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Feynman learning technique

There is a learning technique by Richard Feynman, which is known as the "Feynman learning technique", and consists of four steps: Select a concept to learn. Teach it to a child (or maybe an ...
jsx97's user avatar
  • 133
1 vote
0 answers
42 views

History of functions of bounded variation

I have read that Jordan first defined the concept of variation and studied functions of bounded variation, in his 1881 publication Sur la Serie de Fourier, as referenced here: https://en.wikipedia.org/...
Addem's user avatar
  • 511
3 votes
1 answer
104 views

Who discovered that the electromagnetic tensor is the curvature of a connection?

I can not identify clearly who was the first one to realize that the electromagnetic tensor is the curvature 2-form of a U(1)-connection. Looking at Weyl's work, it seems that he came pretty close to ...
Léo Vacher's user avatar
8 votes
2 answers
1k views

When did "neighbourhood of a point" first appear in the history of Taylor series?

I am trying to track down at what point mathematicians started to use the terminology of expanding a function "around a point" or in the "neighbourhood of a point". Neither Taylor ...
StormyTeacup's user avatar
0 votes
0 answers
52 views

History of prime distribution $\lim_{x\to\infty}\frac{\pi(x)}{x}=0$

Let $\pi(x)$ be the prime counting function. It is well-known that $$\lim_{x\to\infty}\frac{\pi(x)}{x}=0.$$ My question is who is the first person to prove this result? Did Eratosthenes prove this ...
HGF's user avatar
  • 143
0 votes
0 answers
149 views

Instances in which a term initially coined to reject a theory later became the widely accepted term for that very theory after it became the consensus

I'm looking for an instance other than that of the 'big bang' — a term coined by Fred Hoyle to reject the theory being referred to. The theory also later went on to become the consensus with the very ...
Keshonduka's user avatar
0 votes
2 answers
277 views

How was addition and multiplication of natural numbers defined before 1870 (Cantor and modern set theory)?

I know how to define addition and multiplication of natural numbers using set theory, but I think that before Cantor, mathematicians did not try to use set theory as a foundation for mathematics (I ...
pie's user avatar
  • 263
0 votes
1 answer
194 views

Who was Burlet, the one from Burlet's theorem?

The Burlet's theorem is a result in Euclidean geometry, which can be formulated as follows: Theorem. Consider triangle $ABC$ with $\angle{C}=\gamma$. Let $P$ be the point where the incircle touches ...
Emmanuel José García's user avatar
1 vote
0 answers
69 views

How does Math look on Different Planets? [closed]

I have had this theory for a while - basic principles in math were likely known by early humans such as caveman (and possibly some level of understanding might even be possessed by animals). I think ...
stats_noob's user avatar
0 votes
0 answers
48 views

Fossil evidence of common ancestor to Great Apes and Humans

Where can I find documentation of fossil findings about ancient human anscestors, even down to the point of believed divergence between great apes and humans? I heard a skeleton has been found earlier ...
Fraser's user avatar
  • 11
1 vote
0 answers
65 views

What is the earliest documentation of counting and what was it used for?

Counting has been in observed in almost every culture across the world. I think it developed because it proved to be so useful for a range of tasks. I am wondering what the earliest use cases for it ...
Fraser's user avatar
  • 11
0 votes
1 answer
95 views

The history of motivations [closed]

Most histories, that I've encountered, of mathematics about the 18th century and onward focus on a chronology of publications, results, definitions, and similar "pure" interests. However, I ...
Addem's user avatar
  • 511
1 vote
2 answers
132 views

Who discovered the famous combinatorial intepretation of Eulerian numbers?

Eulerian numbers $A(n, k)$ were discovered by Euler in 1755 in his work Institutiones calculi differentialis. In combinatorics, they count the number permutations of the numbers 1 to $n$ with exactly $...
User303131's user avatar
1 vote
0 answers
83 views

What were people looking for when they started to study bounded linear functionals?

Very briefly, my understanding of the initial motivations for studying $L^p$ spaces included interest in the $\ell_2$ space, due to relationships with quadratic forms that arose from searching for ...
Addem's user avatar
  • 511
3 votes
2 answers
289 views

Origin of the name "Loschmidt echo" in quantum chaos studies

The name "Loschmidt echo" is used in quantum physics for the quantity $$ M(t) \equiv \left| \langle\psi_0| e^{i H t/\hbar} e^{-i H_0 t/\hbar} |\psi_0\rangle \right|^2 $$ where $$ H = H_0 + ...
Andrew Steane's user avatar
1 vote
0 answers
60 views

What was John Cantius' contribution to the theory of impetus?

According to Wikipedia, the theory of impetus, which was a precursor to the modern concepts of inertia and momentum, was developed in the West by Jean Buridan, and further developed by John Cantius (...
aquohn's user avatar
  • 111
1 vote
1 answer
90 views

How do I obtain the first column of Plimpton 322 from the other columns?

How is the first column of plimpton 322 derived from the other columns? Consider the first row of the tablet. The second, $b,$ and third, $ c,$ column are pythagorean triples $(a,b,c)= (120, 119, 169)$...
Chris's user avatar
  • 11
2 votes
0 answers
136 views

Origin of the concepts of Stress and Strain

Background & My research So, I recently studied about the concepts of Stress and Strain in my high school physics classes and wanted to know about the history behind the origin and emergence of ...
Bhavya Jain's user avatar
1 vote
2 answers
218 views

Bieberbach’s 1934 lecture on “German mathematics”

Does anyone know of an English translation of Ludwig Bieberbach’s infamous 1934 Berlin lecture, delivered at the annual conference of the Deutscher Verein zur Förderung des mathematischen und ...
James Propp's user avatar
1 vote
0 answers
68 views

Who was the first to define the limit of a convergent sequence with quantifiers $\forall$ and $\exists$?

I mean this definition: A sequence $(u_n)_{n\in \mathbb{N}}$ converges to a limit $l$ if and only if: $$\forall \epsilon>0 ~~\exists N \in \mathbb{N} ~~ \forall n \ge N ~~\vert u_n -l \vert < \...
someone's user avatar
  • 11
3 votes
1 answer
108 views

Which geometer first compared a length (one dimensional) to an area (two dimensional)?

What are sources placing a length (one dimensional) in proportion to an area (two dimensional)? The Greek geometers compared quantities of the same dimension: e.g. the area of a circle is in ...
SRobertJames's user avatar
1 vote
0 answers
35 views

What is the earliest paper in which local edge connectivity was defined?

Let $G=(V,E)$ be a graph with vertex set $V$ and edge set $E$. The Local edge connectivity $\lambda(x,y;G)$ for $x,y\in V$ with $x\neq y$ is defined as the least number $|F|$ such that $x$ and $y$ ...
MMM's user avatar
  • 11
0 votes
0 answers
39 views

De Branges's theorem and perspective on Sheaf theory

As far as I know, there is an intuitive and easy way to think about sheaf theory through the Taylor series. For example, in the case of stalk, which is one of the important concepts in sheaf, we can ...
pokssin's user avatar
  • 309
3 votes
1 answer
240 views

How to "prove" recent analysis theorems without rigor?

I asked this question on MSE here but I was told it would do better here I always wonder how mathematicians proved theorems before Cauchy’s epsilon-delta proof. Since many "recent" theorems,...
pie's user avatar
  • 263
3 votes
1 answer
70 views

When was the term "plate tectonics" first used in geology?

The Merriam-Webster online dictionary writes that the first known usage of plate tectonics in the sense of the geological theory was in 1969. Encyclopedia Britannica credits Alfred Wegener with an ...
Colin Pace's user avatar
4 votes
2 answers
253 views

What is the history of the classification of states of matter?

In my school curriculum, and in many standard presentations such as Wikipedia, it is claimed that there are four fundamental states of matter: solids, liquids, gases, and plasmas. How was this list ...
Rococo's user avatar
  • 41
4 votes
1 answer
580 views

How do we know Hennig Brand's name?

The story of Hennig Brand discovering the element phosphorous is often repeated without citation, and there doesn't seem to be much scholarship about Brand in particular (although the history of the ...
Sam Gallagher's user avatar
1 vote
0 answers
39 views

Hamilton's derivation for the characteristic function in his essay

In Hamilton's "on a general method in dynamics", he starts with varying the function $U$ and writes the equation: $$\delta U=\sum m(\ddot x\delta x+\ddot y\delta y+\ddot z\delta z)$$ Then he ...
A.S's user avatar
  • 11
2 votes
0 answers
74 views

Where can I find Bourbaki's Latin telegram?

In the Bourbaki archives in Lorainne, France, there appears to be a Latin telegram from Nicolas Bourbaki to Marcel Brelot (see reference 486 at https://iecl.univ-lorraine.fr/files/2021/04/...
user avatar
0 votes
0 answers
33 views

Etymology or genesis of the concept of proof

I'm wondering about the origin of the concept of proof in human thinking. Nowadays the concept is a cornerstone of mathematics, but also in law. Did early mathematicians maybe adopt it from the ...
user313032's user avatar
1 vote
4 answers
216 views

Is there a concise but detailed history of electricity?

I have recently become fascinated by the history of electricity. I have researched and come up with the following observations: Static electricity was discovered in early times, by phenomena such as ...
Fraser's user avatar
  • 11
2 votes
1 answer
160 views

What is the relationship between the Newtonian laws of motion and gravity and the Keplerian laws of planetary motion?

In the Wikipedia article for "Kepler's laws of planetary motion," the article suggests that "Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System ...
Colin Pace's user avatar
2 votes
1 answer
156 views

The reason why sheaf theory emerged

Motivation: In any history, there is a cause-and-effect relationship. So I became curious about the situation in which the sheaf theory came to appear. In other words, I'm curious about what problem ...
pokssin's user avatar
  • 309
1 vote
0 answers
41 views

Usage of the word "autonomous" to refer to time-invariant differential equations

At what point in time did the term "autonomous" begin to signify time-invariance within the context of dynamical systems, and what prompted this association?
shamisen's user avatar
  • 111
2 votes
0 answers
89 views

The habit of definition

G. H. Hardy wrote (apropos of the task of assigning values to divergent series): It is plain that the first step towards such an interpretation must be some definition, or definitions, of the 'sum' ...
James Propp's user avatar
2 votes
0 answers
85 views

History of logarithmic potential

I have some historical questions in connections for the notes to a book I am writing. Who the first person to discover that the Coulomb potential in two dimension is $\log(|x|^{-1})$, equivalently ...
Barry Simon's user avatar
0 votes
0 answers
105 views

Seeking References on the History of Scientific Dissemination

recently read a book on the history of science by academic Tatiana Roque. In it, she discusses how, during the Enlightenment, scientific dissemination was a fundamental assumption. Roque writes that ...
Humberto José Bortolossi's user avatar
2 votes
1 answer
442 views

Where does the famous equation $F = G\cfrac{m_1m_2}{r^2}$ come from?

The famous equation $F = G\cfrac{m_1m_2}{r^2}$ is not in Mathematical Principles of Natural Philosophy, as it has been pointed out by a commentator on another question about where the equation is in ...
Colin Pace's user avatar
1 vote
0 answers
131 views

Could Newton have come up with General Relativity? [closed]

I was reading this question. There I read somewhere that he would have discovered modern physics if he had studied electromagnetism and nuclear physics. It was most likely in jest. But I ask How much ...
Alfredo's user avatar
  • 11
0 votes
0 answers
55 views

Why is the standard deviation bias correction factor called c₄?

The term to remove bias from an estimate of standard deviation for a normal distribution is referred to as $c_4$. What is the origin or reason for using that notation for the correction factor?
feetwet's user avatar
  • 101
1 vote
0 answers
95 views

Kekulé and his discovery of benzene

“I was sitting writing at my textbook, but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire, and dozed. Again the atoms were gamboling before my eyes. This time the ...
Harikrishnan M's user avatar
8 votes
1 answer
1k views

DeMorgan's commentary on Euclid's Elements

Augustus DeMorgan wrote comments on Euclid's Elements, which capture many of the most important points. Heath quotes them extensively. I cannot find any source for the original: Where can I see ...
SRobertJames's user avatar
4 votes
1 answer
176 views

Were Julia sets discovered before the Mandelbrot set?

The Mandelbrot set was discovered by Benoit Mandelbrot in 1980. However, Gaston Julia lived from 1893 to 1978. Does this mean Julia sets, in the popular form we know them today, were discovered before ...
Penelope's user avatar
  • 415
2 votes
1 answer
251 views

who invented the one page calendar?

Well, I am not sure if this is the right place to ask but here it goes (if this forum is not the right place to ask, I apologize and certainly moderators will delete my question): i am very curious ...
Humberto José Bortolossi's user avatar
1 vote
0 answers
99 views

Was the "Gauss word realization problem" a kind of unknotting problem?

In Moritz Epple's article "Geometric Aspects in the Development of Knot Theory", Epple writes the following: It has been suggested that one of the earliest tools of combinatorial knot ...
user2554's user avatar
  • 4,499
0 votes
1 answer
93 views

Zahler, Sussman, and Kolata Controversy of 1977

In Steven Strogatz's "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering", Storgatz mentions a "violent controversy" between Zahler, ...
GedankenExperimentalist's user avatar
4 votes
2 answers
740 views

What motivated the idea of the Tschirnhaus transformation of polynomial equations?

As I studied Cardano's formula for the cubic, Tschirnhaus transformation came up as a very important step. The more I studied it the more attractive and interesting it seemed. So I am curious about ...
pokssin's user avatar
  • 309
2 votes
1 answer
111 views

In Geiger-Marsden experiments how was charge of alpha particle and charge of gold atom found?

Here: https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiments Some calculations were done to show how JJ Thomson's model predicts alpha particles will be mostly undeflected by the gold foil. ...
Saif's user avatar
  • 43
3 votes
1 answer
302 views

Who is Paul Graham's father?

In one of his essays, Y Combinator (YC) co-founder Paul Graham (PG) wrote$^\color{magenta}{\star}$ the following. My father is a mathematician. For most of my childhood he worked for Westinghouse, ...
Ooker's user avatar
  • 1,228
6 votes
1 answer
1k views

What was the role of Schmidt in derivation of the Gram-Schmidt process?

When reading the section related to Gram-Schmidt process in the book Linear Algebra and Its Applications by Gilbert Strang, I found a foot note that says: If Gram thought of it first, what was left ...
Tran Khanh's user avatar

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