Questions tagged [mathematics]

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

Filter by
Sorted by
Tagged with
13 votes
2 answers
234 views

What group theoretic results were known for several special cases before the general definition of a group was established?

Many results in group theory were proven for permutation groups before the general definition of a group was established (for example: Lagrange's theorem, Sylow's theorems). However, permutation ...
user avatar
  • 3,019
31 votes
1 answer
4k views

Why is American and French notation different for open intervals (x, y) vs. ]x, y[?

The Americans and the French use a different notation for open intervals: The Americans use (x, y) while the French use ]x, y[. How did this notational divergence appear?
user avatar
15 votes
6 answers
3k views

Have numbering systems other than base ten ever been used or popular?

Base ten makes a lot of sense as a numbering system, given the number of digits humans typically have on their hands. That said, some older money systems weren't based on the number of fingers we ...
user avatar
11 votes
1 answer
744 views

How and when was Bolzano's proof of the Bolzano-Weierstrass theorem rediscovered?

I've always been curious about how great forgotten ideas are rediscovered. This question: Are there written (19th century) sources expressing the belief that the intermediate value property is ...
user avatar
12 votes
2 answers
465 views

What examples led to the modern definition of a topological space?

Today the language of topological spaces via open sets is fundamental in many different areas of mathematics, and it is a bit mysterious that the same formalism successfully captures such a wide ...
user avatar
  • 1,021
10 votes
3 answers
826 views

How come we attribute the general theory of relativity to Einstein?

How come do we attribute general theory of relativity to Einstein when David Hilbert published first?
user avatar
33 votes
3 answers
937 views

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 ...
user avatar
37 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 ...
user avatar
  • 752
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 ...
user avatar
38 votes
6 answers
14k 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.
user avatar
36 votes
5 answers
2k 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 ...
user avatar
  • 2,732
22 votes
6 answers
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? ...
user avatar
  • 1,516
50 votes
3 answers
5k 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 ...
user avatar
  • 8,082
21 votes
2 answers
618 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 ...
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)." ...
user avatar
  • 2,124
17 votes
1 answer
994 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, ...
user avatar
22 votes
2 answers
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?
user avatar
  • 1,507
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 ...
user avatar
  • 736
19 votes
1 answer
3k 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 ...
user avatar
  • 2,124
20 votes
3 answers
670 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 ...
user avatar
  • 2,124
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. ...
user avatar
  • 3,681
23 votes
4 answers
9k 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 ...
user avatar
  • 653
71 votes
3 answers
11k 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 ...
user avatar
25 votes
4 answers
4k 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 ...
user avatar
  • 359
15 votes
1 answer
451 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 ...
user avatar
  • 1,795

1
22 23 24 25
26