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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4answers
250 views

Whatever happened to quaternions?

Quaternions were made up by Hamilton. They are an extension of complex numbers. It is said that he first introduced "3d tertions". He was thinking what the relation between i and j had to be ...
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0answers
94 views

What kind of mathematics had Max Ernst in mind?

Max Ernst was a painter belonging to the Dadaistic movement. One of his paintings shows Euclid in a somewhat, well, let's say Dadaistic fashion (although fashion and Dadaism don't go along well). We ...
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2answers
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When were equivalence classes formalized?

Neither wikipedia or the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized? Footnote: I originally asked ...
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0answers
45 views

Help understanding Egyptian circle

I was reading this Wikipedia page searching for the Egyptian area of circle and there is a following picture there: Trying to understand what is meant by this since it is under the "Area" ...
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1answer
102 views

Aziz of Complex Analysis

Does anyone know about Prof. Abdul Aziz on whose name Aziz's theorem is named? Aziz's theorem is a theorem about the location of zeros of polynomials.
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1answer
130 views

What did Fourier mean by stating that every function can be decomposed into sine and cosine functions?

Fourier stated that every function can be decomposed into sine and cosine functions. Was he referring to periodic functions only? To a certain class only? I ask, because it seems clear (at least to me)...
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Did the sages that composed the earliest version of Surya Siddhanta know for certain that the Sun is not a planet and the Moon not a star?

The Vedic jyotisha acquaints us with the navgraha which includes 'Surya' (by which term the Sun is meant in India today) & 'Chandra'(a modern Indian term meaning the Moon) while it excludes the ...
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1answer
102 views

What does the Fourier transform have to do with heat?

For example the current version of the Fourier analysis article on Wikipedia says the study is: […] named after Joseph Fourier, who showed that representing a function as a sum of trigonometric ...
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0answers
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Collatz letter to Professor Mays

According to a translation of the letter of Collatz to Professor Mays in 1980, Collatz mentions that he hasn't figured out whether the number n = 80 resulted in a cycle or not, concerning the collatz ...
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0answers
100 views

To what level did mathematics develop in the western world without Hindu-Arabic numbers?

To what level did mathematics develop in the western world without Hindu-Arabic numbers? A related question is how were calculations performed without Hindu-Arabic numbers? (I don't know if I should ...
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0answers
32 views

First appearance of relations commutator,anticommutator with quaternion product

My query is the following, what is the first textual reference of the usage of commutator and anticommutator regarding quaternions in a similar way relative how it is done in the wikipedia article of ...
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0answers
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Continuation on Galois’ lost memoir(s): was Poisson right in his review of Galois’ memoir?

A recent question asked whether Galois’ “lost” memoir has been since recovered (similar to Abel’s lost memoir). The memoir referenced in the question is the one Galois submitted to the French “...
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52 views

What is the origin of the “imaginary” in imaginary numbers? [duplicate]

When was the imaginary number, i, introduced? Why was it called imaginary? Isn't it just as imaginary as a negative number? Aren't all numbers imaginary, for that matter? I am not interested in the ...
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7answers
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Is there any example of a long-standing mathematical conjecture whose resolution did not require advanced knowledge?

Famous conjectures whose solutions took decades or centuries were usually resolved with the help of sophisticated theories and techniques unknown at the time the conjecture was first claimed. Is there ...
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2answers
240 views

Who discovered this closed form formula for the n-th prime number?

The following is a formula for the $n$-th prime number ($[\,]$ represents the floor function). Who was the first person to discover it? The value of this formula: people have been exploring the ...
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0answers
94 views

What is the origin of the term “Telescoping Series”?

I looked into Carl. B. Boyer and Morris Kline books of math history, some calculus books like Apostol and Swokowski, many pages on the internet and even the Tractatus de Seriebus Infinitis of Jacobi ...
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0answers
63 views

Counterweights in the overhang problem

In their amazing paper Overhang (Amer. Math. Monthly 116 (2009), 19–44), Mike Paterson and Uri Zwick revisited the old chestnut of how much of an overhang one can achieve by stacking bricks at the ...
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1answer
136 views

Confusion on the original article by Lucas

I am currently researching on all primality tests deriving from Lucas' original paper Théorie des Fonctions Numériques Simplement Périodiques, which is of course known for its great deal of confusion. ...
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1answer
150 views

Why is the number of elements in a group called “order”?

This is a question that I have for a long time, Maybe it is something silly, but I really want to know. Why is the number of elements in a group called "order"? I mean, the word "order&...
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1answer
139 views

Recording current development of research mathematics

Are there historians of science that are systematically recording current activity in research mathematics ? For example, a decade ago there was a lot of stuff through blogs and Mathoverflow, nowadays ...
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2answers
187 views

What are some notable contributions of mathematical logic to mathematics (outside of mathematical logic)?

I have been reading an introductory text in mathematical logic (Holden, 1995). The final chapter presents the resolution of Hilberts's tenth problem concerning the integer roots of an arbitrary ...
3
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0answers
54 views

Why did Øystein Ore's lattice-based approach disappear?

I was watching this series of lectures on universal algebra on YouTube and the instructor, Charlotte Aten, mentioned that Øystein Ore studied lattices with the goal of using lattices as a unifying ...
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1answer
123 views

Lost memoir of Évariste Galois

According to the Wikipedia article on Évariste Galois He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first ...
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2answers
139 views

When did the notion of space, geometric space appear?

When in history did the notion of space, geometric space appear? I. e. when in history geometric space was treated or thought of as a whole, as the site in which all geometric objects exist? When I ...
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0answers
112 views

How did Hamilton conclude the quaternions had to be four dimensional?

I have seen many times before that Hamilton started off believing he would need a three-dimensional system over the reals in order to describe 3D rotations. He considered numbers of the form $a + bi + ...
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2answers
141 views

Origin of the term “field” (in “vector field”)

I am reposting a thread from "physics stack exchange" : I was wondering - Why do we use the word "field" to describe a vector field? i.e., a field is "an expanse of open or ...
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0answers
262 views

Is it true that Empress Elisabeth of Austria did math?

I have encountered a user on Math Stack Exchange with writing in his bio that Empress Elisabeth of Austria ("Sisi") did some math and she was famous for an unsolvable integral: $$\int_{0}^{1}...
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10answers
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Has physics ever given a physical significance to a mathematically abstract idea?

Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
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4answers
327 views

Why are the standards of mathematical proof still unsettled?

Please see the embold phrases below. I'm just a laywoman, and I'm just seeking simple answers. I last took math when I was 17. I read Has the standard of mathematical proofs changed over time?, but ...
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2answers
76 views

Do we know of any ancient 'Introduction to Mathematics' in Ancient Greece, besides “The Elements”? [duplicate]

Given that Euclid's work is titled "The Elements", it is safe to imply that it is a compendium of elementary results of Ancient Greek Geometry. Other works, such as those of Apollonius, ...
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0answers
61 views

Who first proved that the existence of a Euclidean algorithm implies unique factorization?

In Simachew's "A Survey on Euclidean Number Fields", he said that Gauss used the existence of a Euclidean algorithm in Gaussian integers to prove that it has unique factorization. Also, he ...
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2answers
92 views

Different conventions between Fourier Transform and Characteristic Function

While it is clear that there are several conventions for Fourier transforms of intragrable functions on $\mathbb{R}$, I don't think I have ever seen anything different from the three following ...
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2answers
193 views

Reverse subtraction: has any culture had a symbol (call it $\oplus$) where $A \oplus B$ (read in the same direction as in the language) $:= B - A$?

The standard use of the minus sign is such that $A-B$ means you subtract B from A. Thus $$5-2 = 3.$$ Has any culture used a symbol (let's call it $\oplus$) where $A \oplus B$ means you subtract A from ...
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3answers
168 views

Best history of Maxwell and his equations

I've done my B.S. in Electrical Engineering as well as mathematics but I'd like to get a proper, or complete history of Maxwell and the history of his derivation of the equations and the newness of ...
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1answer
151 views

Origins of Zariski topology

Why did Zariski feel the need to define his famous topology? Was this notion used in one form or another prior to him in algebraic geometry?
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0answers
60 views

Origin of Lang's proof of the Cayley-Hamilton theorem

Is the proof of the Cayley-Hamilton theorem given by Serge Lang in Algebra (page 561) an original one, or has it been borrowed from some earlier sources? Who came up with it first? (Lang's proof is ...
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0answers
104 views

Is it true that Mathematicians have a short shelf-life / peak early?

I have always heard this claim that, out of all disciplines, Mathematicians have the shortest 'shelf-life'. More specifically, that they peak early in their twenties (i.e. present their most important ...
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0answers
77 views

Who first defined velocity and acceleration?

I'm asking who was the first to use and define velocity and acceleration in the modern, now standard way, with velocity being the first derivative of position and acceleration being the second ...
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0answers
60 views

Did anyone ever propose the distinction between “divergent to infinity” as opposed to “divergent but with finite average”?

There are different regularization methods that allow us to ascribe finite values to divergent integrals, series or sequences. Still, in my view there is fundamental difference between divergent ...
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1answer
251 views

Did Euler produce any Russian text?

Wikipedia says that Euler (1707 - 1783) "mastered Russian and settled into life in Saint Petersburg" in 1727. Did he produce any Russian text, mathematical or personal? I can only find Latin,...
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0answers
52 views

How did Roger Cotes come up with logarithm form of Euler formula?

I have been trying to get my head around how Roger Cotes first discovered Euler Formula. I knew how Euler did it, but I wanted a new perspective, especially from someone who discovered it earlier. ...
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2answers
176 views

Is there any English translation of this Gergonne paper?

This is the paper: “Variétés. Essai de dialectique rationnelle”. Annales de Mathématiques pures et appliquées, tome 7 (1816-1817), p. 189-228 (“Varieties. Essay about rational dialectic”, By J.D. ...
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1answer
88 views

Did anyone ever propose a hypercomplex numbers system with more than one anisotropic axis?

The real number axis is asymmetric against zero: for instance, multiplication of two negative or two positive numbers will produce a positive number, a square root of a negative number is not real, ...
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1answer
66 views

Mathematical research institutes similar to Banff and Oberwolfach [closed]

What other institutes such as these two exist for a visit by a scientist for an undisturbed period of short research? Ideally with a good landscape. Dagstuhl is another one I found.
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63 views

Beltrami's Essay on the Interpretation of non-Euclidean Geometry

I am reading the Essay of the title written by Beltrami in Italian and I found a specific point of the essay which in my opinion could be fully clarified only if compared with its translations. At the ...
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0answers
118 views

Origins of Stone duality

My question is a mix of mathematical and historical, if you consider my question will be better answered in the mathematics community, please tell me. I want to know the historical roots of Stone's ...
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2answers
476 views

A branch of mathematics which refused to be rigorous?

I'm currently in a class on formal mathematics/formal logic/axiomatic set theory. Someone asked, "At the end of the day, as mathematicians, why do we care about rigor?" My professor gave an ...
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1answer
116 views

First time the real numbers were axiomatized as the “unique complete ordered field”

(originally asked at M.SE: https://math.stackexchange.com/questions/4094361/first-time-the-reals-were-axiomatized-as-the-unique-complete-ordered-field) I'm looking for historical references on the ...
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57 views

What is the middle name of George A. Grätzer?

What is the middle name of George A. Grätzer?
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0answers
64 views

Appearance of the Dirac delta operator in Laplace's work

I found a reference to the following article ; O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat. Issled. Vyp. 20 (1975), 303-308, 381. I don't ...

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