Questions tagged [mathematicians]

For questions about those who do mathematics.

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6
votes
1answer
149 views

History of summing integers with natural powers

In my 10th class school material, it is given that Aryabhatta discovered the following formulas: $\sum n=\dfrac{n(n+1)}{2}$ $\sum n^2=\dfrac{n(n+1)(2n+1)}{6}$ $\sum n^3=\dfrac{n^2(n+1)^2}{4}$ Is ...
10
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2answers
4k views

The history and motivation of eigenvectors

I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
8
votes
1answer
727 views

Did Gauss say “there have been but three epoch-making mathematicians, Archimedes, Newton and Eisenstein”?

In Wikipedia I found this claim by E.T. Bell in his Men of Mathematics. However in the next paragraph it says that "it is doubtful that Gauss put Eisenstein in the same league as Newton", which makes ...
5
votes
0answers
181 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 ...
12
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0answers
269 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. ...
6
votes
1answer
142 views

English translation of Omar Khayyám's mathematical work

Is there any current English translation of the mathematical works of Omar Khayyám?
4
votes
1answer
887 views

Lagrange buried in the Panthéon

Why is Lagrange buried in the Panthéon in Paris, but not any other French mathematicians or theoretical physicists? I would understand if they were not represented at all, but it seems absurd to ...
3
votes
1answer
363 views

Galois quote about his refused work

I read (page 10 here, in portuguese) that Galois used the following phrase when his memoirs wasn't accept by the French Academy of Sciences: Oh! Innocent cherubs! Could someone give references or ...
4
votes
1answer
381 views

What did Lagrange do with his quantity (the Lagrangian in classical mechanics)?

When I was learning classical mechanics, I was quite baffled by the Hamilton's principle, since it involves a quantity named after Lagrange. So, it seems that the principle was not discovered by ...
7
votes
4answers
612 views

Is there a biography of Ramanujan for mathematicians?

Like many mathematicians, I have long been fascinated by Ramanujan's work and also by what little I know of his life. I would like to learn more, but have found the standard book on this subject (...
3
votes
1answer
184 views

Timeline of Leibniz' Propositional Logic

Gottfried Leibniz developed a system of propositional logic in the late 1600's, which wasn't published until 1903, when it was discovered in the Royal Library of Hanover by Louis Couturat. How did ...
17
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3answers
2k views

Source for Hilbert's famous quote “Mathematics in Göttingen? There really is none anymore”

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
12
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3answers
546 views

What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?

I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I ...
17
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0answers
700 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 ...
5
votes
1answer
176 views

Non-standard model of arithmetic and Gödel's theorem

I've read Skolem's paper on his non-standard models of the arithmetic ("Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ...
8
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1answer
3k views

Why did Laplace invent the Laplace transform?

Why did Laplace invent the Laplace transform? What was the context? Was it before Fourier or after?
12
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1answer
12k views

Who invented short and long division?

I am curious who came up with algorithms that we use today to manually solve mathematical division problems, such as short or long division; how were they established or standardized that way and why?...
13
votes
1answer
653 views

Was Pólya’s “How To Solve It” originally written in German or English (or some other language)?

I seem to fail at googling a simple question: In which language did Pólya originally write “How To Solve It” (or “Schule des Denkens”, as is the German title)? Did he translate the book himself to ...
3
votes
0answers
94 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 ...
3
votes
2answers
420 views

Who discovered the difference between the infinities?

As we know, there is a difference between the (infinite) size (or cardinality) of the integer numbers and the size of the reals ($\aleph_0$ and $\mathfrak c=2^{\aleph_0}$). Who discovered it first?
9
votes
1answer
2k views

Who really invented the integration symbol?

Most of the sources online say that Leibniz invented the sign. There's also this answer on this site which says so. That is fine. But recently when I was watching Cosmos, I noticed this: See the ...
6
votes
1answer
2k views

First use of Bernoulli's inequality and its name

The Wikipedia article “Bernoulli's inequality” says, that this inequality is called after the mathematician Jacob Bernoulli. Was he the first one using the inequality? Why is this inequality named ...
2
votes
1answer
362 views

How did Archimedes complete this impossible task? [closed]

I am reading this book on Archimedes, famous mathematician of his days and now, and it was found that he caculated the amount of sand in the known Universe at his days, which is from Mercury to ...
12
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1answer
299 views

Who blocked publication of “Mathematics in USSR. 1958-1967”?

A while ago, in USSR there were published two very voluminous collections entitled "Mathematics in USSR for 30 years. 1917-1947" and "Mathematics in USSR for 40 years. 1917-1957". These collections ...
14
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3answers
945 views

3 Poles and 3 Texans who had read “Principia Mathematica”

To quote Bertrand Russell, "My Philosophical Development", Simon and Schuster, N.Y., 1959, p. 86: I used to know of only six people who had read the later parts of the book [Principia Mathematica]...
4
votes
2answers
365 views

Historical Instances of Set Theory

Context: I've been reading a lot about Set Theory lately, and how it suddenly sprung onto the mathematical scene in the late 1800's, thanks largely to Cantor. But it seems strange to me that no one ...
4
votes
2answers
319 views

Alexander Grothendieck; Where had he been all this time? [closed]

Recently, I heard that the great Grothendieck have passed away(RIP). But until last year I've been aware that he is lost from the world. So how could they figure out his death? My resources on this ...
31
votes
5answers
8k views

Who introduced the Principle of Mathematical Induction for the first time?

Can you tell me the name of the mathematician, who introduced the Principle of Mathematical Induction for the first time? (with reliable source). Please don't say De Morgan because I have read the ...
17
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3answers
4k views

Who created topology, and when, and what problems led to this creation?

Who created topology, when did that happen, and how was it discovered?
24
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6answers
86k views

Discovery of zero

I have read at many places that zero was discovered by Aryabhata but when i was discussing this with my mathematics teacher he told me that zero had already been discovered before Aryabhata and it was ...
42
votes
2answers
10k views

Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?

I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...
8
votes
2answers
195 views

Leibniz's stand on axioms and definitions

Recently while discussing with a friend he claimed that Leibniz was fond of proceeding axiomatically and from definitions. I find this hard to believe. My conception is that Leibniz was more ...
19
votes
4answers
18k views

Did Abraham De Moivre really predict his own death?

At the last point of his life, he noted that he slept 15 minutes extra every night then he calculated that he would die on the day that the extra 15 minutes a night accumulated to 24 hours. That day ...
13
votes
2answers
468 views

When did the people start using the portraits of the two Euclids interchangeably?

According to the folks of Wikipedia, this is the portrait of Euclid of Alexandria (the "Father of Geometry"): Yet, I read several years ago on MathOverflow that the individual in the ...
22
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3answers
2k views

How did Gauss become the “the prince of mathematicians”?

Gauss is probably the most famous mathematician today, his face even appears on one of European bills. But he did not have a charismatic personality, like Galois, nor was particularly interested in ...
36
votes
3answers
3k views

What motivated Cantor to invent set theory?

I can't imagine mathematics without sets, but the question "what was mathematics like before there were sets" is not answerable, I think. Instead, a good answer to the title question should cover a ...
22
votes
6answers
2k views

Why were so many pre-18th century Mathematicians polymaths?

It is well known that famous names such as Gauss, Euler and Newton were polymaths as well as their main fields of study and contributed from optics to ship building. Why was this the case in the past? ...
22
votes
2answers
2k views

Hilbert's reaction to Gödel's incompleteness theorems

Is it known how Hilbert initially reacted to Gödel's incompleteness theorems upon their announcement at the Königsberg conference in 1930, or their publication in 1931?
19
votes
3answers
511 views

What was the connection between David Hilbert and Stefan Banach?

The so-called "Hilbert space" is named after mathematician David Hilbert. Later, this was generalized into "Banach spaces" by Stefan Banach. My understanding is that Hilbert was ...
66
votes
4answers
10k views

Why was Évariste Galois killed?

It is well known that Évariste Galois died a young man. I have heard that he died in a duel. What was the duel about? More rather what is the back story behind his death and did he really write down ...
67
votes
3answers
9k views

What evidence is there that Fermat had a proof for his Last Theorem?

Aside from the fact that Fermat was a genius, is it probable that he actually did have a proof? Some specifics that I think would point one way or another: Would the mathematics of his day allow him ...

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