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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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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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Is it acceptable in academic literature to use “acceleration” when discussing processes that do not involve displacement, distance, velocity [on hold]

Is it acceptable to use "acceleration" and "uniform acceleration" in describing physical processes that do not involve displacement, distance, speed, velocity? Or must we use a more awkward ...
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99 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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60 views

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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106 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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74 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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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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36 views

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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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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198 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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218 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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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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5answers
429 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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288 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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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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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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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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145 views

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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167 views

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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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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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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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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337 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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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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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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73 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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143 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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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 ...