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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What paragraph was written by Emanouil Atanassov to solve problem 6 on the International Mathematical Olympiad in1988?
From Wikipedia, "Emanouil Atanassov, Bulgaria, solved the problem in a paragraph and received a special prize.". The reference links to this page, https://www.imo-official.org/participant_r....
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Q: Babylonian tablet for pi=3.125
I read an article about Babylonian pi. https://numberwarrior.wordpress.com/2008/12/03/on-the-ancient-babylonian-value-for-pi/
The author wrote that Babylonians used 25/8 as pi. But, he could not show ...
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How did Ruffini manage to extend the methods of Lagrange in order to “prove” the insolvability of the general quintic equation?
Since Lagrange published his Reflections papers during the early 1770s — around 30 years before Ruffini took up and extended the subject — I was wondering if there were any results that were ...
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How did the Greeks label their axes?
In the current era, we label the Cartesian plane in x and y as our basis vectors, but what did the Greeks use to label their axis? The Greeks were around long before Descartes, so did they even use ...
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On the history of development of the concept of complex numbers [closed]
The history of how the concept of complex numbers developed is convoluted.
On physics.stackexchange questions about complex numbers keep recurring. It seems to me this indicates that when authors of ...
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116 views
Meaning of certain identities of Gauss on theta functions
Volume 3 of Gauss's werke contains an unpublished treatise with the title "Theory of new transcendents" (p.433-481 of the same volume). On page 441 of the same volume appears an interesting ...
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What was Newton's road to his discovery of “Puiseux series” and “Newton polygon”?
In my opinion, one of Isaac Newton's greatest achievements in the "purer" aspects of mathematics was his discovery of Puiseux series; power series with fractional exponents. According to p.6 ...
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Who studied kinematics before Galileo? Did Galileo base his kinematic research on the previous work of any other scientist?
Galileo is known to have studied kinematics through his work with projectiles. How did he first consider researching motion and velocity? Was he inspired by previous work done by earlier scientific ...
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Was Lagrange the first to have used generalized coordinates?
I was wondering if Lagrange was the first to use generalized coordinates as defined by their wikipedia article.
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127 views
What did Newton's teacher contribute to the Fundamental Theorem of Calculus?
Isaac Barrow was one of the professors who taught Isaac Newton at Cambridge. According to this page, he is said to have made contributions to the Fundamental Theorem of Calculus that was devised by ...
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114 views
What steps did Richard Feynman take to devise his Integral Trick?
Richard Feynman is considered to be one of the greatest minds in physics, and has won many accolades as a result of his research in areas such as quantum mechanics and particle physics. However, I am ...
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92 views
How did human beings come to realize the concept of counting numbers? [closed]
Human beings keeping count is as old as recorded history; however, how did humans first think about keeping documentation and counting numbers? Is there any defined period in history where numbers ...
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116 views
Has any large group of people used a base other than 10, 20 and 60 for ordinary purposes?
Wikipedia's list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different ...
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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 ...
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86 views
The Roman numeral system continues to lack a zero digit today. Would zero ever get its own Roman numeral digit in the future? [duplicate]
This question is a follow-up to: Why didn't the number zero (0) have a Roman numeral of its own?
The number zero did not have an official Roman numeral symbol in the first place, and it still ...
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How did Yao came up with his minimum spanning tree algorithm?
I recently stumbled upon this text about Yao's algorithm for the minimum spanning tree (MST) and I was wondering if there are some preceding algorithms (other than Sollin's algorithm) that were ...
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Who introduced the comma notation for partial derivatives?
In general relativity, it is common to use the comma notation for partial derivatives
$$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$
Where did this notation first appear? Was it ...
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Why do we use Leibniz's “version” of calculus instead of Newton's?
I understand that they invented calculus independently at roughly the same time, but why do we use Leibniz's terminology/notation rather than Newton's?
For example, why don't we use "fluxion"...
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What mathematical problems did the Sicilians need Arab help with in 1229? Did the Arabs solve these problems?
An incident in the negotations of the Sixth Crusade is described as Frederick II asking help from Arab scholars with some mathematical problems:
... and the sultan graciously allowed Frederick to ...
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How did Kolmogorov came up with his formalization of intuitionistic logic?
According to this article Kolmogorov published a paper in 1925 in which he attempted to formalize Brouwer’s intuitionistic mathematics.
In that paper there are the following logical formulas:
\begin{...
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112 views
When was the function 1 + cos(x), aka the vercosine, given a name?
Nowadays, when one searches for little-known trigonometric functions, one usually finds a list containing the versine, coversine, vercosine, and covercosine. When using this list, $1+\cos(x)$ is given ...
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What are the direct predecessors of Lagrange's theory of quadratic forms?
I was reading Stillwell's Mathematics and its History, where Lagrange's theory of quadratic forms is synoptically presented, and I was wondering of what are the direct predecessors of the theory.
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Where is this statement of Bourbaki's Dieudonné from and what does it mean?
In a few places, such as this web page, I have read the following statement about Jean Dieudonné, who was a founding member of the French "secret society" of mathematicians, Nicolas Bourbaki:...
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Interpretation of a short note of Gauss on the resolution of a special system of inhomogeneous linear equations by roots of unity
My question refers to a 2-pages fragment of Gauss, entitled: "Note on the resolution of a special system of linear equations", which is found on pages 30-31 of volume 8 of his works. In this ...
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What mathematical theorems were known in the Americas prior to European contact?
A comment on another site brought the article How Does Race Affect a Student's Math Education? to my attention. In the article, the author observes (emphasis mine),
But she’s also constrained by the ...
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Newton as the first one to establish numerical analysis as a new field of study
I was reading about the history of Newton's Method. Newton used a cubic equation, $x^3 - 2x - 5 = 0$, to show the efficacy of his method around 1670. I was wondering that why Newton would choose this ...
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132 views
Why are complex numbers called 'complex'?
I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained.
I also ...
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Has Cantor's irregular enumeration of rationals ever been discussed?
Enumeration of all positive fractions recently has gained renewed interest (see the list below).
By translation invariance we can be sure that in all intervals (n, n+1] of the real axis, there are the ...
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History of points with coordinates notation
In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, ...
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How did percolation theory come to be established in network science, and who first studied it?
According to the textbook "Network Science" by Albert-László Barabási, percolation theory is a specialized branch of both mathematics and physics [1]. It involves node clustering in a ...
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174 views
Why was the original typesetting of Number Fields by Marcus so horrible?
Does anyone here know what technology or instrument was used to typeset the first edition of the well-received textbook Number Fields by Daniel A. Marcus? I ask because the original edition looked ...
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When and where was Legendre's Conjecture first published?
When and where did Legendre first publish or write about his conjecture that there is a prime between consecutive square numbers?
$$n^2 < p < (n+1)^2$$
I have looked through edition 1 and 2 of ...
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Is there an English translation of Kronecker's proof of Infinitude of primes?
Is any English translation of the following paper available?
H. Hasse, Vorlesungen ¨uber Zahlentheorie, Second edition, Springer-Verlag, New York, $1964$ (L. Kronecker, $269–273; 440–442; $ K. Hensel, ...
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93 views
Reference for Euler's Introductio in Analysin Infinitorum
In the following answer it has been claimed that "The reference here is not to Euler's 1737 "factorization" of the harmonic series but to 1748 Introductio in Analysin Infinitorum, where the identity ...
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Lessons from apparent paradoxes in geometric limits
1) Zeno's oxymoronic fleet, stationary arrow: One of the earliest infinity paradoxes, of course, is the flying arrow of Zeno which can't possibly be moving since it takes a finite amount of time to ...
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Nobel Prize for Applied Mathematics
There is no Nobel Prize for mathematics. However, have there been any Nobel Prizes for the use of applied mathematics to model the real world?
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Could a “field” have non-commutative multiplication originally?
Today, when the term "field" is defined in algebra, it is almost always stipulated that all fields are commutative. However, the author of these lectures says that this has not always been the case:
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Who first identified $\frac{n}{\ln(n)}$ as an approximation of a prime counting function?
Gauss, in his 1849 letter to Encke, mentions that he noticed the primes have a density approx $\frac{1}{\ln(n)}$.
In that letter, he also mentions an integral function for approximating the prime ...
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What is the history of these prime counting function approximations?
I am reading several sources and there seems to be a lack of clarity, and some contradiction, about the origins of the most recognised prime counting function approximations:
$\pi(n) \sim \frac{n}{\...
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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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What problem was solved by introducing the dimension of a vector space?
In linear algebra, we care a lot about dimensions. I get why it’s useful but not why it’s such a big deal. So I wondered what problem was solved historically by introducing a rigorous definition of ...
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How was mathematics used in World War II to “act on the right amount of intelligence”?
In the movie "The Imitation Game", Alan Turing along with his team crack the German encryption machine Enigma but advises his superiors to not act on all decrypted intelligence, as that might lead to ...
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184 views
What mathematics did Isaac Newton learn at school?
Since Sir Issac Newton invented a lot of modern mathematics, what mathematics did he already know? Since he was standing on the shoulders of giants which giants was he speaking of?
I presume he knew
...
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Handbook of proofs
Do you know any handbook where original proofs of mathematicians' of the past theorems and facts are in modern notation? For example, for the Archimedean spiral etc
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How did the definition of each “ordered set” come about?
I could get a little intuition about preset, poset, and toset. e.g. A toset is, in effect, a linearly ordered set, and a poset is a set in which no more than one element in the same order exists, ...
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When and WHY did mathematicians start turning their attention to imaginary exponents?
When and WHY did mathematicians start turning their attention to imaginary exponents? I read on Wikipedia about Euler's correspondences with Bernouille and such, but it doesn't answer what exactly ...
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What did Noether contribute to the theory of integral invariants?
What did Emmy Noether contribute to the theory of integral invariants that wasn't already done by, e.g., Sophus Lie in his 1902 Über Integralinvarianten und Differentialgleichungen?
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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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Literature on Mayan mathematics
I asked this question on math.se and they sent me here.
It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system.
Except for these facts, I'...
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Who first called the Brouwer Fixed Point Theorem “the crumpled paper theorem”?
Wikipedia attributes the remark to Brouwer himself, but I am extremely skeptical. Their citation goes to a webpage of a ? French educational TV show, where the remark appears to be a fictionalized ...
