Questions tagged [mathematicians]
For questions about those who do mathematics.
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Is it the 'd' or 'D' operator?
Philip J. Davis' article on the history of the gamma function (PDF) mentions how Leibniz proposed the iterated differential operator (p. 851 in the upper right corner, or p. 3 of the PDF, about half-...
6
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1answer
95 views
Who first proved that only primes of the form $4k+1$ divide odd integers of the form $n^2+1$?
I am writing a paper and I would like to cite the person(s) who proved that only primes of the form $4k+1$ can evenly divide odd integers of the form $n^2+1$?
For example, if $n=8$, $n^2 + 1 = 65$ ...
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1answer
137 views
Why didn't John von Neumann win the Turing Award, Fields Medal or Nobel Prize?
From what I've read in Wikipedia, John von Neumann made a stupendous number of contributions to economics, computer science and mathematics. Why, then, didn't he receive a top award in any of these ...
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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 ...
7
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1answer
190 views
Did the author of Alice in Wonderland make any substantial original discoveries in mathematics?
Charles Lutwidge Dodgson, better known by his pen name of Lewis Carroll, was a mathematics lecturer at Oxford University and today is primarily famous for his fanciful stories laced with mathematical ...
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13answers
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Examples of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right?
What are the most glaring examples -- if any -- of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right?
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0answers
74 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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1answer
74 views
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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2answers
117 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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2answers
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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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1answer
93 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
...
3
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0answers
63 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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1answer
68 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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1answer
84 views
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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106 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 ...
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38 views
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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1answer
67 views
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 ...
4
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0answers
148 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
359 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 ...
4
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1answer
180 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 ...
4
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1answer
191 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 $):
...
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1answer
166 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
611 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
130 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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0answers
95 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
133 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 ...
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1answer
220 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
476 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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1answer
392 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
165 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
144 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
534 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
103 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
215 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
88 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
226 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
64 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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0answers
90 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 ...
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3answers
200 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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1answer
135 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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332 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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2answers
173 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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103 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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105 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)] =>...
