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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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mathematical development

I have two questions regarding the development of mathematics: 1) Is there an example where in mathematics, a collaboration has led to the discovery of another result? I already know something like ...
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Level of maths of engineers in the Industrial Revolution

Did engineers like I.K. Brunel and his contemporaries employ calculus in their constructions? Or did they work just with 'rules of the thumb' and useful 'laws' like the square-cube...? What was the ...
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Why are permutations ($_nP_r$) called differently in non-English languages (“variations” in German)?

First of all, you should be at least a little familiar with combinatorics to understand that question. Some often used calculator keys in stochastic are the nCr and nPr ones. Edit: I've first asked ...
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If John Michell was more well known, would he rank above Isaac Newton in the history of science? [closed]

John Michell proposed black holes in the 18th century, hundreds of years before Schwarzschild and Einstein. His ideas were said to to be away head of his time, that he died in obscurity. I assume ...
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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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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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Who first proved Fubini's theorem for abstract measure spaces?

Fubini's theorem relates the double integral of a function $f(x,y)$ to an iterated integral with respect to $x$ and $y$. The basic idea of this theorem for Riemann integrals of continuous functions ...
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What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with the topic of anything Fourier during my undergrad days. Until recently when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of ...
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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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Irrational numbers math in old Roman age [duplicate]

I know that Hippasus proved that $√2$ is irrational number. My question is how were they doing the mathmatical operations like multiplication for rational numbers like 1.41421356237 I can do ...
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129 views

Why do we call Chinese monoid “Chinese”? Why not “American”?

Why do we call Chinese monoid "Chinese"? Why not "American"? You can find the definition of Chinese monoid from Wikipedia. https://en.wikipedia.org/wiki/Chinese_monoid
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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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How did Romans do multiplications?

The Romans hadn't indian numerals, but what 's worse hadn't the decimal system, yet produced amazing works of engineering and architecture. How was that possible? It's troublesome to make simple ...
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167 views

Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
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Original document of the Gaussian integral

The Gaussian integral $$\intop_{-\infty}^{\infty} dx \exp(-x^2) = \sqrt{\pi} $$ is done in a very smart way. But where is the original document?
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190 views

Who used the symbol $S_n$ for “rotation reflection” as a symmetry operation?

I am looking for the origin of the symbol $S_n$ used by chemists to denote the symmetry operation consisting of a $\smash{\frac{2\pi}n}$ rotation ($C_n$) about an axis and a reflection in a plane ...
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2answers
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Has the standard of mathematical proofs changed over time?

Why I asked this question : https://gallica.bnf.fr/ark:/12148/bpt6k90195m/f54.image p 50-51, in course of Cauchy, a proof of the intermediate value theorem. Now, that's not a proof. And I learned ...
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What are some good books that interweave the history of math and art from renaissance onward?

Ever since learning about projective geometry and its birth in the world of art, I’ve been intrigued to learn more about their union and how they influenced each other. I’m specifically looking for ...
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Did Eudoxus really set out to partition irrationals (Dedekind cuts) with rationals or was that a mere side effect we perceive through our modern POV?

I've been intrigued by the similarities between what Eudoxus' Theory of Proportions and Dedekind cuts. However, I wish to question this "perceived similarity" and would like to where the flaws are, ...
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63 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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English equivalent for a German idiom concerning integration

In German there is phrase concerning the complexity of finding the integral of a given function in contrast to the simplicity of finding its derivative. It has various slightly different formulations ...
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Where did Pi come from? [duplicate]

How did ancient mathematicians discover pi? I have looked across several websites and none of them seem to give a straight answer. How did they calculate this irrational constant?
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Centroid in Babylonian Mathematics

Are there any problems in Babylonian mathematics that deal with finding the centroid of some plane figure?
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History of the Gauss Circle Problem

The Gauss Circle Problem: find the number of integer lattice points inside a circle. My question is: why was Gauss studying this problem? Was it just math for math's sake, or was this a part of a ...
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111 views

Origins of molecular orbital diagrams?

Does anyone remember who proposed molecular diagrams for simple molecules as taught today in most general chemistry texts? I cannot access Hund's original article, however, Mulliken's early articles ...
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When and why was inversive geometry created/studied?

I have been revisiting math from my highschool through undergrad. I picked Courant’s excellent What is Mathematics? The flow is well so far. However, in one of the chapters he introduces inversion - ...
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Jordan's Paper on the Jordan Canonical Form

In which paper, did Jordan introduce/prove the Jordan canonical form?
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In which 1644 publication did Pietro Mengoli first pose the Basel Problem?

I find numerous claims that the Basel Problem was first posed by Pietro Mengoli in 1644. However, I am unable to find even the name of the publication (or book or letter) in which this was supposedly ...
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126 views

Why is umbral calculus not used more widely?

Recently I have encountered the so-called Umbral calculus. The main idea of this field is to treat indices as exponents, applying simpler techniques available to exponents and switching everything ...
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82 views

An english translation of Cauchy's “Cours d'Analyse”

I am quite interested in the origins of our modern way of understanding analysis. I know that Augustin-Louis Cauchy was one of pioneers regarding a rigorous foundation towards real and complex ...
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1answer
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Gregory's integration of $\sec\theta$

The integral of the secant function was first correctly conjectured by Henry Bond in the 1640s, and Isaac Newton was aware of his conjecture in 1665, although no proof was published until 1668. Of ...
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Did Nikolai Luzin plagiarize?

Luzin was accused of plagiarism and other misconduct by Kolmogorov and other students during the Luzin Affair of 1936. Were these allegations actually true?
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“Species” and “terms” meaning polynomials and monomials

I found in some old Latin texts and their translations that polynomials were once called "species" (if I understand correctly that they meant the same thing, but it looks like it). And their ...
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Were there proofs of the Lebesgue Differentiation Theorem without using maximal functions?

Is there a proof of the Lebesgue Differentiation Theorem that does not involve the Hardy-Littlewood Maximal Function? For example, did Lebesgue prove it? If there is such a proof, where can I find it?...
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When was the first appearance of the abbreviation RSA?

When was the first publication of the abbreviation RSA (Rivest, Sharmir, Adleman) because it does not appear in Martin Gardner’s article of 1977 which is at the following url: https://simson.net/ref/...
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How did the integer degrees angles counting being first adopted in geometry and mathematics? [duplicate]

The purpose of this question is trying to know originally how did counting in integer degrees angles from (one degree to $360$ degrees) being adopted basically in geometry, despite the impossibility ...
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4answers
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Mathematics development can sometimes **exceed** the practical needs, right?

I read below paragraph from the book "A Friendly Introduction to Number Theory": The use of "$i$" to denote the square root of negative $1$ dates back to the days when people viewed such numbers ...
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When was the nine point conic discovered?

I wonder when was discovered the nine point conic. English Wikipedia article about it https://en.wikipedia.org/wiki/Nine-point_conic is misleading. The nine point conic wasn't discovered in 1892. In ...
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202 views

What was the main language in science/mathematics between 1850 and 1950 and beyond

The second half of 19th century and first half of 20th century are golden age of modern mathematics and science, as many important ideas and theories were proposed and developed within that period of ...
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231 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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Origin of Compactness

According to Wikipedia https://en.wikipedia.org/wiki/Pavel_Urysohn, Urysohn and Alexandrov first formulated the modern definition of compactness. In which paper did they do this? Is there an English ...
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66 views

Existence of Pythagoras Resources

I am aware that approximately two years ago a question was posted on the existence of Pythagoras. After two years, I want to gain more incite on the thought of those on this site. I was drawn to the ...
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477 views

What was the main language in science/mathematics before 1850

I know that English is the most popular language to write scientific/mathematical papers after World War 2. I also know that in the second half of 19th century and first half of 20th century, German ...
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294 views

History of hypergeometric equation

It is known that Gauss studied hypergeometric equation $$x(1-x) \dfrac {d^2y}{dx^2}+(c-(a+b+1)x)\dfrac {dy}{dx}-aby=0$$ I would like to know something about history of this equation: 1) If $a=b=c=0$...
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107 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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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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2answers
174 views

Dirichlet's Proof of the Convergence of Fourier Series

Where can I find Dirichlet's proof of the convergence of Fourier series?
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Did amateurs ever produce important proofs or similar?

Background Mathematics and some areas of physics and computer science have the peculiar appeal that some problems and results are easy to understand and it is conceivable that somebody armed with ...
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1answer
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Reference - Schwarz's Proof of Clairaut's Theorem

Where can I find a copy (online) of Schwarz's paper that proved Clairaut's theorem for mixed partial derivatives? His paper is: Schwarz, H. A., "Communication", Archives des Sciences Physiques et ...