
2
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1answer
319 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?
1
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1answer
75 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?
2
votes
2answers
154 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
votes
2answers
79 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
195 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
51 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 ...
5
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0answers
87 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 ...
4
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3answers
152 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
119 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 ...
5
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2answers
203 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 ...
4
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2answers
155 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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0answers
93 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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0answers
91 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)] =>...
4
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1answer
191 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
97 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 ...
8
votes
6answers
397 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
votes
1answer
151 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
74 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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2answers
179 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
120 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 ...
6
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2answers
194 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
89 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 ...
3
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1answer
381 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 ...
3
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4answers
123 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
211 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 ...
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0answers
3k 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
votes
1answer
117 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 ...
4
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1answer
195 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 ...
5
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0answers
200 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
171 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, ...
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1answer
131 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
109 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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0answers
120 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
88 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
82 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 ...