All Questions

0
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0answers
6 views

What is discovered first, electricity or electron?

It always bugs my mind to think which comes first, it feels like the egg or the chicken problem. When i was reading about the discovery of the electron i found that the charge to mass ratio of the ...
0
votes
0answers
6 views

Influence of Poincaré on Julia and Fatou

Poincaré was one of the major precursors of the modern theory of dynamical systems, notably through his famous memoir on the 3 body problem, and subsequent discovery of homoclinic intersections and ...
0
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0answers
5 views

Hydrogen electrode and its electrode potential

In electrochemistry, all electrode potentials are quoted with reference to the standard hydrogen electrode. Its value is assigned to be 0 volts. I have been searching for the origin of this convention ...
1
vote
0answers
51 views

Has ordering people along a Ape to Human diagram, as a measure of dehumanization for people in general, been validated in any way? [on hold]

Has ordering people along a Ape to Human diagram, as a measure of dehumanization for people in general, been validated in any way? Because it seems, if confronted with such a diagram and asking ...
20
votes
1answer
4k views

How was Lagrange appointed professor of mathematics so early?

It is well-known that in 1755 Lagrange was appointed Professor of Mathematics at the Royal Artillery School in Turin. He was 19. His work up until then involves correspondence with Euler. Was he ...
3
votes
1answer
56 views

Mellin's original paper on his transform

There is no link on wikipedia to his work. This is really a nice transform. There is coherent theory behind. I am curious what motivated him to invent this transform.
3
votes
1answer
91 views

When did people start to state and justify properties of arithmetical operations?

I have question regarding the history of the idea of founding mathematics (specially arithmetic) on a logical basis. What I'm interested in knowing is, at what point historically people started to ...
6
votes
2answers
409 views

Where did Ptolemy compare the Earth to the distance of fixed stars?

I read the following in C. S. Lewis, Miracles (page 77-8) The immensity of the universe is not a recent discovery. More than seventeen hundred years ago Ptolemy taught that in relation to the ...
2
votes
2answers
37 views

Bainbridge's test of mass-energy equivalence

Kenneth Bainbridge was an early pioneer of mass spectroscopy. The Wikipedia article about him says: He used this instrument to verify Albert Einstein's mass-energy equivalence, E = mc2 with a ...
3
votes
2answers
91 views

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, ...
2
votes
1answer
46 views

Apparent contradiction in Copernicus' Commentariolus

There seems to be a contradiction in the assumptions that Copernicus makes when attempting to explain the motion of the planets: http://dbanach.com/copernicus-commentarilous.htm Assumptions 1 and 3 ...
0
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0answers
43 views

What are some good books on history of mathematical thought? [closed]

And if possible books that could be downloaded for free
-2
votes
0answers
115 views

Is this Heisenberg joke actually real? [closed]

This is the story 15 of the page Physics Jokes (emphasis mine): This is apparently a true story. It took place just outside of Munich, Germany. Heisenberg went for a drive and got stopped by a ...
2
votes
0answers
49 views

What was the structure of first course in sociology?

I read that Max Weber supported the anti-positivist approach to sociology in Ludwig Maxmilian University of Munich. So I want to know the academic structure of the first course he appealed for. I ...
2
votes
1answer
73 views

The convention for speakers to refer to themselves at the board with a single initial

I found an interesting question on Math SE asked by @KCd, but it is over four years old without a clear answer. Since it seems to be more on topic here than on Math SE, I thought to post it here in ...
11
votes
2answers
1k views

When were vectors invented?

Encyclopedia Britannica says, In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express ...
2
votes
0answers
73 views

Were notable physicists great at math or computing? [closed]

Were famous or popular physicists like Galileo, Newton, Einstein, Feynman predominantly mathematicians or scientists (computing, experimenting, engineering, etc.)? I am curious if people like the ...
1
vote
0answers
50 views

When did the term “order” come into use as the highest exponent in an expansion?

Answer(s) to the question What is a 3rd-order Fresnel lens? are disappointing to me, in that the term 3rd order does not refer to anything like a third-order series expansion. But this leads me to a ...
1
vote
0answers
22 views

Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
2
votes
0answers
32 views

Who introduced concept of capacitance matrix

We know of two ways of representing voltage-charge relations of an assembly of conductors: $V_j=\sum P_iq_i$ and $Q_j=\sum C_iv_i$ Who introduced these equations for the first time and though one can ...
7
votes
1answer
106 views

What actually led Feynman to the path integral formulation of quantum mechanics?

It is commonly known that Feynman's path integral was inspired by Dirac's observation that the kernel is proportional to $\exp{i\hbar S}$. It was Feynman, however, who had the idea of expressing the ...
6
votes
1answer
67 views

History of a contour integral method for summing series

A folklore result I have seen used in evaluations of infinite sums is the following clever use of the residue theorem: $$\begin{align*}\sum_{1}^\infty f(k)&=\frac1{2\pi i}\oint f(z)\pi\cot\pi z\,\...
2
votes
1answer
111 views

How did philosophers and scientists in the 18th century view mathematical explanation?

The 18th century saw a rise in the use of mathematical formalisms to account for natural phenomena. Works of Lagrange, Euler, d'Alembert, etc., were groundbreaking in the history of mechanics and ...
4
votes
1answer
75 views

Using paper of known density to calculate area under a curve [duplicate]

Ive never seen a source for this, but I had a professor a few years back that a low tech way of calculating the area under a curve (definite integral) was to use a piece of paper with known thickness/...
2
votes
1answer
136 views

What is the origin of the four cardinal directions (North, East, South, and West)?

Why are there four? I would guess it was fixed after the egocentric/"relative" directions (left, right, front, back). Or was it because human used to consider the ground as flat and 2-dimensional? How ...
2
votes
2answers
87 views

Origin and use of the adjective “improper” in mathematics

Anybody with elementary mathematical education will have seen improper fractions to refer to fractions where the numerator is greater than or equal to the denominator. At a certain point in calculus ...
5
votes
1answer
90 views

Equivalence principle before Einstein [duplicate]

In a German interview some physicists were asked, what they would ask Einstein, if he were alive today. One of them wanted to know how Einstein came up with the idea of the equivalence principle, that ...
1
vote
1answer
78 views

Who is credited for formalising the theory of isomorphisms?

The concept of an isomorphism is very interesting: a rigorous, formal way of expressing similarity between two objects. When and how did this idea of similarity become formalised as a bijective ...
7
votes
2answers
169 views

Was there early opposition to Newton's mechanics?

Scientific theories are rarely accepted immediately. Even if the evidence for a theory is impeccable, there will be some stragglers who resist it for lack of understanding. More interesting is when a ...
5
votes
2answers
92 views

Who are credited for angle transformation formulae and law of sines in trignometry

I'd like to who are credited for discovering angle transformation formulae $$ \sin(A\pm B)=\sin(A)\cos( B)\pm\cos(A)\sin(B) $$ $$ \cos(A\pm B)=\cos(A)\cos( B)\mp\sin(A)\sin(B) $$ $$ \tan(A\pm B)=\...
4
votes
1answer
72 views

How was the value of the electron's spin ($\pm \frac{\hbar}{2}$) first determined?

The value of the electron's spin is $\pm \frac{\hbar}{2}$. In the paper where Pauli introduces his Pauli matrices he already knows the value of spin. I'd imagine it was through the Ster-Gerlach ...
3
votes
0answers
77 views

Old geometry terminology

I was reading Ramsey's 1927 paper "A Contribution to the Theory of Taxation" and came across the following paragraph: "We have $\lambda_1 = \mu_1,\ldots,\lambda_m = \mu_m$, $m$ hyperplanes ($n-1$ ...
3
votes
0answers
23 views

How did Cassini measure the “Cassini state” of the Moon? What measurements were made and what did the data look like?

The Phys.org article Physicists provide first model of moon's rotational dynamics, accounting for the solid inner core describes the September 2018 paper by Christopher Stys and Mathieu Dumberry The ...
6
votes
1answer
66 views

The minimax theorem from 1928 to 1956

Minimax theorems are beautiful saddle-point results regarding conditions on a function $f$ under which $\max_x \min_y f(x,y) = \min_y \max_x f(x,y)$. In the common "normal form" game case, $x$ and $y$ ...
6
votes
1answer
136 views

Why is there little scholarship devoted to Book II of Newton's Principia?

Books I and III seem to receive the bulk of attention by Newton scholars, and historians more generally. However, I'm sure an in-depth study of Book II would shed light on Newton as a thinker -- for ...
1
vote
0answers
155 views

What is the origin of Arabic numerals

I was taught that the numerals {0,1,2,...,9} are from the Arab alphabet. But they look completely different from today's Arab letters. I wonder what is the origin of Arabic numerals? Edit: The web ...
3
votes
1answer
140 views

How did Einstein know the Avogadro Number?

Wikipedia says the Avogadro number was determined by Perrin in 1908. But Einstein used the value $$N=6\times 10^{23}$$ as early as 1905 in order to estimate the size of the fluctuations of an ...
4
votes
1answer
66 views

Did Bohr comment on Bohm's interpretation of quantum mechanics?

Bohm published his interpretation of quantum mechanics in 1952. Comments on Bohm's work from Einstein, Heisenberg und Pauli are cited in the corresponding wikipedia article (https://en.wikipedia.org/...
6
votes
1answer
132 views

What's that on Euler's head? Does the head covering shown in Emanuel Handmann 1753 painting signify scholarship?

This may be borderline off-topic but this is the only place that I can think of ask this particular question. I've always seen images of Leonhard Euler with a "hat" or head covering that is ...
1
vote
0answers
34 views

Does anyone know articles or books about what the notion of difficulty in science, especially physics?

In physics, many problems were known at their time to be very challenging, for example the notion of heat, or how to understand the ideal gaz law, or the phase transition criticial behaviors, etc. And ...
5
votes
3answers
307 views

Who are the top mathematicians who were ignored due to their unconventional approach?

A perfect example would be Srinivasa Ramanujan It is known that the conventional community throughout history have been close-minded towards great men of science and mathematics.(eg. Galileo) ...
4
votes
1answer
71 views

Meaning of a cryptic sentence by Gauss on “the mobility of figures in the hyperbolic plane”

G. Waldo Dunnington writes in pages 189-190 of his biography of Gauss: Among the axioms of geometry which do not depend on the parallel postulate are those which secure the free mobility of a ...
1
vote
0answers
59 views

Which kinds of academic revolutions has philosophy of science indentified so far and when?

Recently, I had an interdisciplinary discussion with some friends about Industry 4.0, internet of things,...which brought up the question, which kind of academic revolutions apart from industrial ...
4
votes
1answer
82 views

Why was the 'differential entropy' from information theory so named?

The entropy of a distribution $p$ on a discrete set $\mathcal{X}$ is defined as $$H(p) = -\sum_{x \in \mathcal{X}} p_x \log p_x.$$ Shannon in his classic paper [1] defines the analogue for continuous ...
4
votes
2answers
158 views

How long has the order of priority of arithmetical operations been widely taught in high schools?

Browsing Facebook, I often come across posts like this, to test peoples' understanding of order of operations. This inevitably prompts a deluge of answers that either misunderstand the concept or ...
2
votes
1answer
49 views

Where to find some early discussions of the Equinox(es)?

Said quickly, solstices are rather perceptible while the equinox is a mental construction. Archeoastronomical evidence shows that neolithic people already had knowledge about the solsticial points on ...
-2
votes
1answer
108 views

Is Newton going to be the new Aristotle? [closed]

As general relativity and quantum mechanics become more accessible, is Newton going to become the new Aristotle, as the example of being wrong and misleading humanity for centuries? (as opposed to the ...
11
votes
2answers
172 views

History of various definitions of topology

I have been reading Point Set Topology for a while, and turns out that there are various possible ways to define a topology. Most popular one is using open set axioms. Another one is using closure ...
5
votes
5answers
185 views

Remarkable numerical calculations before electronic computers

I know the story that Cole found the factoring of the big number $2^{67}-1$. Is there any other remarkable achievement of hand calculation?
2
votes
2answers
138 views

What made Euclid/Heron define line as a length without breadth and point as that with no part?

A point is that of which there is no part. And a line is a length without breadth.$^1$ If above definition on point, expresses on point as to be indivisible length, as seems to be expressed in ...

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