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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13
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2answers
538 views

Were transcendental numbers considered rare, pre-Cantor?

Because the real numbers are uncountable and the real algebraic numbers are countable, there are uncountably many transcendental numbers. So there are far more transcendentals than rationals. With the ...
12
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3answers
2k views

Why is “Cardano's Formula” (wrongly) attributed to him?

Apparently, Cardano had learned a formula for solving cubic equations from Tartaglia, who had sworn him to secrecy, and in any event, not to publish it without giving Tartaglia due credit. Cardano ...
13
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0answers
465 views

Conditionally convergent series

I am looking for the original reference discussing a specific, elementary example of a rearrangement of series converging to a value different from the original series. In what follows, I give some (...
33
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4answers
4k views

Whose shoulders did Newton stand on?

In a letter to Robert Hooke in 1676, Newton wrote: If I have seen further it is by standing on the shoulders of giants. Do we know which giants Newton was referring to? And was he referring to a ...
12
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1answer
200 views

When was the modern field theory approach to Galois theory developed?

It is well known that Galois, and other mathematicians around that time, considered Galois groups to be permutation groups and approached Galois theory in this manner. At some point the theory took a ...
10
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1answer
397 views

What is the history behind the Erdős number?

The Erdős number is used as a tool to study how mathematicians cooperate to find answers to unsolved problems. But what is the history behind the Erdős number?
11
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1answer
730 views

Who was Elissaeus Judaeus?

There is an interesting web site called Mathematical Genealogy http://genealogy.math.ndsu.nodak.edu/ which lists about 140000 mathematicians with their student-advisor relations. I think that this ...
14
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1answer
335 views

When and why were mathematics and magic considered synonymous in England

In 1555, John Dee was arrested for "calculating". According to his MacTutor biography: At this time mathematics in England was considered to be equivalent to the possession of magical powers and ...
11
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1answer
292 views

Division of the circle and compass constructions

It is well known that every construction that can be performed by a compass and a ruler can be also performed by a compass only. This is a good (and difficult) exercise in elementary geometry. My ...
10
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1answer
1k views

What is the truth behind “The Turk” (the mechanical chess machine)?

It was in lime light for more than a century (late 18th century to late 19th century). They say it was inspected and found fake. But, what was fake about that. There are stories that this machine won ...
22
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3answers
4k views

When was zero actually introduced in mathematics?

Children learn counting things, naturally like, 1, 2, 3, ... and so on. Because it seems obvious to them. But, zero is something we need to teach them about. As far as my understanding goes zero was ...
19
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4answers
1k views

Books on the history of linear algebra

I'm quite desperate to understand the historical motivation and origin of all of the "geometrical" concepts of linear algebra, namely: The concept of thinking of elements of $\mathbb R^n$ or some ...
5
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1answer
287 views

Did Bertrand Russell leave the Second International Congress of Mathematicians to read Giuseppe Peano's Formulario?

The Wikipedia page on Giuseppe Peano claims the following: At the conference Peano met Bertrand Russell and gave him a copy of Formulario. Russell was so struck by Peano's innovative logical ...
11
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4answers
305 views

Concept of a function and Idea of a formula as a function

Enderton Elements of Set Theory, p. 43 (1977, Academic Press), writes: There was a reluctance to separate the concept of a function itself from the idea of a written formula defining the function. ...
18
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1answer
486 views

What is the modern significance of Theaetetus's classification of quadratic irrationals?

Before Eudoxus's theory of proportion there was a theory of irrationals based on continued fraction expansions, which Fowler calls anthyphairesis. Theaetetus is said to develop a classification of ...
13
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2answers
610 views

Why is Leibniz less well regarded?

A well-known and specific example is that Leibniz is less well regarded than Newton for his calculus, the reason being notation, Leibniz notation lets you incorrectly work with derivatives as ...
40
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3answers
2k views

What led to the fall of Göttingen?

Göttingen was the place in which many important mathematicians such as Riemann worked. It was also one of the main locations for the development of quantum theory in the twenties (e.g. Heisenberg, ...
41
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3answers
3k views

When exactly (and why) did matrices become a part of the undergraduate curriculum?

Let me tell what I know about this. It is well-known that Heisenberg invented matrix multiplication himself, in his great paper that is considered part of the foundation of quantum mechanics. This was ...
17
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1answer
385 views

What specific problems motivated Poincaré's work on topology?

The McTutor biography on Poincaré says: Poincaré's Analysis situs, published in 1895, is an early systematic treatment of topology. He can be said to have been the originator of algebraic topology ...
11
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3answers
965 views

When did architects learn how to calculate load on building members accurately?

For many years, large buildings with impressive spans between the building columns were erected without precisely calculating what loads the columns, walls, and buttresses would have to support. Load ...
13
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2answers
188 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 ...
27
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1answer
3k 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?
14
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6answers
2k 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 ...
11
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1answer
602 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 ...
12
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2answers
388 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 ...
10
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3answers
640 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?
29
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3answers
689 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 ...
34
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3answers
2k 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 ...
16
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1answer
874 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 ...
36
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5answers
10k 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.
34
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5answers
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 ...
22
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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? ...
47
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3answers
3k 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 ...
21
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2answers
481 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 ...
19
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3answers
1k 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)." ...
16
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1answer
762 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, ...
20
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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?
13
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3answers
1k 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 ...
17
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1answer
2k 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 ...
18
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2answers
421 views

What was the connection between David Hilbert and Stephan Banach?

The so-called "Hilbert space" is named after mathematician David Hilbert. Later, this was generalized into "Banach spaces" by Stephan Banach. My understanding is that Hilbert was German and Banach ...
26
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2answers
1k 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. ...
61
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5answers
9k 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 ...
23
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4answers
8k 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 ...
64
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3answers
8k 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 ...
23
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4answers
3k 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 ...
15
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1answer
397 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 ...

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