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Questions tagged [mathematicians]

For questions about those who do mathematics.

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Who was the first person who emphasis the importance of proof?

I think it should be an ancient Greek mathematician who was interested in proving all triangle has inner angles summing to 180 degree? Was it Thales?
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95 views

Why do mathematicians call ~ 'twiddle'?

Every one of my lecturers have always called it this, as do I, despite the fact that I know its properly called 'tilde'. Does anyone have any clue where this convention comes from and why it might ...
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Modern Views on Pythagoras [duplicate]

I've done a lot of research on Pythagoras and the Pythagoreans and am currently in a state of uncertainty. I do believe Pythagoras existed, but I am unsure if he can be given credit to hardly anything ...
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Irrational numbers math in old Roman age [duplicate]

I know that Hippasus proved that $√2$ is irrational number. My question is how were they doing the mathmatical operations like multiplication for rational numbers like 1.41421356237 I can do ...
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Does anybody know the history of how Peter Gustav Lejeune Dirichlet came up with the “nowhere continuous” Dirichlet function?

So I am writing a research paper on the properties of the Dirichlet function (the function with 1 if x is rational and 0 if x is irrational), and I wanted to include some historical background on how ...
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66 views

Cantor's fortune

Wiki says that his transfinite numbers met opposition: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics,[8] and Leopold Kronecker's public ...
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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 ...
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1answer
65 views

Gregory's integration of $\sec\theta$

The integral of the secant function was first correctly conjectured by Henry Bond in the 1640s, and Isaac Newton was aware of his conjecture in 1665, although no proof was published until 1668. Of ...
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Did Nikolai Luzin plagiarize?

Luzin was accused of plagiarism and other misconduct by Kolmogorov and other students during the Luzin Affair of 1936. Were these allegations actually true?
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How did the integer degrees angles counting being first adopted in geometry and mathematics? [duplicate]

The purpose of this question is trying to know originally how did counting in integer degrees angles from (one degree to $360$ degrees) being adopted basically in geometry, despite the impossibility ...
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Example of: Two researchers working on the same question but get opposite conclusions [closed]

I wish to know about whether such example exists, could someone please help and tell me some stories about this? p.s: Also I wonder why such thing can happen. I wish the two main characters in the ...
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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 ...
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Kronecker's aphorism [duplicate]

The common translation of Kronecker's "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" is something like "God made the integers, all else is man's handiwork." But I have ...
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Existence of Pythagoras Resources

I am aware that approximately two years ago a question was posted on the existence of Pythagoras. After two years, I want to gain more incite on the thought of those on this site. I was drawn to the ...
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143 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 ...
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4answers
326 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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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 ...
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167 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 ...
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1answer
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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 $): ...
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1answer
163 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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603 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, ...
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1answer
106 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. ...
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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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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 ...
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185 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 ...
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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 ...
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2answers
340 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 ...
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316 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 ...
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1answer
159 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 ...
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1answer
131 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 ...
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1answer
455 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?
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1answer
95 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?
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2answers
183 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, ...
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2answers
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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 ...
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1answer
204 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 ...
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1answer
59 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 ...
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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 ...
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175 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 ...
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126 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 ...
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297 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 ...
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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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101 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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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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224 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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106 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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567 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 ...
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165 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 ...
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75 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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2answers
254 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 ...
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1answer
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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 ...