Questions tagged [math-history]

Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

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Historically, when have the the real numbers been constructed via the "positive" (non-negative) reals first, and then usual real numbers second?

There has been something that has been bugging me for the longest time, at least since grad school. In the teaching of mathematics, during the construction of the "usual" real numbers, why ...
Rex Butler's user avatar
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Math notation ideal [closed]

I have been playing with Math notation thinking if it was possible to simplify our current notation. First I thought that it would be unnecessary to use any base system besides the Unary numeral ...
PageSteiner's user avatar
2 votes
0 answers
170 views

Why most math books don't give names for theorems? [closed]

In many rigorous math books, theorems are only labeled with numbers (in most cases, i.e., unless the names of the theorems are too famous to omit) rather than ‘number of theorem’ or ‘Mathematician’s ...
pie's user avatar
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History of the development of graph theory

I’m looking for a book or reference on the history of the development of graph theory. I would especially appreciate something with both technical and historical details. An example of something like ...
Aidan W. Murphy's user avatar
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72 views

Adjunction symbol

What are the reasons for the adjuction symbol $F\dashv G$ for a pair of functors $F:C\to D$ and $G:D\to C$? There is no explanation or motivation in the article of Kan where, afaik, adjunctions are ...
Jochen's user avatar
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540 views

Three Notions of Small

I’m currently learning about the history of the development of the Lebesgue integral in Thomas Hawkins’s book “Lebesgue’s Theory of Integration; It’s Origins and Development” Hawkins is stressing how ...
Joe's user avatar
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Is this Corollary a historical or modern product?

I saw this Corollary on page 21 of this book "Introduction to commutative algebra" by Atiyah and Macdonald. Corollary 2.5. Let $M$ be a finitely generated $A$-module and let $a$ be an ideal ...
user1274233's user avatar
1 vote
1 answer
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What is the origin of the terms fences, funnels, and separatrix in differential equations?

What is the origin of the terms fences, funnels, and separatrix in differential equations? I am not asking what they mean but rather who introduced them and how. They seem to be very recent terms, ...
SRobertJames's user avatar
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Who named the first fundamental form?

This is a historic question for which I couldn't find an answer on google or on the math history books I have at hand. The first fundamental form $I$ of a surface $S$ embedded in $\mathbb{R}^3$ is, ...
Henrique Augusto Souza's user avatar
-2 votes
1 answer
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About a historical note on a famous series

Currently, I'm doing research on the history of the Basel problem and I happen to notice a small gap. Not on the history of the aforementioned problem per se, since its history is very well documented....
Vaskara_GRek_O's user avatar
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Ten coordinate systems published by Newton

Around 1670, following Renee DesCartes' mid-century introduction of the Cartesian Coordinate system, Isaac Newton is supposed to have identified ten different coordinate systems. I am seeking to ...
Gwendolyn Anderson's user avatar
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When were negative numbers fully accepted into mathematics? [closed]

Dedekind gave a construction and explanation of integers and rational in 1858. This was as ordered pairs of natural numbers. I'm not sure if this was the standard view of these objects after this ...
Demon's user avatar
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Why is the Monster group called that?

This is a bit of a soft question, but why is the Monster group called that? Does it have any connection with monster models in model theory? I would be interested to learn who came up with that ...
user107952's user avatar
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Old Identity of Cauchy's

So I'm reading this old paper by Cauchy's from 1847, and at one point, he merely states without proof the following identity: let $n$ be an odd prime number, and let $\rho$ be an $n^{\text{th}}$ root ...
StormyTeacup's user avatar
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Why is none trying to find the value of $\displaystyle\sum_{n=1}^\infty\frac1{n^n}$?

I wish to know the exact value of $$\sum_{n=1}^\infty\frac1{n^n}.$$ I've found on the internet some mentions of the equality (the Sophomore's Dream, as I've learned) $$\sum_{n=1}^\infty\frac1{n^n} = \...
Alma Arjuna's user avatar
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1 answer
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Is there anything currently that generates rejection from the mathematical community? [closed]

Is there anything currently that generates rejection from the mathematical community, as happened with the complex roots of algebraic equations?
FRED ANTHONY VIGORIA HUALLA's user avatar
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Fermat's (hypothetical) erroneous proof

Until Wiles' proof of Fermat's last theorem all proposed proofs have been erroneous. It is not known which proof Fermat himself had in mind - but it is assumed that it was erroneous, too. Have there ...
Hans-Peter Stricker's user avatar
6 votes
1 answer
187 views

Has there ever been a substantial change in notation resulting from a landmark theorem?

Often times the notation we use for mathematical concepts is based in part on properties of that concept. For example, the notation $|A| = |B|$ in set theory means there’s a bijection between $A$ and $...
templatetypedef's user avatar
6 votes
5 answers
211 views

Eliminating $\theta$ from $x^2+y^2=\frac{x\cos3\theta+y\sin3\theta}{\cos^3\theta}$ and $x^2+y^2=\frac{y\cos3\theta-x\sin3\theta}{\cos^3\theta}$

An interesting problem from a 1913 university entrance examination (Melbourne, Australia): Eliminate $\theta$ from the expressions $$x^{2}+y^{2}=\frac{x \cos{3\theta}+y \sin{3\theta}}{\cos^{3}\theta} ...
Red Five's user avatar
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1 answer
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What makes Itô processes special?

As I understand it, Itô processes are those semi-martingales whose finite variation part is an integral (against Lebesgue measure) and whose (continuous local) martingale part is a stochastic integral ...
famous mortimer's user avatar
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The physical motivation of simplex

I read that homology, cohomology, and simplex emerged due to physical motivation on our country's blog. However, I cannot attach a link because my country is not an English-speaking country. For ...
user1274233's user avatar
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0 answers
116 views

Motivation about "Analysis Situs"

I read Poincaré's paper called Analysis Situs. And here's the thing about chain complex. (Page 104 in this file) That being given, let ${ε}^q_{i,j}$ be a number which is equal to zero if ${a}^{q−1}...
user1274233's user avatar
1 vote
2 answers
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Can $i$ be conceptualized as a free variable?

Stuart Hollingdale's book Makers of Mathematics states the following: In 1833 Hamilton read a paper to the Royal Irish Academy in which he pointed out that the plus sign in $a + ib$ was a misnomer, ...
Theo H's user avatar
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Why does “propositional calculus” have the word “calculus” in it?

We define “calculus” like this: “Calculus is the mathematical study of continuous change.” But if that’s the case, then why is the study of (true or false) propositions and their relations called: “...
user avatar
1 vote
1 answer
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Do the mathematicians/physicists that come up with these useful formulas picture the equations in their head? [closed]

For example in this three blue one brown video he shows the visualization of the derivative of x^2 it's relatively easy to see how it works and intuitively I could see how I could come up with this ...
Stef's user avatar
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2 votes
0 answers
99 views

History of Cohomology's formula $d^2=0$

I understand that the formula $d^2=0$ is an essential formula in all cohomology. So I suddenly became curious about the history of the formula $d^2=0$. Of course, this formula overlaps with Gauss's ...
user1274233's user avatar
4 votes
2 answers
748 views

What was Newton's proof of the Product Rule and why was it "not satisfactory"?

Piermont (1928) : As is well known, the proof that Newton gave in his Principia that $(uv)' = uv'+vu'$ is not satisfactory. What was Newton's proof of the Product Rule and why was it "not ...
user182601's user avatar
6 votes
3 answers
1k views

Why did abstract group theory take its current form?

These days, I'm interested in group theory. Why is the group axiom the way it is now? As an example, among mathematics, algebra has fundamental properties called associative property, commutative ...
user1274233's user avatar
3 votes
0 answers
82 views

Why are categorical limits and colimits not swapped?

After having understood direct limits of direct systems and inverse limits of inverse systems, as well as the corresponding categorical notions of colimits and limits, I'm left wondering why the ...
T0mstone's user avatar
7 votes
3 answers
320 views

Projective spaces: why adding points to make linear intersections work make everything else work too?

The (real) projective plane is often motivated by the issue of lines in $\mathbb R^2$ having exactly one intersection, except in the case of parallel lines. The solution is to mimic what we see when ...
D.R.'s user avatar
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1 vote
2 answers
144 views

Reason behind notation of $\frac{d^{2}y}{dx^{2}}$ [duplicate]

Why is the notation the way it is? Is there any history behind it, or any logic which I am not aware of?
Krrish Gupta's user avatar
1 vote
0 answers
112 views

Proving a remark of Gauss on quaternions and spherical triangles in a more transparent way.

In the fragment "Rotations of Space" (1819) in which Gauss outlined the general properties of a quaternions algebra, Gauss stated the following: Given three consecutive scales with the ...
user2554's user avatar
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1 vote
0 answers
309 views

Why the development of mathematics was very slow between Ancient Greece and Descartes?

Update :I asked This question on HSM here In my studies of mathematics (I am not very good at mathematics, I only studied real analysis and some linear algebra), I noticed that mathematics can be ...
pie's user avatar
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0 votes
1 answer
139 views

Why does Lucas get credit for Fibonacci's progression?

A so-called "Lucas Number" is, to me, nothing more than a standard Fibonacci progression of $n_2+n_1$ with a different starting point. There are infinitely many similar progressions, so why ...
mkinson's user avatar
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3 votes
3 answers
122 views

What Is the Significance of Geometric Construction?

So, when I was in high school, I learnt several geometric drawings such as bisecting line segments or angles, to constructing a square whose area is the sum of two other squares etc. using a ruler and ...
Della's user avatar
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1 vote
1 answer
121 views

How's Schwartz theorem stated?

I saw the following theorem in class. Theorem (Young): Let $f:\mathbb{R}^2\to\mathbb{R}$ partially differentiable with partial derivatives both differentiable at $x_0\in\mathbb{R}^2$. Then $f_{xy}(...
Luca T. Castrillón's user avatar
2 votes
0 answers
73 views

Who discovered that logarithmic integral is asymptotic to prime counting function?

We know that Gauss discovered that $\pi(n) \sim \frac{n}{\log(n)}$. This is also known as prime number theorem. Prime number theorem also says $\int_0^{n} \frac{dt}{\log(t)} \sim \pi(n)$. The question ...
Severus' Constant's user avatar
1 vote
1 answer
242 views

κ̄₀ for Mercury—Formula (BIS—Different definition of the term/angle)

Following my other question about a specific “hidden” formula in Ptolemy’s model for Mercury, I am now looking for yet another “hidden” formula, this time the one used to find $\bar\kappa_0$ so that $...
Pierre Paquette's user avatar
2 votes
1 answer
69 views

Lilvati as a good source to learn math. [closed]

I usually like Sanskrit text and reading their literature I am wondering if I can reinforce my math skills with this ancient Lilvati text it goes over the basics, but I find it may be handy, yet I don'...
Haridasa's user avatar
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1 vote
1 answer
59 views

Why do we preference coordinate maps rather than their inverses in manifold theory?

A manifold $M$ of dimension $n$ is certified as such by checking for the existence of a covering $\{U_i\}$ of $M$, each of which is equipped with a homeomorphism $\phi_i : U_i \to \mathbf{R}^n$, ...
While I Am's user avatar
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2 votes
1 answer
173 views

Proving a connection noticed by Gauss between lemniscatic functions and spherical geometry.

In p.415 of volume 3 of Gauss's werke one can find the following remark of Gauss: [Later note]: I. $$\alpha+\delta+\gamma = \pi [=\varpi]$$ set $$\mathbb{sinlemn}(\alpha) = \mathbb{tang} (a), \...
user2554's user avatar
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4 votes
1 answer
139 views

Examples of PDEs that found application after discovery

I am a 2nd year mathematics undergraduate in the UK and recently took an introductory elective in partial differential equations. The focus was on solving some classical examples, all arising from an ...
TCWS's user avatar
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-3 votes
2 answers
231 views

When and why was $-1 \times -1$ defined to equal $1$?

When and why was $-1 \times -1$ defined to equal $1$? My thoughts was that since the rational and natural numbers shared similar algebraic properties, maybe they wanted distributivity to hold for the ...
Fraser Pye's user avatar
1 vote
0 answers
50 views

Etymology of the term "stabilised" for Heegaard splittings

A Heegaard splitting of a 3-manifold $ M = H \cup H' $ is stabilised if there exist essential discs in $ H $ and $ H' $ whose boundary curves intersect transversely at a single point. Equivalently, a ...
Alex Elzenaar's user avatar
4 votes
1 answer
324 views

κ₀ for Mercury—Formula

I refer here to Ptolemy’s epicycle-and-deferent model of the Solar System, specifically that of Mercury (see drawing). In this model, Mercury (not shown) revolves on an epicycle of center C, which ...
Pierre Paquette's user avatar
2 votes
1 answer
161 views

Leibniz's 1684 Solution to De Beaune's Problem

In his 1684 text, "A New Method for Finding Minima and Maxima," Leibniz solves an inverse-tangent problem posed by De Beaune that basically asks what kind of curve will have a constant ...
MrMagoo's user avatar
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1 vote
0 answers
218 views

Meaning of some results of Gauss on cyclotomic numbers.

In an unpublished fragment of Gauss entitled "on the theory of complex numbers", written by him around 1810, Gauss made early inroads into the theory of cyclotomic numbers, which are ...
user2554's user avatar
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3 votes
1 answer
98 views

When does the concept of random variable first appear?

I am writing an essay on the history of Probability Theory for a class project. While writing it, I wondered where the concept of random variable first appeared. Obviously not in its current form as a ...
Frank William Hammond's user avatar
3 votes
1 answer
202 views

Art historian trying to identify math diagrams in a painting

In a painting called 'Catastrophe Theory' from 1983, the German painter Sigmar Polke included the math diagrams shown in the linked image below (for another image see here: https://www.sfmoma.org/...
milque_toast's user avatar
17 votes
1 answer
2k views

Full list of Conway's anti-Hilbert questions?

Perhaps several sources, but most notably Wikipedia, list the open question of whether Beggar-my-neighbor (a game introduced to me in the UK as "Draw the Well Dry") terminates as an example ...
May Emerson's user avatar

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