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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Why did Cantor (and others) use $\mathfrak{c}$ for the continuum?

Kontinuum is German for continuum, but Cantor used $\mathfrak{c}$. Revision. J.W.Perry questions whether or not Cantor ever in fact used the symbol $\mathfrak{c}$. I must admit I just assumed that he ...
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What was the best approximation of π known to ancient Babylonians?

Wikipedia's Babylonian mathematics says that the ancient Babylonians usually used a round value for $\pi$ (3). But they knew a more precise value: Babylonian texts usually approximated π≈3, ...
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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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Where in Gauss's nachlass did he pose the problem of connectedness of a surface?

On p.98 of the book "Mathematics of the 19th Century: Geometry, Analytic Function Theory", the authors mention a note written by Gauss in 1840: In 1840 Gauss wrote a note in which he introduced the ...
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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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Origin of $\ll$ notation

Vinogradov introduced the notation $$f(x) \ll g(x)$$ to denote that for some $C>0$, we have $|f(x)|\leqslant C\,g(x)$ for all $x$ under consideration; usually for all $x$ larger than a fixed ...
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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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109 views

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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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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Did du Bois-Reymond invent the diagonal argument before Cantor?

The Wiki article on Cantor's diagonal argument mentions that the first use of a diagonal argument was in the work of Paul du Bois-Reymond in 1875. This would be one year after Cantor's first proof of ...
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Did the ancient Greeks have zero in their number system?

I was taught that the Arabs introduced zero in their Arabic numerals and it was depicted as a decimal point. They got their number system from India in turn in Sanskrit where the zero digit was also ...
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Who introduced random variables into probability?

I used to think that the answer is Kolmogorov. So the Shafer-Vovk's review of Kolmogorov's famous 1933 axiomatization of probability surprised me a bit:"Today, what Frechet and his contemporaries knew ...
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I am searching for a book of this form and content, is there any?

I would like to know is there a book that is both a history of mathematics and a collection of open problems? I know that there exist many books that cover either larger or smaller periods of the ...
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104 views

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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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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417 views

What brought about the need for real analysis and formal logic in recent years?

I can't seem to find a clear, definitive, non-circular answer on this. For centuries and centuries, we've been doing mathematics in one form or another, be it geometry and pictures, or inventing ...
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1answer
200 views

Cantor's fortune

Wiki says that his transfinite numbers met opposition: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public ...
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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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Are Euclid's theorems and proofs due to Euclid?

Some appear to argue that much of the Elements by Euclid is a compilation of knowledge handed down to Euclid from his predecessors. On the other hand, some credit the proof, of the Pythagorean theorem ...
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187 views

Why didn't Euclid try to assign numbers to lengths?

Preliminary note: With "Euclid" I don't mean a person but the mathematicians of the Euclidean period of which Euclid (if he had been one person) was a representative. I imagine that Euclid could have ...
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164 views

Has Euclid stated Cauchy's theorem?

Cauchy's Rigidity theorem says that if the corresponding faces of two convex polytopes are isometric (congruent) then the polytopes are related by a (proper or improper) motion. Cauchy's biography (...
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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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Translations of “Sur le théorème de Zorn”?

Are there any translations of the following into English, German, or Russian? Nicolas Bourbaki, Sur le théorème de Zorn, Archiv der Mathematik, Volume 2, pages 434–437, November 1949. Any help is ...
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Where did the term “set-builder notation” come from?

In math stack exchange I often see notations like $\{x\in\mathbb Q:x^2<2\}$ being called instances of set builder notation. When I went to school we (that is, I, my fellow students, my teachers, ...
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Where are Pierre Samuel's videos of Bourbaki proceedings available?

Wikipedia's article on Pierre Samuel claims (uncitedly): He was a member of the Bourbaki group, and filmed some of their meetings. A French television documentary on Bourbaki broadcast some of this ...
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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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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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What is the origin of the Collatz conjecture?

When was the $3x+1$ problem first proposed? At Wikipedia, I found the following statement (without citation): The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who ...
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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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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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What new mathematics was inspired by biology and chemistry?

While physics and astronomy sported mathematical models for centuries mathematical chemistry and biology appeared relatively recently. Most of the interaction seems to go one way, established ...
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202 views

Was further research done about the invention of Algebra?

In his book “A History of Mathematics”, Carl Boyer mentions that both AlKhwarizmi and Abd ElHamid Ibn Turk wrote their books on Algebra (“Aljabr w Almuqabla” and “Logical Necessities” respectively) at ...
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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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What was the connection between David Hilbert and Stefan Banach?

The so-called "Hilbert space" is named after mathematician David Hilbert. Later, this was generalized into "Banach spaces" by Stefan Banach. My understanding is that Hilbert was ...
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Material on the History of Mathematical Spaces

First and foremost, I am aware that a similar question has been asked here and has been touched upon elsewhere. I have found these discussions very compelling but a bit light on external reference, ...
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Was Hilbert ambivalent about set theory?

There is the well-known quote of Hilbert: "No one shall drive us from the paradise which Cantor has created for us." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (...
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203 views

Are there any records that show how Hilbert came to “invent” or “discover” Hilbert spaces?

I think it's fuzzy as to whether or not this question is appropriate to ask on this site. The reason I ask it that the characteristics of Hilbert spaces are very much used in expressing quantum ...
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Hilbert's reaction to Gödel's incompleteness theorems

Is it known how Hilbert initially reacted to Gödel's incompleteness theorems upon their announcement at the Königsberg conference in 1930, or their publication in 1931?
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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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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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How were derivatives of trigonometric functions first discovered?

When proving them the "modern" way (from first principles) it seems impossible to get around proving the identities $$\lim_{x\to 0}\frac{\sin x}{x} = 1$$ and the related $\cos$ limit. This itself ...
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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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652 views

Why is the Halting problem attributed to Alan Turing?

The halting problem is a very famous example from computability theory of a problem that is undecidable. It is often said that the proof of its undecidability was given by Alan Turing, indeed ...
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Is there a Martin Gardner's article archive available online?

Martin Gardener was a great recreational mathematics expert and his column "Mathematical Games" is an all time hit. But is there any archive available online consisting of his articles (...
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How has the definition of a tensor today changed compared to its original definition?

On page 71 of The Absolute Differential Calculus by Levi-Civita, a very clear definition of a tensor is given in terms of how the coefficients of a multi-linear form transform, such that the product ...
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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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