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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19 views

What are some historical exemples in physics of heuristic proofs of mathematical results?

In the proceedings of the XIth International Congress of Mathematical Physics Edward Witten wrote (p. 704) [$\dots$] when a mathematical result is really relevant to a physics problem it often ...
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Are there any mathematicians who expressed non-trivial sets of rules on how to do research?

I recently saw a paper where there are presented some rules on how to learn mathematics (and do research) which were firstly articulated by Lagrange. Are there any similar rules that were expressed ...
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What were Riemann's “semi-physical” methods?

In John Von Neumann's The Mathematician one can read that [$\dots$] even after the reign of rigour was essentially re-established with Cauchy, a very peculiar relapse into semi-physical methods took ...
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Was Morse code the first practical application of binary encoding of information?

As I understand schemes for sending different symbols over different wires were implemented but the simplicity of Morse's dot or dash made it the easiest to read and/or implement. It seems similar to ...
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78 views

Was Giuseppe Peano one of the greatest mathematicians of his era? [closed]

Besides the Peano axioms which perhaps brought him fame but which are considered a refinement of similar previous axioms Peano seems to have done relatively little original work. Does the rest of his ...
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1answer
108 views

When did mathematicians suspect that $\pi$ is irrational?

The title says it all. The irrationality of $\pi$ was proved by Lambert in the 18th century, but the Greeks at the time of Pythagoras already knew that $\sqrt2$ and the golden ratio were irrational. ...
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153 views

How did ZFC become the standard foundations of mathematics?

I would like to hear about the historical and technical reasons for why Zermelo-Fraenkel set theory with the axiom of Choice became the dominant standard for the foundations of mathematics. The system ...
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Why didn't the ancient Greeks consider 1 to be odd?

The Wikipedia page on parity currently says: The ancient Greeks considered 1, the monad, to be neither fully odd nor fully even Why didn't they consider 1 as odd? (I am assuming they already had the ...
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Who coined the Hawaiian Earrings?

I hope to know who first used the name "Hawaiian Earrings." Barratt, Milnor(1962) says "This example was suggested by Steenrod" in its Introduction: https://www.ams.org/journals/...
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Where did Leibniz explore the product rule of differential calculus?

In what book/letter did Gottfried Wilhelm Leibniz explore the product rule as part of differential calculus?
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How did the Vietnamese manage set up the Vietnamese Mathematical Society during the Vietnam War?

The Vietnamese Mathematical Society was set up in 1965 by Le Van Thiem and Hoang Tuy. Both had studied in Europe, the former in Paris and Germany and the latter in Moscow. By 1965, the Vietnam War, ...
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Why isn't the history of mechanics dated from Archimedes time?

It's often said - and more often written - and perhaps, even more spoken of - that modern physics began with Galileo due to his application of mathematics to motion. This is the position taken by ...
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Timeline for the earliest work on Frobenius problems

If $a, b$ are positive and coprime integers, then the set of linear combinations of $a$ and $b$ with nonnegative coefficients is all integers past $(a - 1)(b - 1)$; i.e. $\{ \lambda_1 a + \lambda_2 b :...
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When was the “Law of Propagation of Error” first stated?

This is my first time posting on HSM, so please bear with me if it's off-topic. I can move it to Stats.SE or Mathematics.SE if necessary. A widely cited 1966 paper (with currently 1030 citations) ...
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430 views

What does “given in species” mean in old geometry textbooks?

I recently came across the term "triangle given in species" in Hatton's Projective Geometry. Searching in archive.org turned up other examples (such as this) of 19th century texts, and it ...
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Did Hardy and Ramanujan miscalculate these values?

When I read Dickson's History Of The Theory Of Numbers Vol-2, I found that there seems to be a mistake in the approximation of partition numbers p(200). For this reason, I found the original text ...
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When did Kolmogorov complexity begin being applied to real world objects and ideas?

I was looking at this paper about "Low complexity art" which involves kolmogorov complexity and I was wondering of when did that complexity theory began being applied to other things that ...
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What was the first trigonometry book ever to appear containing most (or all) things we study nowadays in trigonometry

What was the first Trigonometry book ever to appear containing most (if not all) things we study nowadays in Trigonometry? I have heard that Pythagoras never wrote any book and that we have very few ...
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73 views

Where did the contour integral sign appear for the first time?

A simple question: Where did the contour integral sign appear for the first time? Wikipedia says that it was introduced by physicist Arnold Sommefield in 1917 ( Table of mathematical symbols by ...
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68 views

What's the history of experimentation by simulation? [closed]

How did the essemtial general purpose algorithms for simulations evolve over the past 50-100 years?
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59 views

English translation of Xu Yue's Shushu Jiyi?

Is there an english translation of Xu Yue's Shushu Jiyi? This is the work, around 190 CE, often described as containing the first description of the abacus. It is often associated with China's "...
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Question about the significance of “Gauss-Legendre quadrature”

I want to understand why, according to several sources, Gauss's discovery of Gaussian quadrature in his 1814 article was "the most significant event of the 19th century in the field of numerical ...
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What is the history on the term 'co-domain'?

I am wondering if anyone knows any more on the history of the term 'co-domain' as it relates to functions. Two sources I found: Russell and Whitehead, Principia Mathematica, 1915, page 34 : the class ...
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146 views

Why is Dirac delta named after Dirac when the concept was already over two centuries old?

Please explain why the Dirac delta function was named after Dirac, who lived in the 20th century, and what was so special about it. I ask this because it is used in Green's function which pre-dated ...
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93 views

Origin of (f×g)(x) and (f∘g)(x) notations

Who and when began the writing of function multiplication, $f(x)×g(x)$, as $(f×g)(x)$ and of function composition, $f\big(g(x)\big)$, as $(f∘g)(x)$?
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Origin of identity: $\int\limits_{-\infty}^{\infty} \exp\{ - \pi x^2 - 2 \pi^{1/2} a x\} \,da = \exp\left\{a^2\right\}$

A 1959 paper written by J. Hubbard called "Calculation of Partition Functions" and published in Physical Review Letters contains the following identity (Equation 2): $$\int\limits_{-\infty}^{...
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What are some archaeological discoveries from Ancient Civilizations that baffled mathematicians? [closed]

The Ancient Civilizations of Earth are highly advanced than accredited for. Their respect for numerology throughout various parts of Earth is interesting. It baffles me how they did it with such ...
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82 views

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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87 views

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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2answers
119 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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129 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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76 views

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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139 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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121 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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96 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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128 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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94 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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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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