All Questions
4,128
questions
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Why does Eratosthenes method for calculating the circumference of the Earth requires the city of Alexandria and Syene to be in the same meridian?
I'm reading a book where the author claims that in order for the method of angles and proportions used by Eratosthenes to work, the two cities would have to be located in the same meridian, or at ...
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1
answer
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Historical examples of frauds discovered because someone tried to mimic a uniform random sequence
So, I'm preparing a talk about the well known fact that humans are bad at the task of generating uniformly random sequences of numbers when asked to do so.
I would like to spice the talk a bit by ...
- 121
1
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1
answer
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The origin and use of the term "equianharmonic" (elliptic function)
In Weierstrass notation, the principal elliptic function $\wp$ is a solution of the differential equation
$$ (\wp')^2= 4\wp^3 -g_2\wp -g_3. $$
The case when $g_3=0$ is called lemniscatic (it ...
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3
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How and when did scientists first determine that hydrogen was the lightest element?
Cavendish first isolated hydrogen and recognized it for what it was; Lavoisier realized that water consisted of hydrogen and oxygen; Dalton used hydrogen as the basis for relative atomic weights by ...
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Before metric length units were based on the speed of light, how were sub-units accurately derived from the reference bars?
Its my understanding that before metric units of length were based on the speed of light, there were reference bars that were used to calibrate other (mostly calibration) equipment.
How were these ...
2
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1
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129
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What advances in statistics did measure-theoretic probability theory allow?
I've Googled this question in several different ways and I get a lot of hits, but nothing answering the question.
To flesh out the subject line a little, I'm interested in understanding where, in the ...
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2k
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Inscriptions on Newton's tomb
Whiteside in "The Mathematical Principles underlying Newton's
Principia Mathematica" wrote
.. if we can give credence to an account in The Postboy of 12 April 1731, his tomb in Westminster ...
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113
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Euler's "comfortable" series
I am reading Proofs and Confirmations by David Bressoud.
On page $150$ is a long excerpt by Richard Askey, from "How
can mathematicians and mathematical historians help each other?"
There is ...
- 233
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121
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The role of symmetry in mathematics and the half-angle formulas
It seems that the most impressive theorems of classical geometry always have to do with "half of something". Consider the following examples:
The three medians of a triangle meet at the ...
8
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3
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2k
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How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors?
I have wondered if the apparently complex arrangement of the sails of early 19th century vessels was reflective of a lack of understanding of the optimal arrangement of such sails (since modern ...
- 1,041
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Influence of Edmund Landau's list of four problems
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers: Goldbach's conjecture, the twin prime conjecture, Legendre's conjecture (that there ...
- 1,068
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199
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Gate 44 at the Colosseum in Rome: XLIIII or XLIV? When and why the change?
We teach our children in school that 4 is written in Roman numerals as IV and not as IIII but at the Colosseum in Rome, gate 44 is identified as XLIIII and not as XLIV.
When did the change from IIII ...
2
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2
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132
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History of Speed - is it really new? [duplicate]
I was writing a paper on the basics of calculus, and of course the study of velocities plays a big part in that. In introducing the problem statement, I started with a classic word problem, "...
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223
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Original source of these 2 trigonometric identities
I am interested in knowing what is the original source/author of the following identities:
$\tan{\frac{\alpha}{2}}\tan{\frac{\beta}{2}}+\tan{\frac{\alpha}{2}}\tan{\frac{\gamma}{2}}+\tan{\frac{\beta}{2}...
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28
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Were Priestly and Davey wrong about about "Order: A Theory with A View" being written by Ivan Rival?
The textbook Introduction to Lattices and Order by Priestly and Davey mentions in its first edition preface:
In a proselytizing article, Order: a. theory with a. view [in Kla.ssifikation und Ord:nung,...
- 299
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0
answers
67
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What was probability like before Kolmogorov?
How was probability studied or understood before Kolmogorov axiomatized it?
I mean Bernoulli and Gauss had already started inventing and using distributions way before Kolmogorov came into the scene. ...
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1
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0
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49
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Who first stated the three polarizers experiment in quantum mechanics?
In my experience, Dirac is most often cited as the origin of this thought experiment. However, from what I've read in his Principles of Quantum Mechanics, he never actually introduces the idea with ...
- 1,009
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0
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23
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Who gave right hand thumb rule for circular loop of current conducting wire?
To find magnetic field due to current conducting straight wire we have Maxwell's Right hand thumb rule, Which says "Put your right hand thumb in the direction of current then curled fingers shows ...
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0
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72
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Why is bachelors' unknotting called as such and who discovered it?
Bachelors' unknotting is a way to show that all tame knots are isotopic to the unknot, by tightening a knot to a point. Why is it called 'bachelors' unknotting'?
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85
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Who gave right hand thumb rule for circular loop of current conducting wire?
To find magnetic field due to current conducting straight wire we have Maxwell's Right hand thumb rule, Which says "Put your right hand thumb in the direction of current then curled fingers shows ...
- 1
2
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0
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145
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Zermelo's or Fraenkel's early consideration of something equivalent to countable Replacement
I have now claimed a few times on the internet, based on something (sensible!) I read, that at some point in the 1920s, that Zermelo at one point considered as a set theoretic axiom (schema) something ...
- 167
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1
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197
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Why did Clairaut's theorem take so long to prove?
I was reading the Wikipedia on Clairaut's Theorem (Symmetry of second derivatives) and the article accounts the significant amount of time and failed proofs occurred before the theorem was made fully ...
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1
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75
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What factors influence whether an invention is not patented?
Various inventions that have become well-known were never patented, including matches, emoticons, and the magnetic strip. Other noteworthy examples include the polio vaccine (Jonas Salk), monoclonal ...
- 241
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3
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233
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Before Einstein did people realize about a falling man not feeling weight?
I understand that Einstein was able to draw remarkable conclusions and was set on the path of General relativity when he realized that a falling observer not feeling his own weight.
But is it believed ...
- 1,041
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96
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Was the effect of gravity completely anticipated by the first to ascend in balloons and later airplanes?
I understand why the effects of gravity are felt in both balloons and high-flying planes and I believe that while it could have been calculated using Newton's law of gravitation, was there speculation ...
- 1,041
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91
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Naturally occurring elements in other planets and their natural satellites other than earth [closed]
Naturally occurring elements
Is it possible to find natural elements in other planets and their natural satellites other than planet earth?
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0
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42
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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 ...
- 299
5
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2
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1k
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What was 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.
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1
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126
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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 ...
- 5,211
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46
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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, ...
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2
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2k
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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 ...
- 1,041
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82
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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_\...
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70
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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 ...
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2
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173
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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?
user65203
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100
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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. ...
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45
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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
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1
answer
68
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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?
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0
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93
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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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0
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49
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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
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84
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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?
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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
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1
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138
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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&...
- 527
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174
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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 ...
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1
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151
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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 ...
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1
answer
145
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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.
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118
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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 ...
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283
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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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232
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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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83
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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 ...
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109
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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,...
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