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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2
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4answers
168 views

What problem was solved by introducing the dimension of a vector space?

In linear algebra, we care a lot about dimensions. I get why it’s useful but not why it’s such a big deal. So I wondered what problem was solved historically by introducing a rigorous definition of ...
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4answers
2k views

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

In his famous estimation of $\pi$ by inscribed and circumscribed polygons, Archimedes uses several rational approximations of irrational values; a typical example is that he states, without ...
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1answer
157 views

What mathematics did Isaac Newton learn at school?

Since Sir Issac Newton invented a lot of modern mathematics, what mathematics did he already know? Since he was standing on the shoulders of giants which giants was he speaking of? I presume he knew ...
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1answer
716 views

What is the history of angle quintisection (division into five equal parts)?

I was reading lately that the quintisection of an angle is possible with paper folding (origami). Now, in contrast to the trisection of an angle, a problem which was discussed historically, and was ...
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0answers
74 views

History of $\sin(nx) = 2^{n-1} \prod_{0}^{n-1} \sin\left(x + \frac{\pi k}{n}\right)$

What is the name of this identity? Who discovered this identity? What is the history behind this? I have looked up on Wikipedia with little documentation of the identity see finite product of ...
33
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0answers
387 views

The origin(s) of the word “elliptic” [closed]

The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ...
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0answers
52 views

How was mathematics used in World War II to “act on the right amount of intelligence”?

In the movie "The Imitation Game", Alan Turing along with his team crack the German encryption machine Enigma but advises his superiors to not act on all decrypted intelligence, as that might lead to ...
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1answer
150 views

What is the basis of the claim that $F_5$ was fully factored in 1732?

The Wikipedia Page on Fermat numbers states that $F_5$ was "fully factored" in 1732. This appears to be the same time that Euler found that any factor of a Fermat number $F_n$ was of the form $$2^{n+...
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2answers
408 views

What caused or contributed to Euclid's Elements and Synthetic Geometry falling into disfavor?

Euclid's Elements could tout to have the longest and most famed publishing history of any book ever written. First written in 300 B.C., Euclid's Elements became the standard text from which ...
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2answers
517 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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1answer
355 views

Were ancient Romans so bad at computations before Arab numerals?

It is often said that Romans (see below) had a terrible number system, which made computations a mess. I do believe this, but I'm suspicious of the claim that nobody had better ways to do computations ...
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3answers
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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 ...
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0answers
73 views

Handbook of proofs

Do you know any handbook where original proofs of mathematicians' of the past theorems and facts are in modern notation? For example, for the Archimedean spiral etc
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0answers
51 views

How did the definition of each “ordered set” come about?

I could get a little intuition about preset, poset, and toset. e.g. A toset is, in effect, a linearly ordered set, and a poset is a set in which no more than one element in the same order exists, ...
4
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2answers
172 views

For many years, were Emmy Noether and Helene Braun the only female mathematicians to obtain habilitation at Göttingen University?

Emmy Noether was the first woman in Germany to obtain habilitation in 1919. But I remember to have heard in the debate concerning the situation of women in academic mathematics that took place on the ...
4
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1answer
127 views

When and WHY did mathematicians start turning their attention to imaginary exponents?

When and WHY did mathematicians start turning their attention to imaginary exponents? I read on Wikipedia about Euler's correspondences with Bernouille and such, but it doesn't answer what exactly ...
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1answer
80 views

What letters are used in this paper by Halin (1976)?

I was trying to read an older paper about treewidth by Halin (1976). He used different hand-written labels, obviously Sütterlin: I assume the hand-written letters to be (from top to bottom and from ...
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1answer
149 views

Origin of Gauss-Newton method

The Gauss-Newton method can be derived from Newton's method, but I am unable to see how Gauss was linked with this method. It seems unlikely that he himself worked on the method, but I am at a loss.
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1answer
250 views

Calculation of Gauss leading to 18:7 resonance between orbits of Jupiter and Pallas

After Gauss helped relocate Ceres, he studied the orbit of the asteroid Pallas and discovered (1812) that Jupiter and Pallas have an orbital resonance that is nearly equal to 18:7. For instance, using ...
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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.
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2answers
7k 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 ...
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1answer
57 views

Invariance principle for stability in the sense of Lyapunov

On Wikipedia this article about the invariance principle and article states that The general result was independently discovered by J.P. LaSalle (then at RIAS) and N.N. Krasovskii, who published ...
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2answers
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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: $$1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6}$$ This seems to have come up in his ...
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1answer
42 views

What did Noether contribute to the theory of integral invariants?

What did Emmy Noether contribute to the theory of integral invariants that wasn't already done by, e.g., Sophus Lie in his 1902 Über Integralinvarianten und Differentialgleichungen?
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2answers
184 views

Why did pre-17th century mathematics mostly come from Italy but later mathematics came from France, Germany and England?

The Renaissance created a number of prominent mathematicians. However, later in the 18th and especially 19th century, Germany and France became the hot centers of mathematical thinking.
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1answer
285 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 ...
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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 ...
3
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1answer
105 views

Is it fair to say that the Space Race incentivized research in pure mathematics?

I've only heard personal anecdotes about perceived stimuli and economic support to research in pure mathematics in the 1960s, presumably tied to the space race of the time. Is this something we can ...
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0answers
91 views

Why do we often minimize in optimization?

Because of the following relation, \begin{equation*} \inf(S) = -\sup(-S), \end{equation*} minimization and maximization is essentially the same thing. However, take any optimization routine in R for ...
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0answers
47 views

Where can I find Lagrange’s equilateral triangular solution for arbitrary masses?

This answer to What kind of triangle is formed by three unequal masses in a circular restricted three body orbit? explains that In the Newtonian limit, an equilateral 3-body solution exists for any ...
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0answers
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Literature on Mayan mathematics

I asked this question on math.se and they sent me here. It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system. Except for these facts, I'...
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Who first called the Brouwer Fixed Point Theorem “the crumpled paper theorem”?

Wikipedia attributes the remark to Brouwer himself, but I am extremely skeptical. Their citation goes to a webpage of a ? French educational TV show, where the remark appears to be a fictionalized ...
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What was Kolmogorov’s point of view in the philosophy of mathematics?

Today the standard interpretation of intuitionistic logic is the Brouwer-Heyting-Kolmogorov-interpretation which was presented independently by Arend Heyting and Andrei Nikolajewitsch Kolmogorow. ...
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0answers
77 views

Origin of the term 'index of a subgroup'

The index of a subgroup $H$ in a group $G$ is the number of distinct cosets of $H$ in $G$. Why did someone decide to call this an 'index'?
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3answers
4k views

Writing Mathematical Symbols in 20th century

As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
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0answers
65 views

First uses of the Ping-Pong Lemma

I am interested in knowing the origins of this useful result, but I haven't been able to precisely pinpoint the context of its first use. Most texts seem to indicate the result originally comes from ...
2
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1answer
463 views

Grand Prix in Mathematics of the French Academy of Sciences

I'm interested in the mathematical problems proposed for the grand-prix of the French Academy Of Sciences, from its beginnigs in 1666 to the present. Are there any books or articles with the precise ...
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0answers
94 views

Cryptography in Japan before Meiji

I have a question related to Japan History and cryptography record. As you may know, Meiji is the period in Japan between 1868 and 1912, in which occidental reforming was performed. After (and ...
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0answers
101 views

Origin of Fourier Transform (1878)

I located Joseph Fourier's book, Analytial Theory of Heat (1878), but at first glance it looks like it is all about heat. What did Fourier call the Fourier transform? When did he first use it?
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2answers
182 views

Was the United Kingdom the only faction in the Second World War that used Operations Research?

I'm aware of work done by the Army Operational Research Group from the United Kingdom's Ministry of Supply. I know Stigler's Diet Problem came out in 1939, if I'm recalling that correctly. However, I ...
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2answers
2k views

What are the uses and the origin of the constant $e$?

It was to my understanding that the constant $e$ came about as a result of simplifying the differentiation of an exponential. For example, the derivative of $2^x$ is $2^x \cdot \ln 2$; for $3^x$ it'...
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0answers
55 views

Who discovered Napier's number?

Who discovered Napier's number? I read Bernoulli calculated it, Napier discovered it but it is e because of Euler. I know how Bernoulli calculated it but where did Napier see it?
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19answers
2k views

Literary works authored by mathematicians

At a first glance, Mathematics and Literature look like two completely unrelated subjects. I wonder whether there are examples of acclaimed mathematicians which wrote novels, poems, or other ...
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0answers
59 views

Did the mathematician Garrett Birkhoff ever work with or mention Feynman's path integrals?

Did Garrett Birkhoff ever work with Feynman's path integral? Did he ever work in his Many-Histories interpretation? Or at least, did he mention it in any of his articles?
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1answer
85 views

Significance level $\alpha$ values - who devised to use $\alpha = 5 \%$?

In a statistical hypotheses testing a significance level $\alpha$ has to be set. The most often, $\alpha$ is set to be 5 %, sometimes 1 % and 10 % values are used. Value of $\alpha$ tells us what is ...
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2answers
865 views

Arithmetic calculation before the 17th Century

Apparently Dijkstra wrote in an article in Datamation1 in 1977: It's very illuminating to think about the fact that some – at most four hundred – years ago, professors at European universities ...
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1answer
95 views

Were $\sigma$-algebras defined for probability?

If you want a crash course in $\sigma$-algebras and probability spaces, you should absolutely read this amazing answer by @Sycorax on Cross Validated. Sycorax says something in particular though that ...
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 ...
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0answers
40 views

First historical register of an improper fraction [duplicate]

I'm looking for the earliest known written register of an improper fraction, that is, a numerical fraction in which the numerator is greater than the denominator (like 3/2). By the way, who invented ...
2
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1answer
97 views

Laplace's Treatise of celestial mechanics

I am interested in nineteenth-century astronomy and Laplace's Treatise of celestial mechanics is often mentioned as one of the most significant contributions to science in this period. The more than ...

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