All Questions
4,337
questions
2
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Is there a comprehensive list of Ancient Greek mathematical writings?
Much of the Ancient Greek's mathematical philosophy texts have survived from antiquity and passed to modern times. Also, texts previously thought to be lost are being occasionally rediscovered (...
- 121
0
votes
1
answer
118
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Question about Felix Klein's "Development of Mathematics in the 19th Century"
The original version of these photos is Felix Klein's "Development of Mathematics in the 19th Century"
In second photo
In this book, it says class-field and decompose 2 into $(1+i)$ and $(1-...
- 125
0
votes
0
answers
79
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Who invented bit permutations like shuffle, butterfly and bit-reversal?
This question is about a class of periodic permutations,that are produced by applying finite permutations to the binary digits of all integers.
In lack of a better name, they shall be called bit ...
- 101
-1
votes
1
answer
112
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Technical papers or monographs without a single mathematical equation
Recently, I stumbled upon a historically important monograph on a technical subject, which explained complex physical phenomena without a single mathematical equation. I forgot the name of the author, ...
- 1
0
votes
1
answer
89
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Who first introduced the term "necessary condition" in mathematical language?
I recently delved into a discussion about a statement attributed to the renowned mathematician and philosopher, Benjamin Peirce. In this statement, he refers to mathematics as "the science that ...
8
votes
1
answer
1k
views
Where did the popular idea of spacetime come from?
[This question is about popular conceptions and therefore goes into strange directions, don't get too shocked]
The notion of spacetime can be traced back to roughly the 18th century where some people ...
- 741
2
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0
answers
49
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Was there any discourse between Dirac and Einstein that was recorded in print or noted?
I read in Wiki they were together at the Solvay Conderence. There is also a note from 1926 letter to Paul Ehrenfest, Albert Einstein wrote of a Dirac paper, "I am toiling over Dirac. This ...
- 1,213
0
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1
answer
157
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Who was the scientist who first showed that helium has a bound state, and was he a nazi?
I remember from my quantum course that the first person (I believe in 1927) to show that helium has a bound state, using the variational principle, was a nazi. It was remarked by my professors that he ...
- 109
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0
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53
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Compressed air vs steam -- how much more or less efficient? [closed]
I believe steam engines could run on compressed air. Not sure what sort of changes needed to be made but would not using compressed air be more efficient because no need to carry coal or wood to ...
- 1,099
4
votes
1
answer
106
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Who first referred to the number of nonzero entries of a vector as its $\ell_0$ norm?
It is common in the compressed sensing literature to refer to the number of nonzero entries of a vector as its $\ell_0$ "norm." The scare quotes are there because strictly speaking, the $\...
- 1,216
0
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0
answers
36
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How was the Binomial Distribution function developed?
I don't understand the binomial pdf. How was it developed? What's the logic behind it?
- 9
3
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2
answers
486
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Did Euler know Ancient Greek?
In a previous question on this website: What was Euler's first language?,
Alexandre Eremenko wrote the following about Leonard Euler:
There is little doubt that he also learnt French in his ...
user18960
3
votes
1
answer
103
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"Équation de Maxwell-Thomson"
In French, Gauss' law for magnetism (no magnetic monopoles) is, sometimes at least, referred to as Équation de Maxwell-Thomson. What is the historical justification of this?
- 33
0
votes
1
answer
89
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Reconstruction of Newton's axioms
Hilbert reconstructed Euclid's axioms. Is there an equivalent restructuring of Newton's axioms, or are they considered consistent?
- 187
1
vote
1
answer
333
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How to find the first appearance of a theorem?
I often have questions of the "who predicted and proved this theorem when and in what context?" kind.
There are two ways I can think of.
Read books on the history of mathematics.
Find ...
- 13
3
votes
0
answers
65
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Did the Romans really use the binomial formula to calculate products?
I'm not quite sure if this is the right place to ask this question (in fact, I was redirected to this SE from the Math Stackexchange), but it's probably more fitting than the original posting place.
I ...
- 131
0
votes
1
answer
251
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Any notable large proof that took a long time before anyone checked it?
Have there been any examples in the past where a large proof is claimed but nobody takes the time to check and that has been proved/disproved after a long time? I am not interested in proofs that were ...
- 2,317
0
votes
0
answers
56
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Who was the first to use bijections?
I know that Bourbaki were the first who used the word 'bijection', but one-to one functions were for sure used before them. So do you aware of the earliest examples of one-to-one correspondences?
- 101
1
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1
answer
93
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Where can I find the Royal Society report on the controversy over the invention of differential calculus?
Where can I find the report on the Leibniz–Newton calculus controversy mentioned in this article?
In 1712 the Royal Society in England wrote a report purporting to settle the matter — except, the ...
user18960
5
votes
0
answers
47
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When were arrows first used to visualise vectors?
I guess the use of arrows to visualise vectors came before the general notion of vectors, so a more precise question is: when where arrows first used to visualise physical (or mathematical) quantities ...
- 1,640
0
votes
0
answers
43
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Semmelweis had no explanation?
That Semmelweis noticed a huge drop in mortality among new mothers simply by having doctors wash their hands between patients.
But according to https://en.wikipedia.org/wiki/Ignaz_Semmelweis he did ...
- 1,099
1
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0
answers
39
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Probability in Ancient Greece and Rome -- Dice vs Divination?
My understanding is that probability theory is 16th or 17th century but games of chance existed 2000 years ago -- even if more complex probabilities were not understood by ancients, surely they ...
- 1,099
2
votes
2
answers
164
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Did the plum pudding model of the atom make any successful predictions?
Bohr’s model of the atom predicted hydrogen’s spectral emissions lines —— a huge success.
What about Thomson’s plum pudding model? Did it make any successful predictions?
- 121
0
votes
2
answers
108
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Did the ancients know about the law of universal gravitation?
Just looking into the dialogue by Plutarch "De facie quae in orbe Lunae apparet" and my impression is, they knew the law of universal gravitation quite well.
For instance, it is argued that
...
- 642
0
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0
answers
35
views
Ideal gas equation, mercury thermometer and temperature
Initially water thermometer were used to measure temperatures around the 1600s, then in 18th century mercury was used in thermometers because it expands linearly with temperature. But how do they know ...
- 101
1
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0
answers
65
views
Why did early pioneers in polio research not win a nobel?
If we consider the two early pioneers in the fight against the polio desease to be Dr Jonas Salk and Dr Albert Sabin, why then did they not win Nobel Prizes?
Seems to me to be enough of a tremendous ...
- 397
7
votes
1
answer
903
views
How does Legendre transformation in classical mechanics relate to Adrien-Marie Legendre?
I tried to look for the history of Legendre transformation, which transformed Lagrangian mechanics to Hamiltonian mechanics, usually formulated as
$$
\begin{cases}
p_i = \frac{\partial L}{\partial v_i}...
- 173
6
votes
3
answers
8k
views
Why didn't Einstein propose any metric solution to his equations?
I've read about general relativity (GR) recently and something stroke me: Einstein came up with his equations in 1915, linking the metric of spacetime to the distribution of energy (more exactly, to ...
- 219
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0
answers
95
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The 'Behold' proof for the Pythagoras theorem: who is the true author? Where was it published first time? [duplicate]
The Pythagoras theorem has many proofs. one of them is the famous Behold one:
I am trying to trace back the authorship and the original work where this proof is presented first time. there are a lot ...
1
vote
0
answers
92
views
Motivation to extend sin and cos to angles > 90 degree
What was from a historical point of view the motivation to extend the definition of sin and cos to angles larger than 90 degree?
- 181
3
votes
1
answer
125
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Who was the first woman to complete the physics and mathematics program in Zürich?
According to descriptions of Mileva Marić, Einstein's first wife, she was the second woman to complete the mathematics and physics program at the Zürich Polytechnikum. However, nobody points out who ...
- 2,317
-3
votes
1
answer
114
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is the shape of the Greek letter pi inspired in the Lion's Gate at Mycenae? [closed]
some references put that the shape of the Greek letter pi is inspired in the lion's gate at Mycenae:
The Symbolism of the Greek Alphabet" by Thomas Taylor(1833)
"The Secret Life of Symbols&...
2
votes
1
answer
309
views
The role of the Elements in the development of mathematics
The Elements are often regarded as the cornerstone of the axiomatic approach to mathematics. However, mathematical textbooks have served as the foundational pillars upon which writing style, language, ...
- 1,259
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0
answers
33
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Who was the first to make a Stern-Gerlach experiment with two magnets?
I'm trying to fill a conceptual gap I have in the history of physics
In 1922 Stern and Gerlach make their experiment, proving that electrons have intrinsic angular momentum, however it takes a while ...
5
votes
1
answer
121
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How did the concept of local field emerge and develop in mathematics?
When I was studying class field theory, I saw local class field theory. However, I suddenly became curious about local fields, not local class field theory. As far as I know, the local field is the ...
- 125
2
votes
1
answer
156
views
Did Cardano predict the date of his death then commit suicide on that date?
Morris Kline (Mathematics in Western Culture, 1953):
It is said that he prognosticated his own death and committed suicide on the date predicted in order to maintain his reputation as an astrologer.
...
- 121
6
votes
2
answers
863
views
First appearance of the "four triangles and a square" proof of the Pythagorean Theorem
A well-known proof of the Pythagorean Theorem is illustrated in the figure below:
This figure shows a square with side lengths $a + b$, dissected into four right triangles (each with area $\frac 12 ...
- 565
0
votes
1
answer
96
views
Where to find average man/woman drawings as proposed by Quetelet?
Where to find average man/woman drawings as proposed by Adolphe Quetelet? Drawings along the years would be very nice. He proposed the idea of average man in 1835 (see https://historyofinformation.com/...
1
vote
0
answers
39
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Dissemination of Calculus in China
Much has already been written about the dissemination of Euclidean geometry into China: https://www.maa.org/press/periodicals/convergence/mathematical-treasure-euclid-in-china, https://academic.oup....
- 243
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0
answers
40
views
Understanding Grassmann's Approach to Algebras over Vector Spaces?
According to Hermann Grassmann and the creation of linear algebra by Desmond Sander, Grassmann was able to identify all the important notions in linear algebra in his book "Ausdehnungslehre"....
- 101
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0
answers
71
views
Why did Abel choose 6064321219?
In August 1823, Abel wrote a letter to Holmboe with a date:
Copenhague, l’an $ \sqrt[3]{6064321219} $ (en comptant lafraction d´ecimal).
$ 1823 \frac{215}{365} < \sqrt[3]{6064321219} < 1823 \...
- 101
4
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0
answers
33
views
Who found the formula for sequential Stern-Gerlach experiments and when?
Today we know that if you make sequential Stern-Gerlach experiments, where the magnetic fields are at an angle $\alpha$, then the formula for the ratio how the beam splits is
$$p_{1}=\cos^2 \bigg(\...
1
vote
1
answer
58
views
Kepler's Mysterium Cosmographicum with regular polygons: in which nesting order?
Kepler tried to use regular polygons before using the 3D platonic solids in his Mysterium Cosmographicum.
My question is: which regular polygons did Kepler try to use and in what nesting order?
1
vote
1
answer
186
views
What motivated the development of the theory of perspective during the Renaissance? [closed]
It is said that the theory of perspective in art was greatly developed during the Renaissance because of the search for reality at this time: more realistic representations.
My question is what ...
1
vote
0
answers
72
views
What are Weber class field's weak points?
These days, I'm interested in class field theory.
I know that Weber first made his own 'class field' and then Hilbert made his own field, 'Hilbert class field'.
By the way, were there so many weak ...
- 125
2
votes
1
answer
79
views
How was light polarization interpreted when first discovered?
Malus first discovered light polarization just before 1810, but Maxwell's equation stuff came around 1860s. How was polarization interpreted before the EM theory?
- 23
2
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0
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57
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What were the initial physical applications of vector calculus such as curl, div, circulation, and flux?
In what context where vector calculus concepts, such as:
Circulation
Flux
Curl
Divergence
first developed? I had assumed they were developed first in fluid dynamics, since the flow of water is ...
- 163
0
votes
0
answers
61
views
Why the sphere eversion problem emerged?
Sphere eversion is the process of turning a sphere inside out in a three-dimensional space. See also this animation on YouTube: Outside in (2011) and picture below. My question is, what is the ...
2
votes
1
answer
244
views
Use of blackboard bold "ℝ" to refer to real numbers?
I was looking at Wikipedia's wonderful table of the history of certain mathematical symbols, and there was a certain glaring omission: the use of ℝ to apply to the set of all real numbers. They have ...
- 226
2
votes
2
answers
147
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Was René Descartes an arrogant man?
In a Youtube Video by author AnotherRoof, the author described Descartes as an "arrogant" person who is right, quoting the sentence "I think, therefore I am". However when I am ...
- 159