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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85 views

Where can I get early 20th century books on electronics and mathematics?

I have been searching for books on electronics and mathematics of early 20th century.I found a link which was released in 1950 but that was in russian language.Can I find these books in universities ...
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1answer
2k views

Who discovered pigeonhole principle in mathematics?

The principle was used as early as late 1760s by Lagrange but are there any earlier uses of it in math?
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1answer
264 views

When did the concept of palindromic sequences first appear in mathematics?

I have been reading one of Lagrange's works where he mentions palindromic sequences in the context of Periodic continued fractions. I am wondering if that was the first time that palindromic sequences ...
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1answer
72 views

Superscripts and constants in Diophantus’ Arithmetica

Diophantus’ notation for higher powers of the unknown includes a superscript, usually written as a lowercase or uppercase upsilon - e.g., $\Delta^{\upsilon}$ as the square. It is not clear to me ...
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1answer
76 views

Where did Euler prove 'his' theorem on homogeneous functions?

Where in Eulers writings can I find a proof of his homogeneous function theorem: $y$ is a homogeneous function of degree $k$ in $x_1,\ldots,x_n$ iff $ky = \sum_{i=1}^n x_i\frac{\partial y}{\partial ...
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1answer
63 views

What is the origin of “banana brackets”?

"Banana" brackets are used to denote catamorphisms: Another notation found in the literature is . These symbols are very similar to the composition of a $($ and a $|$, is this similarity more than ...
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0answers
79 views

What exactly was Lagrange's “grave mistake” with respect to rotating bodies under hydrostatic equilibrium?

A comment below What would be different about satellite orbits if Earth were prolate? Would we have Sun-synchronous and Molniya orbits? got me reading Wikipedia's Jacobi ellipsoid which begins: ...
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1answer
156 views

What was Copernicus trying to mean with 'Mathematics is Written for Mathematicians'?

I'm interested in really understanding what Copernicus was getting at with the quote 'mathematics is written for mathematicians'. He clearly isn't referring to the rigorous nature of mathematical ...
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1answer
54 views

Who is Wanner from Rosenrock-Wanner (ROW) methods?

I've spent some time with a search engine trying to find out about Wanner, a person whose surname is mentioned in the name of Rosenbrock-Wanner (ROW) methods primarily used for iteratively solving ...
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1answer
107 views

Who first proved the “acute angle principle” in fixed point theory?

After getting such an informative response on my first question, I have another theorem discussed in our lecture who´s origin I am interested in (sometimes called the "acute angle principle"): ...
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History of Reciprocity Laws

Does anybody know a freely available overview of the history of Reciprocity Laws, especially the Cubic and Biquadratic ones? Wikipedia I know about Franz Lemmermeyer's book "Reciprocity Laws", but ...
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Any idea on how Lagrange came up with similar functions concept in (proto)group theory?

Lagrange defines "similar functions" as functions of the roots of an equation where they change values only at the same kind of permutations of the roots. What's a possible predecessor of the idea of ...
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Are there widely accepted math symbols using non-Latin alphabets or characters other than Greek and Hebrew?

We have $\pi$ and $\aleph_0$ borrowed from Greek and Hebrew alphabets. Are there widely accepted math symbols using non-Latin alphabets or characters other than Greek and Hebrew? A related question ...
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2answers
108 views

Have orthogonal complex matrices appeared in the literature?

According to https://en.wikipedia.org/wiki/Orthogonal_matrix, https://en.wikipedia.org/wiki/Unitary_matrix, and Friedberg et al.'s Linear Algebra (4th edition), a matrix $A\in F^{n\times n}$ is ...
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4answers
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Are there theorems that have been truly lost?

Related: Are there any theorems that become "lost" and discarded over time? Is there a 'lost calculus'? The questions above use the term 'lost' to refer to theorems that exist in ...
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Why didn't Euclid use equations or numerals in his proofs?

I think the Elements would have been a lot more concise if he did.
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1answer
109 views

Why positive definite matrix rather than positively definite matrix? [duplicate]

"Positive definite matrix" is a standard term in mathematics, espeically linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called "positively definite matrix"?
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149 views

Why do we call it a “positive definite matrix” rather than a “positively definite matrix”?

The term positive definite matrix is a standard one used in mathematics, especially in linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called a positively ...
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2answers
299 views

Does Euclid's Elements acknowledge a concept of 0, either directly or indirectly?

From what I understand Euclid avoided infinity, and so I'm wondering how Euclid might have dealt with the concept of 0 in the Elements.
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1answer
161 views

History of “independent and dependent variables”

I have a lot of questions that can be summed up by "whats the history of independent and dependent variables?" Here is a list of those questions: Where does our conception of independent and ...
6
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1answer
151 views

Did Gosper or the Borweins first prove Ramanujans formula?

This is a copy of my question on MSE (https://math.stackexchange.com/questions/3372432) because this forum seems better suited for historical questions: In 1985, Gosper used the not-yet-proven ...
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1answer
1k views

Who started calling the matrix multiplication “multiplication”?

As I searched for linear algebra, I found it odd that the linear map composition corresponds to the multiplication of matrices. Considering the intuition that the repetition of addition is ...
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57 views

Who first wrote the eigenvalue/eigenvector equation? [duplicate]

Who first wrote the eigenvalue/eigenvector equation $$Ax=\lambda x,$$ where $A$ is a linear operator and $x,\lambda$ the corresponding eigenvectors, eigenvalues?
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1answer
188 views

Alexander Grothendieck's “stolen” correspondence in 1985?

On the website that now displays the part of Grothendieck's archives that had been held at the University of Montpellier, it is mentioned that: Dans une lettre adressée à Monsieur Lefranc datée du ...
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1answer
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Einstein praising Sophus Lie

p. 153 of Raúl M. Falcón Ganfornina and Juan Núñez Valdés, “Mathematical Foundations of Santilli Isotopies,” trans. Alan Aversa, Algebras, Groups, and Geometries 32 (2015): 135–308. quotes (but does ...
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1answer
315 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 ...
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1answer
247 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
66 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
169 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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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 ...
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1answer
86 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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29 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
138 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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4answers
245 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 ...
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1answer
181 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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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
75 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
3k views

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
102 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
80 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
147 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.?
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1answer
54 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
47 views

Who first distinguished number theory and numerology? [duplicate]

Who first distinguished number theory and numerology?
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1answer
153 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
76 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 ...
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1answer
162 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 ...
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1answer
155 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
152 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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118 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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386 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 ...

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