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

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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 ...
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Why statistical moments are called moments?

According to the Jeff Miller's Earliest Known Uses of the Words of Mathematics "Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
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Failures in math

I would like to have help in producing examples of mathematicians that, in some sense I'll explain below,turned their career into failure. I am mainly interested in examples from XIX and XXth century. ...
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History of group theory character tables (as used in physics and chemistry)

Does anyone know who started using the symbols A, B, E, T (First column, left) for showing irreducible representations of symmetry groups? In older maths books I see capital gamma. Herein A= totally ...
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Who discovered the expansion for factorial as successive difference of integers?

Who discovered the following theorem $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(n-r)^n=n!$$
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Etymology of Some Terms Used in Ratio and Proportion in Old Algebra Textbooks

In older algebra textbooks for high school (mainly 19th century) four properties of ratio and proportions were used. The properties were Invertendo, Alternendo, Componendo, and Dividendo. This ...
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Foundational crises in non-Western historical mathematical communities

In Foundations of Set Theory by Fraenkel, Bar-Hillel, and Levy (1973), the authors argue that there have been three distinct periods of crisis in the foundations of mathematics. The first was ...
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95 views

Why was Courant's “Methods of Mathematical Physics” suppressed, by the Germans, during WW2?

In the preface to Methods of Mathematical Physics Richard Courant, the author, wrote that the book was suppressed by the National Socialist rulers(Nazi) of Germany. Hence, my question. Thanks.
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Help translate from German a quote by Hermann Weyl in Space Time Matter

I would like to find an accurate translation to the following quote from Space Time Matter: Man muß gegen diese Orgien des Formalismus, mit dem man heute sogar die Techniker zu belästigen beginnt, ...
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Was there an intentional purge of all audio recordings of Alan Turing?

The YouTube video Alan Turing's lost radio broadcast rerecorded contains a re-enactment of Alan Turing's lecture broadcast by the BBC. In the introduction, the narrator (James Grimes, also of the ...
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In history of algebra, who was the first to add one equation to another equation?

In history of algebra, who was the first to add one equation to another equation? Someone gave me the name of an Italian mathematician of Renaissance period, but I lost the email. I wish to make it a ...
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On the creation of analytical geometry

Of all mathematical creations, the one of using graphs to describe planes and 3D space seem to me the most strange ones. My head almost can't admit that space can be represent by three numbers. If I'...
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Priority on lemniscate of Gerono?

The Lemniscate of Gerono is a special case of the Lissajous curves. The dates for the two mathematicians are fairly close: Gerono (1799-1891) and Lissajous (1822-1880). Historically who has priority ...
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92 views

Is there an analog of Ginga style in mathematics? [closed]

Ginga is a highly creative and elegant form of playing soccer or football. It was the playing style of legendary footballers like Pele and Garrincha. What I want to know is whether there is a similar ...
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84 views

What were the early uses of differential equations for modeling chemical reactions?

What are some of the original examples of uses of differential equations for modeling and analyzing chemical reactions, particularly those relevant to biochemistry, involving proteins and enzymes? ...
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2answers
321 views

How influential was the Kerala school to European development in Calculus?

Did it influence the work of Newton or Leibniz, i have often heard that Europeans "stole" calculus from the Kerala school, these are views often parroted by Indian nationalists, but how accurate is it?...
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64 views

Author of a review in *Mercure de France*

Would anyone know a way to figure out who wrote the (rather dithyrambic) review of D'Alembert’s Opuscules mathématiques, vol. 6 (1773), found in Mercure de France, April 1773, pp. 127-132? It seems ...
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142 views

What is Newman's “infinite number of curves”?

In John Henry Newman's The Idea of a University (c. 1850), he writes that, in mathematical science, we are told of ...the existence of an infinite number of curves, which are able to divide a ...
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71 views

What field will we be remembered for developing? [closed]

I had a course on History of Mathematics this semester and it seemed that each civilization became known for developing a particular area of mathematics. For example, Arithmetic and Ancient Egypt/...
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Reference Request: Books on the work of Imre Lakatos

What are the best works summarizing, discussing or criticizing the work of Imre Lakatos? What are the pros and cons of said works? Which would you recommend picking up first if one has read some but ...
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126 views

Who extended the Euclidean algorithm to derive the Bezout identity?

Euclidean algorithm is an algorithm that produces the greatest common divisor of two integers. It was described by Euclid as early as in 300 BC. On the other hand, the extended Euclidean algorithm ...
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69 views

Who coined the term “uniform” as in “uniform distribution”?

During the late 16th century and early 17th century, published work about probability theory (e.g. Liber de ludo aleae by J. Cardan published in 1663 but writen around 1564) studied dice games using ...
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What is history behind Smith-Volterra-Cantor sets?

Looking at Wikipedia, I see that fat Cantor sets are also called Smith-Volterra-Cantor sets. Another name which is sometimes associated with these sets is Hermann Hankel. I suppose that Cantor's name ...
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112 views

Riemann's moduli and Dedekind's modules: any connection?

The concept of a moduli space goes back to Riemann's count of $3g-3$ (or $3p-3$, in older notation) coordinates to describe Riemann surfaces of genus $g$ when $g > 1$. See the bottom of p. 33 here, ...
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143 views

Indiana Pi Bill: Other attempts to establish mathematical truth by legislative fiat?

Wiki: The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative ...
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Who introduced moments of a random variable first?

When, by whom and in which paper where moments of a random variable used first in probability theory?
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219 views

Mathematics PhD dissertations that opened a new field of research

I propose this as a companion wiki page to the one about PhD dissertations which contain a solution to an open problem in the style of big-list questions, thinking ...
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1answer
58 views

Was Captain Cook’s voyage to observe the transit of Venus going to enable better ship navigation at the time?

On a recent visit to the Royal Observatory at Greenwich I was struck by its proximity to the Naval Academy next door. The theme of the history of clocks and development of astronomy was driven by the ...
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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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157 views

When it was discovered that cubic equations always have roots?

Every cubic equation (with real coefficients) has a real root. Who was the first person who proved this? Is it already contained in Bombelli's Algebra?
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135 views

Earliest known usage of letter gamma “Γ” for reducible representation in group theory

Does any know the earliest known usage of the Greek letter gamma for showing a reducible representation of a group? This symbolism is commonly used in character tables in chemical applications of ...
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1answer
84 views

Straightedge and compass

According to most discussions of Euclid's Elements, this work - and indeed, much of Ancient Greek geometry - should be seen as engaged in the game of figuring out what can be done with straightedge ...
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191 views

How was the sum of squares formula discovered by Archimedes?

AFAIK, Archimedes is credited with discovering the following formula for computing the sum of squares: $1^2 + 2^2 + 3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}$ This seems to have come up in his quest for ...
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Alligation - when and why did it disappear?

I have a book from 1795 where the mixing of quantities is done by Alligation. Depending on the supplied data this can be Partial, Alternate, Medial or Total. When I asked several teachers 'how would ...
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105 views

The Principia Mathematica's missing chapters

The numbering of the chapters of Bertrand Russell and Alfred Whitehead's Principia Mathematica is the following : 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 25, 30, etc overall, ...
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129 views

Definitions of continuity pre-Dedekind

In his article on "Kant's Theory of Geometry", Michael Friedman claims that: (...) before Dedekind mathematicians would commonly give what we call the definition of denseness when explaining what ...
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108 views

First appearance of the product symbol ($\Pi$)

As far as I can tell, the first occurrence of the sum notation ($\Sigma$) was in Euler's book Institutiones calculi differentialis: Quemadmodum ad differentiam denotandam usi sumus signo $\Delta$, ...
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157 views

When did the mediant (“freshman sum”) of two fractions first appear in mathematics?

I have been reading about the history of Farey fractions and I am intrigued by the appearance of the mediant in the Farey tree and related objects. After a bit of searching, Nicolas Chuquet's ...
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245 views

How were variables used and understood in (particularly) 19th century maths?

Context: I have been thinking about Frege's Begriffsschrift, where he introduces a version of what we now think of as the standard quantifier/variable notation. Philosophers who write on Frege tend to ...
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277 views

How was the focus/directrix property of conic sections discovered?

I've always thought that defining conic sections by a locus of points w.r.t the ratio of the distance to the focus and directrix was always "too artificial" - how does one actually discover this ...
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119 views

What caused or contributed to Euclid's Elements and Synthetic Geometry falling into disfavor?

Euclid's Elements could tout to have the longest and most famed publishing history of any book ever written. First written in 300 B.C., Euclid's Elements became the standard text from which ...
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100 views

Does an English translation of Bombelli's L'Algebra exist?

I'm looking for an English translation of Rafael Bombelli's L'Algebra. From what I can tell searching the usual corners of the web, it doesn't exist, but I'm asking here just in case. I'm ...
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1answer
319 views

Who Invented The Number Line?

Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?
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131 views

What astronomical reason led to the creation of the trigonometric sine and cosine?

Sines and cosines are commonly introduced as ratios of sides of a triangle with its hypotenuse and attributed to ancient Indian scholars. However, I've never actually thought of the reason for ...
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147 views

Why didn't Euclid's Elements treat conic sections?

There's a well known treatise by Apollonius on conic sections, but these objects are absent in Euclid's Elements. Why? If I were to guess, I'd say that conic sections cannot be constructed using a ...
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334 views

Who coined the term “iff” for “if and only if”?

The OED's entry for "iff" lists this as the earliest usage: 1955 J. L. Kelley Gen. Topol. vii. 232: "F is equicontinuous at x iff there is a neighborhood of x whose image under every member of ...
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154 views

What is the international standing of Italian mathematics?

Being Italian, I have a biased view on my homeland's mathematical impact in the world, so I would like to get some impartial opinion on the topic. I would measure the mathematical relevance in terms, ...
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64 views

Invention of matrix symbols

Who first did use the symbol $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ for a matrix and similarly $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$? Why do these two ...
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Who invented the method of characteristics? [duplicate]

It is a technique introduced in many textbooks. But they never mention its origin. Who first used this method?