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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1answer
127 views

Collection of open problems in Partial differential equations

Except Navier-Stokes equation, are there any other interesting open problems in partial differential equations? I want to know the collection of problems, which are easy to understand but ...
5
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1answer
120 views

Do North Koreans use Latin letters in their equations?

Do North Koreans use Latin (and Greek) letters in their equations? On the one hand, being such an isolationist country, I wouldn't be surprised if they used the Korean alphabet (조선글) in their ...
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1answer
46 views

When was the inverse quadratic interpolation method first used?

Do you know anything about it? I couldn't really find something useful on web.
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0answers
156 views

Writing functions on the right

In group theory, writing functions on the right is a common, though not universal practice. Thus, given mappings $f$, $g$ and group element $\alpha$, one might write $\alpha f$ and $\alpha (f \circ ...
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63 views

Italian Mathematics

After reading this question, I remembered seeing on our department webpage somewhere that for PhD studies one must show a competency in either German, French, or Russian, but Italian was acceptable ...
2
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1answer
74 views

Where does $M$ for expected value in Russian papers come from?

In modern papers in statistics, it is common to use the sybmol $E[X]$ to refer to the expectation of a random variable $X$. While reading (a translated version of) "Convergence Rate of Nonparametric ...
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27 views

History of Path algebras

I want some references that point the inventor of Path algebras and history/evolution of these algebras from the first idea. If possible. I tried to search in many different places, but all times, ...
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1answer
99 views

What is the ancient cosmic canon of proportion and its role in the history of science?

Who had direct inside knowledge of the canon through the alleged secret oral tradition? Some possible examples that have been alluded to include Pythagoras, Plato, Euclid, Copernicus, Galileo, Kepler, ...
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3answers
144 views

Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

In the book "What Do You Care What Other People Think?", Feynman talks about how in the 16th century Niccolo Tartaglia discovered a solution to cubic equations. He says while this was not a major ...
3
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1answer
109 views

Were decimal fractions known in Europe before Stevin?

It is commonly[1,2] held that Simon Stevin introduced the decimal number system with the decimal point (at least in Europe) in his 1585 book De Thiende. However, in della Porta's book Magia Naturalis, ...
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1answer
1k views

Why do many names of technical and scientific subjects end with “ics”?

The names of many technical and scientific subjects, like mathematics, physics, statistics, etc., etc., end with letters "ics". What is meant by this, if anything? Was there any logic behind it or is ...
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1answer
67 views

What was the chain of theories that led to relativity? [closed]

Can you briefly sketch the sequence of math theories that were necessary for Einstein to figure out a convincing background for relativity?
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2answers
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Who discovered the covering homomorphism between SU(2) and SO(3)?

Who discovered this? It is quite nontrivial and very important in quantum mechanics.
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1answer
73 views

Who first proved that the spectrum of an operator is contained in the closure of its numerical range?

We have recently proven in our functional analysis II lecture that the spectrum of an operator is contained in the closure of its numerical range. On the German wikipedia page for the numerical radius ...
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0answers
74 views

Who first proved Fubini's theorem $n$th order integrals?

Who first proved a generalized Fubini theorem for integrals of order $≥3$? An $n$th order integral is $$\underbrace{\underset{x_n}\int\underset{x_{n-1}}\int\ldots\underset{x_1}\int}_{n} f(x_1,x_2,\...
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1answer
136 views

Did Cauchy ever deal with double or triple integrals?

Did Cauchy ever deal with double or triple integrals? Did he give rigorous proofs of multivariable integral calculus like what came to be called Stokes's theorem, the divergence theorem, etc.?
9
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1answer
51 views

Seven bridges of Königsberg - did people know that it was impossible? [duplicate]

I'm not sure if this is the most suitable site for the question. Please feel free to modify or move my post! I have heard that people really walked a lot in Königsberg, trying to solve that seven ...
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1answer
42 views

Who first distinguished number theory and numerology? [duplicate]

Who first distinguished number theory and numerology?
4
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1answer
128 views

Are Euclid's theorems and proofs due to Euclid?

Some appear to argue that much of the Elements by Euclid is a compilation of knowledge handed down to Euclid from his predecessors. On the other hand, some credit the proof, of the Pythagorean theorem ...
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0answers
74 views

Where does the notion of “three crises of mathematics” come from? [duplicate]

Update: It can be traced back to Fraenkel-Bar-Hillel's Foundations of Set Theory, originally published in 1958. Further discussions can be seen at the linked question. The notion of "three crises of ...
5
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1answer
134 views

When did mathematicians transition from peg and rope to straightedege and compass?

In the 19th and 20th centuries, the student of classical Greek geometry used "straight edge and compass". A. Seidenberg uses the terminology "peg and cord" in proposing that altar construction ...
2
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1answer
126 views

First time the unique factorization theorem was called FTA

First of all, a comment, before this gets marked as a duplicate: I have searched this website for the question I’m asking and I’m aware that this exact question has been asked before. However, Eric ...
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1answer
148 views

I can't comprehend the sentence in Euclid Elements [closed]

I am Korean, and I thought I can understand majority of english sentences, but this is really hard to translate literally for me. Even though I asked it to my English teacher, he did not know either. ...
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0answers
103 views

Reference Request: Comment about Contradictions Proof Method Related to John G. Thompson

I read in a PDF document where the author made a comment that it is “dangerous” to use indirect proof method/contradiction proof method (as far as I can remember, and of course I am paraphrasing) as ...
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1answer
303 views

Why 1 was source of numbers even though ancient Greeks knew about irrational number?

In Ancient Greek, most people like Pythagoras thought 1(monad, unity) is no number, but it is ruler and beginning of all other numbers. And Pythagoras thought everything is number. But they found ...
3
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1answer
148 views

How did Hagoromo Fulltouch chalk gain so much popularity among mathematicians in the West?

I recently read Hagoromo, the 'Rolls Royce of chalk,' continues writing its legacy in South Korea article recently, and was fascinated by the huge amount of attention this specific chalk is getting. ...
3
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1answer
97 views

Origin of the “law of quadratic reciprocity”

Today, "reciprocity" is the standard mathematical word used for quadratic reciprocity and its generalizations. I found that the name dates back to no later than 1832, when a paper of Dirichlet (...
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1answer
51 views

Did Isaac Barrow also discover the other thing about the inverse relation between area and tangent?

Barrow surely discovered that the tangent to the area curve of a function at a point equals the value of the function at that point. Also, I’ve seen geometric proofs of this. But did he also discover ...
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1answer
327 views

What is the origin of the Chinese Stick Multiplication method?

A while back I came across an interesting method to do multiplication. I don't know what it's called and am interested in when (and who) developed this method. I don't know if it's a mathematical ...
7
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2answers
172 views

Reference Request: Did Descartes leave solving the quintic as an exercise to his readers?

In this document by Jim Brown it is claimed (on Section 3, pg 5) that: [Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the ...
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0answers
62 views

On Trigonometric Methods Available to Aristarchus

Approximately 2300 years ago, Aristarchus proposed a method for determining the relative distances of the sun and the moon in relation to the earth. Specifically, he asserted that when the moon is in ...
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0answers
195 views

How was this equation for pi derived by Ramanujan?

Have we figured out how this series was derived by Ramanjuan? $$\frac{1}{\pi}=\frac{\sqrt{8}}{9801}\sum_{n=0}^{\infty}\frac{(4n)!}{(n!)^4}\frac{26390n+1103}{396^{4n}}$$
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1answer
78 views

Why was Indicial equations named so?

In ODE, in Frobenius method, there's an equation called "Indicial Equation." Is there any particular contextual/historical reason that it is named so?
6
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1answer
105 views

Who invented the gradient descent algorithm?

In connection to the question "Who invented the gradient?", I want to know who invented the gradient descent algorithm?
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2answers
604 views

On the history of Haar measure

Haar measure is a well-known concept in measure theory. Many books are perfectly dedicated to present its existence and uniqueness such as measure theory for D. Cohn. I am looking for a good ...
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3answers
90 views

Does Heliocentrism predate Copernicus?

I have seen this mentioned on the interwebs a few times. people have mentioned that some Greek thinkers and Islamic astronomers came up with heliocentrism before Copernicus and that Copernicus copied ...
0
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1answer
68 views

Was there a more intuitive early proof of the generalized mean value theorem?

I am interested in the early proofs of the theorem. It is often called Cauchy mean value theorem, so perhaps Cauchy proved it first. In all the proofs that I have seen we construct a contrived ...
4
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1answer
146 views

What was the problem that led to Calculus discovery

As far as I remember, Calculus was invented/discover/founded by Newton. But what he was trying to achieve that made him find the limit of of difference approaching zero. how far did he get into ...
3
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1answer
137 views

Were people aware of the “mistakes” in Euclid's Elements before the start of the formalization of Mathematics?

For example, in proposition 1, Euclid assumes that the instersection of the two circles exist, when he shouldn't have. This, among many other things, was corrected quite recently (by Hilbert and ...
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0answers
199 views

Were ancients really so bad at computations before Arab numerals?

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

On the Origin of the Concept of Aliasing & the Discrete Fourier Transform Frequency Axis

The development of fast Fourier transform is attributed to Cooley & Tukey, both have written a lot about it is historical development. However, I am searching early publications which showed how ...
0
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1answer
67 views

Logarithm tables vs multiplication tables

When John Napier and Joost Burgi developed logarithms in the 16th century, they succeeded in replacing long, tedious, error-prone multiplications with table-look-up and addition, giving other ...
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2answers
130 views

Why are “join” and “meet” named as they are?

In the context of partially ordered sets, why are the words for supremum and infimum "join" and "meet"? I find the nomenclature puzzling, especially since the English words "join" and "meet" are ...
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0answers
120 views

What was Havil's source for the statement that G.H. Hardy would offer his Savillian chair to whoever could prove irrational?

In Havil's 2003 book Gamma he states that Hardy offered up his chair in Oxford to whoever could prove that the Euler-Mascheroni constant $\gamma$ is irrational. I'm almost positive I had heard a ...
5
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1answer
177 views

What are some of the unsolved mathematical problems posed and stated clearly prior to the year 1900?

I chose year 1900 because of: "Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and ...
3
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1answer
627 views

Who came up with the convolution theorem?

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain). The ...
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0answers
180 views

Entry in Gauss' Mathematisches Tagebuch (Mathematical Diary)

Does someone have a reference or further explanation on Gauß' entry from May 24, 1796 in his mathematical diary (Mathematisches Tagebuch, full scan available via https://gdz.sub.uni-goettingen.de/id/...
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2answers
2k views

What triggered jesuits' ban on infinitesimals in 1632?

... since the very idea of infinitesimal was foreshadowed by Cavalieri ( "limit") in 1635, then put forward in an indirect way by John Wallis ($1/\infty$) in 1655, and then formalized by Newton ( "$o$...
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2answers
129 views

The relationship between solvability of ruler and compass problems and solvability of algebraic equations by radicals

Galois obtained necessary and sufficient conditions for an algebraic equation (in one variable) to be solvable by extraction of a chain of square roots. A beautiful application of this is to the ...
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4answers
172 views

Are there any sources of mathematicians talking about their research methods?

I recall reading this article that was written to explain how Descartes read philosophy effectively. I am wondering if such analogous tips have been made by past mathematicians?