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38 views

Naturally occurring elements in other planets and their natural satellites other than earth

Naturally occurring elements Is it possible to find natural elements in other planets and their natural satellites other than planet earth?
0 votes
0 answers
24 views

What did George Boole contribute to order theory?

The Wikipedia page says for order theory says: As explained before, orders are ubiquitous in mathematics. However, earliest explicit mentionings of partial orders are probably to be found not before ...
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4 votes
2 answers
689 views

What is the full name of I. Bernard Cohen?

I've seen quite a few of the names I. Bernard Cohen in the history of science book. But I couldn't find what I. meant.
  • 283
3 votes
1 answer
78 views

Why was Principia Proposition 43, Theorem 22 not published?

Why was Proposition 43, Theorem 22, of Newton's Principia not printed? Weinberg, To Explain the World (2015) describes this proposition: In an unpublished “Proposition 43” that did not make it into ...
  • 5,151
0 votes
1 answer
42 views

What is Bertrand Russell citing Gilman for in "On the Notion of Order"?

In the first few pages of "On the Notion of Order", Bertrand Russell has the footnote: The following account of the genesis of order is virtually identical with that of Mr. B. I. Gilman, ...
  • 299
6 votes
2 answers
2k views

First to realize that seasons were reversed above and below the equator?

I assume this conclusion was hard to make empirically in the days of slow travel -- one could not as we can today fly from above the equator to below it and observe the difference in weather and even ...
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1 vote
0 answers
66 views

History of cdf as to how it was defined prior Kolmogorov and how the paradigm shifted from $<$ case to $\leq $ case

Cumulative distribution function is pretty much known and well covered from undergrad to grad probability texts. Specifically if $\mathbf P$ is a probability measure on $(\mathbb R, \mathfrak B_\...
1 vote
0 answers
50 views

Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?

In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum'). Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
1 vote
2 answers
135 views

Motivation of the Hamiltonian formalism

In 1833 Hamilton introduced what today is called the Hamiltonian formalism in classical mechanics. I am wondering what was his motivation. Did he try to solve a specific question?
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1 vote
0 answers
85 views

Why have advocates for positional number systems based on divisibility favoured base 12?

In the early twentieth century, with Esperanto and the like going on, a small movement called "dozenalism" began, with the aim of replacing base 10 with the purportedly more natural base 12. ...
1 vote
0 answers
37 views

question regarding Stern-Gerlach experiment

When Stern-Gerlach experiment was done with quantum electron , two peaks were observed rather than a continuous distribution as in case of small magnets , but how did those peaks confirm that angular ...
1 vote
1 answer
58 views

When did Abel publish his test for the convergence of series?

Did Abel published of testing the convergence of series? If so, when did he published it. Also, did he offer a proof of the test? Or did he simply stated the test?
1 vote
0 answers
87 views

Bit as eighth of dollar vs Shannon's Binary Digit?

https://en.wikipedia.org/wiki/Bit#History does not mention the common usage of bit being an eighth of a dollar -- surely Shannon was inspired by this? This question was asked in 2019 in English ...
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1 vote
0 answers
41 views

Development of Logic: Intuitive use vs what took so long to formalize?

I was encouraged in MathOverflow to ask this question here - so here it goes: As I am reading Frege and Boole, I am struck by that there doesn't seem to be a great alternative to Aristotle's Logic ...
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1 vote
1 answer
79 views

The symbol h for class numbers

We use $h_K$ conventionally to denote the class numbers of number fields $K$. But I have never thought why the letter $h$ was used for it. Why and who used $h$ for the class number?
9 votes
3 answers
2k views

How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

I am reading about the 1900s revolution of math pioneered by figures such as Hilbert. I have seen many articles speak very fondly of these figures due to the fact they tried to study Mathematics ...
5 votes
1 answer
125 views

Early helium spectrum measurements and their challenge for Bohr's quantum mechanics

My understanding is that explaining ortho- and para- helium spectral lines was a key motivation for Heisenberg's new quantum theory. For example, Birthwistle's 1928 "The New Quantum Mechanics&...
1 vote
1 answer
134 views

Was religion not present at all in the Astronomy of the Ancient Greeks?

I attended a lecture on the history of Astronomy and Mathematics, and I was somewhat puzzled by how scientific the early Greeks were. Yes, I am aware that they have many of the greatest mathematicians ...
1 vote
1 answer
137 views

What does this quote by Paul Halmos mean?

I came across the following quote by the famous mathematician Paul Halmos: A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to ...
1 vote
1 answer
110 views

Who introduced the mixed fraction notation?

Who introduced mixed fraction notation? This notion is a source of confusion to me because it may be interpreted as multiplication.
2 votes
0 answers
110 views

The first commutative diagram

Cf. https://golem.ph.utexas.edu/category/2013/07/the_first_commutative_diagram.html Is this the first ever commutative diagram? By commutative diagram I mean anything that shows an equality (or ...
2 votes
0 answers
157 views

Einstein's "answers have changed"

I remember first seeing this anecdote a few years ago in a newspaper article, now I am seeing more frequently in motivational content over the internet, every time with very few additional details. ...
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0 votes
0 answers
224 views

Anecdote about a seemingly possible, but actually impossible task given to students

There is a story I often tell my students about tasks that seem possible but are actually impossible, but I can hardly remember the details, and I am hoping that someone here would remember. Here is ...
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1 vote
0 answers
68 views

How did Euclid arrive at the law of reflection $r=i$?

The law of reflection, $r=i$, is attributed to Euclid. In his Optics text he refers to it, at the end of Page 360 in relation to Graph 19, and says he has demonstrated it in his Catoptrics. But I do ...
  • 111
2 votes
1 answer
95 views

Weyl's gauge theory and railroad tracks

There is a claim I occasionally read that the origin of the word "gauge" refers to a track gauge used in railroad tracks (the distance between two rails). It's a claim I have seen here, here,...
  • 629
0 votes
0 answers
65 views

Why was the germ theory of disease held in disdain?

According to Wikipedia, the germ theory of disease has been held in disdain for centuries in Europe, where the miasma theory was prevalent. Why were scientists so biased against the germ theory?
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4 votes
1 answer
175 views

Continuity, Hausdorff

Is the idea of a continuous map in the point-set model of topological spaces, i.e. that the preimages of opens are open, due to Hausdorff (Grundzüge der Mengenlehre)? For example, does the notion of ...
1 vote
1 answer
105 views

What is the Expected Durability/Digitization Efforts of Pre-Hellenistic works that are made from Materials like Papyrus, Bamboo, Bark, Stone, e.t.c?

Currently, I am reading "Foundations and Fundamental Concepts of Mathematics Third Edition" by Howard Eves, and I have came across this paragraph: In our study of early mathematics we are ...
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5 votes
0 answers
81 views

What was Gauss's algorithmic method to solve a certain "nearest neighbour search" problem in multi-dimensional euclidean space?

In his 1829 paper on a new formulation of mechanics, Gauss presented his principle of least constraint, which parallels previous formulations of analytical mechanics and provides a new point of view ...
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0 votes
0 answers
36 views

Density effect of energy loss of fast ions as a test of relativity

I am thinking about the relation between the Nobel physics committee and Einstein’s relativity theories. It was clear in 1922 based on the bizarre inscription on the committee’s handcrafted diploma ...
3 votes
0 answers
168 views

Who came up with the proof of "Bézout's identity" that uses the well-ordering principle?

Let $a$ and $b$ be two integers not both of which are equal to zero. It is an important and well-known fact that $\text{gcd}(a,b)=ax_{0}+by_{0}$ for some integers $x_{0}$ and $y_{0}$. Even though this ...
1 vote
2 answers
132 views

Comparison of the accuracy of the Ptolemaic and Copernican models

A Japanese book on mechanics says the following (English translation by me): As a young boy, Tycho Brahe became interested in astronomy when he was impressed by the fact that the solar eclipse ...
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2 votes
2 answers
148 views

When was critical mass suspected?

The various famous experiments at Los Alamos where the experimenter would dangerously push two masses of plutonium or uranium near each other and observe increased activity -- was such a phenomenon ...
  • 829
7 votes
1 answer
628 views

Fibonacci and straightedge and compass constructions

In "Mathematical Thought from Ancient to Modern Times" Morris Kline claims (on page 209) that Leonardo da Pisa (Fibonacci) "showed that the roots of $x^3+2x^2+10x=20$ are not ...
3 votes
0 answers
142 views

Were there women inside Bourbaki?

Bourbaki was founded around 1934, they have a limit age of fifty and many mathematicians have passed through it. According to an interview with Chevalley no women have belonged to the group up to 1985....
1 vote
1 answer
84 views

Paradigms in Newtonian physics around 1900

I am thinking about the change from Newtonian mechanics to quantum physics and relativity. I note that we have accepted the words "ultraviolet catastrophe" in connection with the situation ...
1 vote
1 answer
55 views

What are the names of parents of Adrien-Marie Legendre, and their dates of birth and death?

What are the full names and dates of birth and of death of the parents of Adrien-Marie Legendre? I couldn't find this information anywhere online. Not even their names. Thank you.
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2 votes
1 answer
177 views

Did Einstein believe the laws of physics would be replaced by mathematical identities?

I'm sure this wasn't his intention at the outset, but here's my understanding of the history of GR so you can see where I'm coming from: The Einstein-Grossmann "Entwurf" version of the ...
0 votes
0 answers
104 views

What are the second and third "Hebrew Algebras" Mary Everest Boole refer to?

In the book "Philosophy and Fun of Algebra", Mary Everest Boole has a chapter dedicated to what she calls "the first Hebrew algebra" (Chapter 6). She later refers to the "...
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3 votes
0 answers
77 views

What original mathematics arose from Jacquard loom and similar weaving devices?

Research mathematics is seldom directly applicable, but the questions we study are motivated by interplay with contemporary demands. As a combinatorialist, it's apparent that my field has benefited ...
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1 vote
0 answers
91 views

Principia Mathematica and Law of Gravitation

Could anyone, please, point the exact place in "Principia Mathematica" where Newton explicitly stated the expression for the gravitational force between two particles? I mean the fact that ...
2 votes
1 answer
96 views

Searching for book about non-Euclidean geometry that recapitulates the First Book of the Elements

I am looking for a specific book on non-Euclidean geometry that I read in my undergraduate years. The unique characteristic of this book is that the first part of the book started by re-proving in ...
  • 121
0 votes
0 answers
91 views

What did Einstein say about the Dirac equation?

The wiki article on Dirac quotes Einstein as saying of Dirac I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful. and I don't understand Dirac at all. ...
1 vote
0 answers
71 views

Who coined the term "sulphuretted hydrogen"?

Hydrogen sulfide was previously named "sulphuretted hydrogen" but I can't find the person who named/coined it. Although Carl Wilhelm Scheele is credited to have discovered and isolated the ...
4 votes
1 answer
109 views

Thales and measuring vertical angles

According to Wikipedia’s web page dedicated to Thales of Miletus, he came to the idea to prove the equality of vertical angles as a theorem when he saw that the Egyptians, after intersecting two lines,...
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4 votes
1 answer
92 views

What did Nathan Rosen (from EPR) say about Bell's inequality and its violation?

Motivated by this year's Nobel prize in physics, I was wondering whether there are recorded statements by Nathan Rosen (the R in the EPR-paradox) about the Bell inequality and its violation by this ...
2 votes
0 answers
118 views

How were sine and cosine functions computed before the notion of Taylor series?

We know using modern analysis techniques that $\sin x$ and $\cos x$ can be computed by their Taylor series (in fact the Taylor series are given as the definitions of these functions in today's real ...
12 votes
1 answer
1k views

Why was Alain Aspect discouraged from doing his now Nobel-winning work?

In an interview following Aspect's winning of the Nobel Prize in Physics, he claims that John Stuart Bell discouraged him from pursuing his now-famous 1982 experiment on quantum entanglement. The ...
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0 votes
1 answer
71 views

What did physics mean in 17th century?

In a latter to Huygens, Leibniz wrote Nam in applicatione Geometriae ad Physicam saepissime contingit, which is traslated by Blåsjö (p. 67) as For in the application of geometry to physics it happens ...
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1 vote
1 answer
88 views

What was the Ptolemaic system used for?

Ptolemy's model is less accurate than Copernicus', but it is said to have been in use for a long time. What was the Ptolemaic model be used for?
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