# Questions tagged [mathematics]

For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns.

201 questions with no upvoted or accepted answers
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0answers
122 views

### Where can I find Lagrange’s original 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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66 views

### Conjectures mentioned (and proposed) at International Congresses of Mathematics

I guess that every International Congress of Mathematics (Mathematicians) brings up some unresolved issues of various types but that also that at least some (if not all) ICM´s present some new ...
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63 views

### 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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### 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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162 views

### What was Havil's source for the statement that G.H. Hardy would offer his Savillian chair to whoever could prove $\gamma$ 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 ...
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110 views

### Why does Michael Stifel's version of Pascal's Triangle look the way it does?

Today I've come across Michael Stifel's version of Pascal's Triangle, which I've seen referred to as the Figurate Triangle or the Triangle of Figurate Numbers as seen in Combinatorics: Ancient and ...
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185 views

### The Integral as a Uniform Limit of Step Functions

Who first realized that it is possible to define the integral of a function as the limit of the integrals of a sequence of step functions that converge uniformly to the given function? This is ...
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64 views

### Where the term elasticity (of a function) come from?

Elasticity of a function is a mathematical concept that is widely used in economics. In particular, price elasticity of demand or supply. But generally elasticity in economic is the measurement of how ...
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90 views

### How widespread was the belief that the earth is round in Europe until the Renaissance?

Already Greek mathematicians in antiquity b.C. realized that the earth was round, and the idea was operative in Europe ever since. But how widespread was this belief in the centuries until the ...
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293 views

### Strange pattern in Math Genealogy

Math Genealogy, https://www.genealogy.math.ndsu.nodak.edu/search.php is a funny site which aims at listing all PhD's in mathematics, with years, place, titles and advisers. Of course it cannot be ...
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143 views

### Was Riddell's formula really so late?

Riddell's formula for unlabeled graphs is a generating function transformation $$1 + B(x) = \exp \sum_{k=1}^\infty \frac{A(x^k)}{k}$$ which gives the number of graphs whose connected components have a ...
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177 views

### Set Theory, onto and into their relation to spoken language definitions

Does anyone know how the definitions for onto and into map to the spoken language definitions of the words? I compared the Bourbaki definitions to these words and have a suspicion that the German ...
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165 views

### Works of mathematician François Viète

I'm searching for a book or an online copy of complete works of the mathematician François Viète, preferably in English. Any help will be appreciated. Thanks.
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### Kakutani's Lemma

I read this story a while ago, and I'm wondering whether there's any proof that it is true or whether it's just made up? One day Shizuo Kakutani…was teaching a class at Yale. He wrote down a ...
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87 views

### Which is the first reference using the terminology “Chinese Remainder Theorem” for this theorem?

The Chinese Remainder Theorem is one of the fundamental theorems in modular arithmetic. As far as I know, this terminology for the theorem is due to the fact that the Chinese mathematicians were the ...
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135 views

### Did Leibniz interpret his determinant as a volume function?

It might look like not a serious question, since Leibniz discovered Cramer's rule (1684), so it makes much sense that he interpreted the determinant as an expansion factor for a volumetric element. I'...
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101 views

### Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
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120 views

### How is Laugwitz's work on Cauchy viewed by historians?

Detlef Laugwitz is mainly known for his by-now-standard biography of Riemann: Detlef Laugwitz, Bernhard Riemann 1826-1866 : Turning Points in the Conception of Mathematics (1996 - German ed.1996) as ...
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122 views

### Are there any functions which were proposed as elementary by mathematicians but not considered elementary now?

Are there any functions which were proposed by various mathematicians to be included in the set of elementary functions because of their properties but not considered elementary as of now?
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229 views

### Who first used Banach's Contraction Principle to prove the Inverse Function Theorem?

The most common proof of the Inverse Function Theorem in textbooks relies on the Banach fixed-point theorem. QUESTION. It is possible to say, using historical references, which mathematician ...
1answer
119 views

### The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
1answer
176 views

### Are there any mathematicians who expressed non-obvious sets of rules on how to do research?

I recently saw a paper where there are presented some rules on how to learn mathematics (and do research) which were firstly articulated by Lagrange. Are there any similar rules that were expressed ...
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95 views

### Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
0answers
64 views

### How did Fourier determine the coefficients of Fourier series?

I was reading a chapter of Fourier's seminal work "Analytic Theory of Heat". The third chapter of this book was translated by the famous Stephen Hawking in his book "God created the ...
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60 views

### Why are linear forms called “forms”?

My question is about linear forms, quadratic forms, n-linear forms, differential forms and so on. The first term of these names seem clear to me, but I cannot make a link between these mathematical ...
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33 views

### Historical proofs of the series expression for the Bessel function of the first kind

Introduction The Bessel function of the first kind $J_n(x)$ ($n \in \mathbb{Z},\ x \in \mathbb{R}$) appeared early among other topics, in Celestial Mechanics, in the series expression of the true ...
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### How did definitions of a limit vary before the epsilon-delta definition?

My understanding is that before the epsilon-delta definition of a limit, the rigor and soundness of the definition of a limit was not good enough. So, how did the definitions of a limit vary before ...
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141 views

### The mathematics of multiple values

tl;dr Why has the array paradigm, which emerged in the 1950s and 60s amongst mathematicians, and which underpins certain programming languages, apparently failed to capture and maintain interest ...
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72 views

### Finding sources for “computers will become so powerful that special functions will become obsolete” as a zeitgeist

In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations: This continuing and indeed increasing reliance on special functions is a ...
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63 views

### Research about Stafford Beer's claim about a method for solving simultaneous equations unknowingly via a game by kids?

I found this claim in the book "How many grapes went into the wine", in the Artorga section: In 1956 I devised a game for solving simultaneous linear equations in two variables. The theory ...
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92 views

### Why didn't the ancient Greeks consider 1 to be odd?

The Wikipedia page on parity currently says: The ancient Greeks considered 1, the monad, to be neither fully odd nor fully even Why didn't they consider 1 as odd? (I am assuming they already had the ...
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If $a, b$ are positive and coprime integers, then the set of linear combinations of $a$ and $b$ with nonnegative coefficients is all integers past $(a - 1)(b - 1)$; i.e. $\{ \lambda_1 a + \lambda_2 b :... 0answers 44 views ### When did Kolmogorov complexity begin being applied to real world objects and ideas? I was looking at this paper about "Low complexity art" which involves kolmogorov complexity and I was wondering of when did that complexity theory began being applied to other things that ... 0answers 61 views ### What was the first trigonometry book ever to appear containing most (or all) things we study nowadays in trigonometry What was the first Trigonometry book ever to appear containing most (if not all) things we study nowadays in Trigonometry? I have heard that Pythagoras never wrote any book and that we have very few ... 0answers 101 views ### Origin of (f×g)(x) and (f∘g)(x) notations Who and when began the writing of function multiplication,$f(x)×g(x)$, as$(f×g)(x)$and of function composition,$f\big(g(x)\big)$, as$(f∘g)(x)$? 0answers 59 views ### When was the earliest usage of diagrams to represent set relations? According to wikipedia Euler came up with Venn-like diagrams well before Venn but Lull and Leibnitz came up with pictorial representations of set relations even before that. Was Lull the first who is ... 0answers 95 views ### History of$\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 ...
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### 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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### Where did the Delannoy numbers make their first appearance?

I am writing a short exposition on the central Delannoy numbers and would like to find the year which Henri Delannoy first introduced them in a formal setting. I believe Delannoy's initial ...
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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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83 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 ...
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83 views

### When did the term “order” come into use as the highest exponent in an expansion?

Answer(s) to the question What is a 3rd-order Fresnel lens? are disappointing to me, in that the term 3rd order does not refer to anything like a third-order series expansion. But this leads me to a ...
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27 views

### Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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166 views

### Why are there 24 hours in a day?

The question could be answered in a number of ways: Historically (e.g. Egyptians did for <...> reasons) Mathematically (It is a highly composite number) I'm looking for a mathematical answer. I'...
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### Who came up with a number of the theoretical plates equation?

In chromatography, the signal is shaped like a Gaussian peak, and it is plotted against time vs. instrument's signal. https://en.wikipedia.org/wiki/Chromatography#/media/File:Rt_5_12.png (a) One of ...
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134 views

### What pythagorean table looked like?

Pythagoras introduced the multiplication table in Southern Italy about 500 BC, do we know how it looked like? Edit I do not mean the so called pytagorean/multiplication/times table but the actual ...
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### Reference for Math-Physics history book

I am looking for a book on the history of mathematics that would also serve as a book on the history of physics. In the sense that the history of math is developed along with the developments in ...
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84 views

### What evidence is there that the Babylonians used the Babylonain method of estimating square roots?

The Babylonian method for computing square roots is described (among other places) in this Wikipedia article. What evidence is there that they actually used this method? I have found several ...
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58 views

### About Sobolev inequalities

i'm interested in the history of the 2 Sobolev Inequalities. The Gagliardo-Nirenberg-Sobolev inequality and Morrey inequality as here Sobolev inequality . How did these two inequalities arise? What ...
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263 views

### History of PDE's in the 19th Century (part 2)

This is a follow up to this question: History of PDE's in the 19th Century The question I have been given to answer is: The history of partial differential equations in the 19th Century belongs ...