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2 votes
0 answers
23 views

What's the early history of the "inner qantum number"?

Pais in his "Inward Bound" describes the early history of spin. He tells us that Goudsmit and Uhlenbeck interpreted Pauli's "doubled valuedness" as spin, while in turn Pauli re-...
3 votes
3 answers
158 views

Are there any well known mathematicians who were fascists?

I only recently learned that Pascual Jordan, a well known physicist, with significant contributions to the development of early quantum mechanics was a paid up member of the Nazi Party. He in fact ...
-3 votes
0 answers
59 views

What is the connection between dialetheism and Wittgenstein's logical atomism?

Wittgenstein's Tractatus, from my layman's reading of it, is about logical atomism. However, I have recently come across one comment here by one user here - Conifold - who claims that Wittgenstein was ...
1 vote
1 answer
40 views

What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas?

What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas? I was trying to find the first paper that used the term "degenerate/degeneracy" to ...
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0 votes
0 answers
45 views

Were the Euler-Bernoulli beam bending equations used in the design of the Eiffel Tower?

On Wikipedia, I read that the Euler-Bernoulli equations on beam-bending were used in the design of the Eiffel Tower: It was first enunciated circa 1750, but was not applied on a large scale until the ...
  • 9
1 vote
0 answers
29 views

Why was Cauchy studying Schur polynomials and related topics?

Let $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n$ be nonnegative integers. The Schur polynomial $s_{\lambda}(x_1, \ldots, x_n)$ can be defined as the ratio $$s_{\lambda}(x_1, x_2, \ldots, x_n) ...
1 vote
0 answers
71 views

Where is Alfred Tarski buried?

Where is Alfred Tarski buried? He was a famous Polish mathematician. He died in 1983 in Berkeley, California, USA, according to Wikipedia. I tried a search on Find a Grave, but there is no entry for ...
  • 27
2 votes
0 answers
71 views

First use of corner quotes for Gödel numbers

Who first used the corner quotes, ⌜ and ⌝, or $\texttt{\Godelnum}$ with Sam Buss's macro, for the notion of Gödel number? Quine introduced corner quotes, but did not use them for the notion of Gödel ...
  • 149
0 votes
0 answers
28 views

When Was The Leidenfrost Effect First Demonstrated By Touching Molten Metal?

The Leidenfrost Effect is a described as follows on Wikipedia: The Leidenfrost effect is a physical phenomenon in which a liquid, close to a surface that is significantly hotter than the liquid's ...
  • 101
1 vote
1 answer
46 views

Were there non-Western models of projectile motion before Galileo?

When I search for the history of projectile motion, I mostly find outlines starting with Aristotle and discussing Ibn Sina, Tartaglia, Galileo, Newton, etc. and perhaps with a few more Europeans in ...
0 votes
0 answers
41 views

Why Was Sequential Analysis Classified?

In the Introduction of his "Sequential Analysis" Wald writes that Because of the usefulness of the sequential probability ratio test in development work on military and naval equipment, it ...
  • 185
2 votes
0 answers
55 views

History of triangulation

Snell tends to be quoted as the person to develop triangulation in geodesy. I don't believe, however, that triangulation was invented only then. For example, here Al-Biruni is mentioned to have "...
  • 173
2 votes
1 answer
138 views

When did bounties and prize money for open mathematical problems start being a thing?

I'm a science/math journalist [ger] and currently I'm working on an article about the culture of prize money/bounties for solving open mathematical problems (Millennium Prize Problems and such). One ...
  • 21
3 votes
1 answer
93 views

Topologies without the axiom that finite intersection of open sets is open

A topology is a pair of a nonempty set $P$ of points, and a set $Opens\subseteq 2^P$ of open sets that is closed under two closure conditions: arbitrary (possibly infinite) unions and finite (...
  • 33
3 votes
1 answer
98 views

Are there any arithmetic problems studied by Euler still open?

Fermat's last theorem, which Euler had studied in the case of certain exponents, was only solved in the 1990s. Also, a counterexample to Euler's sum of powers conjecture has been found quite recently (...
  • 133
1 vote
0 answers
54 views

What's the difference between Galileo's "impeto" and "momento"?

In Galileo's Two New Sciences, he describes an experiment demonstrating pendulum motion and how the pendulum will rise to the same height from where it started its fall. This discussion can be found ...
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1 vote
0 answers
49 views

How did MMPDS Develop Their Coordinate System for Metals?

How was the L, LT, ST coordinate system for Metals developed and adopted? I am talking with some colleagues about comparing metallic and non-metallic materials. Obviously, "apples-to-apples" ...
3 votes
0 answers
42 views

Unclosed Macroscopic equation from the statistical moments in kinetic theory of gases

I'm interested in kinetic theory of gases, notably its history. I know that, after the pioneering work of Boltzmann who derived the Boltzmann equation, it is possible by taking its statistical moment ...
  • 141
1 vote
1 answer
80 views

What was the quote about known things being trivial and unknown things being impossible?

I am new to this portion of stack exchange and am not sure if this type of question is allowed, but after seeing this, I assume it is. A while back, I remember reading a quote about math that said ...
  • 113
2 votes
0 answers
66 views

Kolmogorov on frequentists versus Bayesians

What was Kolmogorov's attitude regarding the frequentist versus Bayesian statistics controversies? Did he ever write or speak about his own views on Fisher or de Finetti, Jeffreys, etc.? Or were those ...
  • 185
2 votes
1 answer
72 views

Is there a complete translation of "Arithmetices principia" by Peano?

If I understand correctly, Arithmetices principia: nova methodo exposita is one of the most important works covering the axiomatisation of arithmetic. I was surprised that no translation into English (...
4 votes
0 answers
68 views

Did Rayleigh or Ritz prove the Rayleigh–Ritz theorem?

The maximum eigenvalue of a real symmetric (or complex Hermitian) matrix is given as the maximum of the associated the quadratic form: $$ \lambda_{\rm max}(A) = \max_{\|x\| = 1} x^*Ax. \tag{1} $$ This ...
1 vote
1 answer
130 views

How to build a protractor without a protractor?

We all know how to use a protractor, it is taught in elementary school. However, I was wondering what type of knowledge is required to build one from scratch. For instance, was the understanding of $\...
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0 votes
0 answers
37 views

The role of monotonicity in integrating term-by-term preceding Lebesgue's monotone convergence theorem

Given a measure space $(\Omega,\Sigma,\mu)$ and sequence of pointwise non-decreasing, non-negative, measurable functions $\{f_n\}_{n=1}^{\infty}$ on it, Lebesgue's monotone convergence theorem says ...
  • 1
0 votes
0 answers
45 views

What branch of science is it that predicts how people in the past thought?

My friend speculated that people in the past believed that the gallbladder has therapeutic properties because of its distinctive color among surrounding meat - greenish among red. Maybe our ancestors ...
  • 1
3 votes
1 answer
106 views

Who first proved necessity of Euclid's formula for pythagorean triples?

The following well-known formula for pythagorean triples is commonly called Euclid's formula: If $a, b, c$ are three natural numbers with $a,c$ odd, $b$ even, $\gcd(a,b,c)=1$ and $a^2+b^2=c^2$, then ...
  • 113
12 votes
1 answer
160 views

How did 'N. Bourbaki' address a conference?

As I understand it, 'N. Bourbaki' was the pseudonym of a collective of French mathematicians. How, then, did 'it' give a conference talk1 in Columbus, Ohio in 1948? 1 N. Bourbaki, Foundations of ...
1 vote
1 answer
88 views

Definition and Name Change of the Oscillation Function

I have two related questions: Who first defined the oscillation function (perhaps under a different name)? When did the switch from the phrase "saltus function"(*) to "oscillation ...
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1 vote
1 answer
87 views

Why was the concept of momentum invented in the first place, and what is its history?

Why was the concept of momentum invented in the first place, and is it useful in the different discoveries and equations that came after?
2 votes
0 answers
64 views

How the asymptotic expansions of the Dawson integral and $\exp(x^2)\operatorname {erfc}(x)$ were originally obtained?

There are two well known asymptotic expansions of the Dawson integral $F(x)$ and the function $\exp(x^2)\operatorname {erfc}(x)$ as $x \rightarrow \infty$: $$ F(x)\sim (1/2)(1/x+1/(2x^3)+ 3/(4x^5)+\...
  • 21
4 votes
1 answer
353 views

Third law of motion before Newton?

Are there any traces of the third law of motion before Newton's Principia? wiki says Newton arrived at his set of three laws incrementally. In a 1684 manuscript written to Huygens, he listed four ...
2 votes
0 answers
98 views

Why was the idea of "field" introduced?

I read in my Physics textbook that the notion of Electric fields are useful "when we have to deal with time dependent Electromagnetic phenomenon since no information can travel faster than light&...
  • 129
0 votes
0 answers
89 views

Why was it difficult to initially phrase compactness?

From beginnings of topology, it was clear that the closed interval $\left[a,b \right]$ of the real line had a certain property that was crucial for proving such theorems as the maximum value theorem ...
1 vote
0 answers
63 views

Usage of "sphere" as ball's surface vs as ball itself

In everyday English, "sphere" means a round object. People will think of the insides as part of the sphere. In Mathematics it specifically means the surface of the ball. How did the ...
0 votes
0 answers
80 views

Is there any book dealing with the history of both astronomy and geometry?

I am preparing an introductory course on the history of astronomy and geometry for intermediate students. The intention is to teach Copernican heliocentrism, Kepler's laws of planetary motion & ...
0 votes
2 answers
937 views

Did John von Neumann solve any unsolved problem in mathematics?

I have searched and examined legendary stories of the problem-solving skills of von Neumann in mathematics. With George Polya With Dantzig Maybe there are other stories showing that he is a great ...
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1 vote
2 answers
111 views

What is the difference between Newton's definitions and axioms?

What is the difference between definition and axiom? For instance, Newton's Definition 1 reads: (Cohen p. 403) Quantity of matter is a measure of matter that arises from its density and volume ...
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2 votes
0 answers
66 views

Who coined the name "cosmological constant"?

I am aware that Albert Einstein first added the $\Lambda$-term to his field equations in his 1917 paper "Cosmological considerations in the general theory of relativity" (german: "...
  • 129
0 votes
1 answer
70 views

Looking for a book about "mysteries of the universe"

I used to have a book that traced the history of books which had titles like "secrets of the universe explained", "secrets of chemistry exlained", or "secrets of magic ...
  • 85
14 votes
1 answer
3k views

Did most or just few physicists think in 1900 that there was nothing important left to discover?

For example, the whole microscopic world was unknown - isn't that a fundamental problem even bigger than the "two clouds" to solve? They could regard atoms, electrons and other discovered ...
  • 275
5 votes
2 answers
372 views

Old unsolved questions in mathematics

John Stillwell, in his textbook on arithmetic cites Erdos: As the great Hungarian problem-solver Paul Erdos liked to point out, if you can think of an open problem that is more than 200 years old, ...
5 votes
1 answer
101 views

Who is/was R. Alter, who reported 1375298099 can be expressed as the sum of 3 fifth powers in 2 different ways?

David Wells, in his entertaining but non-scholarly Curious and Interesting Numbers (1986, 2 ed. 1997) reports that the positive integer $1 \, 375 \, 298 \, 099$ can be expressed as the sum of $3$ ...
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4 votes
3 answers
796 views

The First Published book on Algebraic Topology

As far as I know, according to google, Eilenberg, Steenrod's book: Foundations of Algebraic Topology was published in 1952, and Spanier's book: Algebraic Topology was published in 1966. My Questions ...
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2 votes
1 answer
111 views

What motivated scientists to define quantities at a point?

We know that quantities can be defined at a point. Let's take density for instance. If we take a volume in some quantity of matter and keep on shrinking it to a point where we can assign a uniform ...
2 votes
1 answer
130 views

What was the pre-Renaissance proto-perspective scaling technique for painting square tiled floors?

I read once (I don't remember where exactly) about an early technique (Early Renaissance) to draw a square tiling floor in perspective. The next row in the drawing is done multiplying the previous one ...
2 votes
0 answers
58 views

When was Lipschitz equivalence first attributed to Lipschitz or did Lipschitz formulate it himself?

In his book Introduction to Metric and Topological Spaces, author Wilson A Sutherland in explaining the equivalence of metrics invoked the definition: Two metrics $d_1, d_2$ on a set $X$ will be ...
3 votes
1 answer
100 views

Who was A.M. Nesbitt, the eponym of Nesbitts Inequality?

Nesbitt's Inequality can be found all over the internet: $$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}$$ This appears to have been first published in 1902 in Education Times, by A.M. ...
  • 1,063
1 vote
1 answer
49 views

Why and when was the kinetic theory of gases generalized to fluids?

I've been reading about kinetic theory of gases, which only deals with gases. I know that the lattice Boltzmann method, which is commonly used to simulate fluid flows, finds its origin in the kinetic ...
  • 141
1 vote
0 answers
53 views

Did Halley, Wren and Hooke use $a=v^2/r$ to infer the inverse square law?

I'm reading Richard Conn Henry's article called "Circular Motion." In it he states that in his De vi Centrifuga Huygens discovered the formula $a=v^2/r$ and that Edmund Halley, Christopher ...
  • 85
5 votes
1 answer
466 views

Who was Antoine Appert, the eponym of the Appert Topology and Appert Space?

Antoine Appert is mentioned in the bibliography of Steen & Seebach's Counterexamples in Topology, but miscited as "Q. Appert". Haven't a clue what Q would stand for so assuming this is a ...
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