Questions tagged [mathematics]

For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns

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Are there written (19th century) sources expressing the belief that the intermediate value property is equivalent to continuity?

As asked in the title: Are there any written sources (from the 19th century) explicitly stating the belief that any function satisfying the intermediate value property is continuous? (I do not ...
Andrés E. Caicedo's user avatar
40 votes
3 answers
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 ...
Ben's user avatar
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16 votes
1 answer
1k views

When was the method of getting square roots (invented by Viète in 1610 and developed by Harriot in 1631) first taught to school children?

François Viète's On the Numerical Resolution of Powers by Exegetics published in 1610 (Viete, 2006, pp. 311-370) introduced one way of numerically solving polynomial equations, a special case of which ...
JRN's user avatar
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40 votes
6 answers
18k views

What is the difference between Calculus of Newton and that of Leibniz?

Are there any differences between the study of Calculus done by Newton as compared to that done by Leibniz? If yes, please mention point by point.
Sameer Shemna's user avatar
36 votes
5 answers
3k views

When did Mathematics stop being one of "the Sciences"?

If you ask a mathematician today, many will tell you that mathematics is not a science. Many physicists, chemists, and scientists in other disciplines would say something similar. Mathematicians will ...
Logan M's user avatar
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22 votes
6 answers
3k 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? ...
Ali Caglayan's user avatar
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53 votes
3 answers
6k views

Which came first, the natural logarithm or the base of the natural logarithm?

The natural logarithm function ($\ln x$) and the base of the natural logarithm function ($e$) are both extremely useful. They're also both closely related: $\ln (e^x)=x$, and $e^{\ln x}=x$. But which ...
HDE 226868's user avatar
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23 votes
2 answers
760 views

In what form does the field of metamathematics exist today?

I was rewriting the Wikipedia article for metamathematics, and it was very difficult to find any references after the 1930s. The most important works seem to have been Gödel's completeness and ...
Brian Rushton's user avatar
19 votes
3 answers
2k views

What mathematical developments/discoveries caused imaginary numbers to gain acceptance at the time (18th century) they did?

In a Wiki article on imaginary numbers it was asserted that "the use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855)." ...
Tom Au's user avatar
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17 votes
2 answers
1k views

The Abacus vs. the Electric Calculator (Nov 12, 1946): Why did the latter lose?

On Nov 12, 1946 the Americans organized a contest in Japan to compare the Japanese Abacus with the American Electric Calculator. The Abacus won: "Civilization, on the threshold of the atomic age, ...
Franck Dernoncourt's user avatar
23 votes
2 answers
3k 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?
Felix's user avatar
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13 votes
3 answers
2k views

Why isn't there a Nobel prize in Mathematics?

While I have heard speculative answers to this question, I do not know one which can be supported. Is there any information explaining why Nobel did not chose to include this topic? Has there even ...
kaine's user avatar
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20 votes
1 answer
4k views

Why did Rene Descartes go to Sweden?

The year before he died, mathematician Rene Descartes accepted an invitation to tutor the brilliant 19-year old Queen Christina of Sweden (some thirty years younger). He apparently died from the ...
Tom Au's user avatar
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20 votes
3 answers
780 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 ...
Tom Au's user avatar
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29 votes
2 answers
2k views

When and how was the geometric understanding of gauge theories developed?

In theoretical physics, the modern perspective on gauge theory is that it is most elegantly described in the 'language' of differential geometry. I am interested in the history behind these ideas. ...
Danu's user avatar
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23 votes
4 answers
11k views

Ancient Chinese numbering system

It has been said that the invention of zero was a great leap forward, not only in abstract understanding, but in the ability to introduce place value notation and do computations; computing using ...
rogerl's user avatar
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75 votes
3 answers
15k 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 ...
Carlos Bribiescas's user avatar
25 votes
4 answers
5k views

Irrationality of the square root of 2

We know that Pythagoreans in Ancient Greece discovered that the square root of two is an irrational number. Why was that discovery historically significant? What value was that knowledge to the ...
Spectre's user avatar
  • 359
15 votes
1 answer
516 views

Cauchy's undead theory

A well known urban legend states that Cauchy's last words to the Academy where: C'est ce que j'expliquerai plus au long dans un prochain mémoire. ("I will explain it in greater detail in my next ...
VicAche's user avatar
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