All Questions
4,412
questions
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A text or YouTube channel with a comparison between pre-Cartesian with post-Cartesian mathematics
Is there some good book or YouTube channel that make a good comparison/distinctions between the mathematics before René Descartes, with the mathematics after Descartes?
In the short article "The ...
16
votes
1
answer
4k
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Autistic Assistant of Gauss used to check Primality
The Arora-Barak book on complexity contains the following sentence with the following footnote, page 128:
In primality testing, we are given an integer N and wish to determine
whether or not it is ...
- 163
3
votes
0
answers
74
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How was crystallography studied before X-ray diffraction?
Nowadays, the crystal structure of some solids can be determined by using X-ray diffraction techniques based on Bragg's law and so on. However, after reading the timeline of crystallography, it seems ...
- 131
2
votes
1
answer
127
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When did the notion of and term "weight" arise in geometry?
The notion of weight of a Hodge structure and its avatars on $\ell$-adic and $p$-adic cohomologies (via comparison theorems modeled on the Hodge decomposition of de Rham or singular cohomology with ...
- 205
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1
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108
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How did Fermat handle Frenicle's challenge to find a perfect number between $10^{20}$ and $10^{22}$?
Even perfect numbers have the form $(2^n - 1)2^{n-1}$ where $2^n - 1$ is a prime number. This restricts the possible values of $n$ to $34, 35, 36, 37$. Since $n$ must be prime, only $37$ has to be ...
- 13
3
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95
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When did modular forms start to get studied via algebraic geometry?
I'm looking, for instance, as to when people started studying modular curves and modular forms as sections of line bundles on them, as opposed to the point of view of modular forms being holomorphic ...
- 255
2
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0
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128
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Who were some of the scientists in the post-war French nuclear weapon project?
The Manhattan project is well known for gathering many top scientists of the century. The Soviet nuclear program seem to have a reduced but still important cast with scientists like Andrei Sakharov, ...
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6
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1
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452
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Cantor, set theory and foundations
Did Georg Cantor ever think that set theory could serve as a foundational system for all of mathematics?
He died in 1918, but Zermelo set theory (just Z, no ZF or ZFC yet) was described in a paper by ...
- 275
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96
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Who were the famous scientists in the post-war British nuclear weapon project?
The Manhattan project is well known for gathering many top scientists of the century. The Soviet nuclear program seem to have a reduced but still important cast with scientists like Andrei Sakharov, ...
- 2,678
3
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162
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Question on Gauss's geometric interpretation of "spherical functions"
In the physics chapter of his biography of Gauss, W.K. Buhler writes the following:
Expansions into series are frequent and important in potential theory. So it does not come as a surprise that ...
- 4,307
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122
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Scientific articles discovered false and useless several years after their publication
I am looking for examples of important scientific articles that have been discovered to be false and useless several years after their publication. I mean:
they stated something interesting and ...
- 273
2
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1
answer
118
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What values of Avogadro's Number did Jean Perrin come up with?
I am currently plundering the contents of the $1969$ reprint of the 2nd edition of Data and Formulae for Engineering Students published by Pergamon International (authors J.C. Anderson, D.M. Hum, B.G. ...
- 1,237
2
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1
answer
110
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Did Darwin know about symbiosis?
The words symbiosis was first used in 1876. This was 6 years before Darwin's death.
Did he know about the concept of symbiosis? Did he mention it in his book?
- 257
6
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1
answer
229
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Earliest mention of permutation matrices, or equivalent? More generally, matrices for arbitrary functions between finite sets?
Permutation matrices I assume have a long history, and would be surprised if they were first considered only long after the work of Shur just after 1900, on the representation theory of $S_n$.
...
- 229
3
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1
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106
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Was Martin Packard of Varian Associates related to David Packard of Hewlett-Packard?
I came across an entry for the Proceedings of the American Physical Society which was published in Phys. Rev. volume 93 page 939 (1954) under the heading "Minutes of the Stanford Meeting December ...
- 133
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5
answers
4k
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Why did Hilbert believe consistency implies existence?
I am reading Sieg's "Hilbert's programs and beyond" and I am having difficulty understanding this quote by Hilbert on page 74:
In the Paris Lecture Hilbert re-emphasized and expanded this ...
- 41
2
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0
answers
129
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How did Grothendieck come in contact with Category theory?
Category theory was formalized around 1950s, and Grothendieck made his breakthrough papers about 10-20 years from that time. I wish to know, how was it possible the ideas of Category Theory were so ...
3
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0
answers
80
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Sylvester's Quote on Determinants
What does the following quote by Sylvester mean?
"A general algebraical determinant in its developed form may be likened to a mixture of liquids seemingly homogeneous, but which, being of ...
- 225
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0
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52
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Ab-initio method (First principle of Mathematics)
Who was the first one to give proof of 1st Principle of Mathematics in calculus (also known as ab-initio method) ,was he newton or someone else ??
2
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0
answers
101
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Was the small Desargues Theorem known to ancient Greeks?
My question concerns the classical Desargues Theorem and its simplest version
The small Desargues Theorem: Let $A,B,C$ be three distinct parallel lines and $a,a'\in A$, $b,b'\in B$, $c,c'\in C$, be ...
- 121
1
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1
answer
89
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Ancient parallax
When ancient Greeks could not observe any parallax, what were the two bodies they were looking at to determine this? I imagine the stars (or a specific star) would have been one of these, but what was ...
- 375
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1
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103
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How the concept of Momentum was discovered?
As we already know that the concept of Momentum was discovered before Newton discovered his laws of motion, but my question is $\rightarrow$ How they discovered the relationship p=mv without knowing ...
1
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0
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81
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In historical studies of mathematics, how to chose the corpus of texts to work with?
When studying the evolution of some concept in the history of mathematics, is there some established practice or methodology for selecting the corpus of texts to work with, or at least for selecting a ...
- 241
3
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1
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104
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First use of ~ and ≍ (\sym and \asymp)
The relations ~ and ≍ are frequently used in math and computer science, at least within number theory and analysis of algorithms. What is their origin?
Definitions
Suppose $g(x)$ is an eventually-...
- 131
5
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1
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212
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Did ancient Greeks have a numerical value for the Golden Ratio
Did they calculate a numerical value for the "extreme and mean ratio" or did they just have ways to construct it geometrically? If so, what value did they use and how did they calculate it?
- 375
2
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1
answer
80
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Are similarities in notation between Hamiltonian mechanics and Box-Jenkins time series forecasting accidental?
The 1833 formalism of Hamiltonian mechanics prescribes phase space coordinates (p,q) as momenta. https://en.wikipedia.org/wiki/Hamiltonian_mechanics
The Box-Jenkins method (1970) of time series ...
- 337
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0
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124
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mind-boggling/curious historical facts that will inspire and attract young people
I am trying to compile a list of mind-boggling/curious historical facts in mathematics that will inspire and attract young people (9–11 years old) to the discipline of Mathematics. Do you have one ...
3
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0
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92
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Where does the "operator to the right" notation originate?
If any of you have ever written code in DirectX, you're sure to have noticed that applying a linear operator $A$ to a vector $x$ is done as $xA$, instead of the (nowadays usual) $Ax$. I wanted to know ...
0
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134
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Grothendieck's complete absorption in mathematical research
I have recently been interested in the history of French Mathematics especially in Grothendieck and his school. I have also been fascinated with Grothendieck's personality.
It is known that during ...
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0
answers
61
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17th or 18th century use of the continued fraction expansion of $(1 + \sqrt D)/2$ to solve the diophantine equation $x^2 - D y^2 = 4$
Can someone please provide an early reference to the use of the continued fraction expansion of $\frac{1+\sqrt D}2$ to solve the Diophantine equation $x^2 - D y^2 = 4$ for a positive integer $D$ ...
5
votes
1
answer
116
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Leibniz conjecture that geometry is a form of algebra
Hermann Grassmann (1840s) verified the Leibniz conjecture that geometry 1s a form of algebra, showing that the geometric figures themselves are algebraic entities, because they are subject to definite ...
1
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0
answers
47
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Where is conditional probability in Bayes' paper
The modern way to get to Bayes' theorem is through conditional probability. How did Bayes get to it? I've read, with crossed eyes, his 1763 paper and I cannot see conditional probability or his ...
- 315
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1
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91
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What is Minkowski problem?
I have a question about 'Minkowski problem' related to Gaussian curvature.
I searched 'Minkowski problem' in Google, Almost all of them were related to Einstein's theory of relativity. So I ask about ...
- 131
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28
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Early sources for surface and bound charges in polarization
I am looking for early sources (references) to the analysis in electrostatics where the polarization vector is rewritten in terms of bound charges and a surface polarization charge.
In terms of what I ...
- 1
0
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0
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40
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Early triboelectricity
I am looking for good sources to quote for early work on triboelectricity. I already have the standard ones, e.g. Benjamin Park (1898) "A history of electricity..", Roller & Roller (1953)...
- 1
3
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0
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179
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Who was the first to understand that there is not a net flux of energy between Sun and Earth, but of entropy?
According to Penrose's Cycles of Time, he starts by reminding the usefulness of the second law of thermodynamics and how it applies to everyday life. In particular, how the net energy of Earth is a ...
- 2,678
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131
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Did Heisenberg say free will could arise from quantum probabilistic mechanics?
I see this view attributed to him a lot during Twitter debates but I never found the source for it
does anyone know if Heisenberg actually held this view/suggested it?
- 409
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1
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122
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Why doesn't John Snow's Voronoi diagram look like one? How was the diagram made? (distance to cholera-spreading water pump in 19th century London)
After about 03:03 in Dr. Trefor Bazett's June 2023 video Why this pattern shows up everywhere in nature || Voronoi Cell Pattern there is a discussion of a diagram representing work by John Snow
John ...
- 2,098
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192
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Who was the first to estimate the vacuum energy discrepancy by 120 orders of magnitude?
Apparently, this discrepancy is one of the "worst predictions" in the history of science. Clearly the vacuum energy calculation depends on many approximations and it is not clear how it ...
- 2,678
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162
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Motivation of Monge-Ampere equation
I have a question about Monge-Ampere equation.
I read a book The shape of inner space by Shing-Tung Yau.
Chapter 5 in this book, Complex-Monge-Ampere equation's explaination was so interesting. In the ...
- 131
2
votes
1
answer
877
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Who was J. M. Gandhi?
I am looking for more information about J. M. Gandhi who is
the creator of Gandhi polynomials. A MathSciNet search finds
only one J. M. Gandhi with 35 publications in Number Theory,
3 in Combinatorics,...
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0
answers
87
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Who is the artist who depicted Tartaglia?
I mentioned in a previous question that I'm writing a young adult novel that explores the discovery of complex numbers. I might want to include an illustration of Tartaglia. All of the illustrations ...
- 139
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0
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83
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Have there ever been any schemes for the classification of experiments?
There have been several book classification schemes, for example: Dewey Decimal, Library of Congress, etc. Have there been any experiment classification schemes, i.e. sets of criteria by which to ...
- 81
1
vote
2
answers
105
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To what extent were Riemann surfaces a precursor to algebraic geometry?
I read that Riemann started studying the so-called Riemann's surfaces in the second half of the 19th century, introducing tools like meromorphic functions and meromorphic 1-forms. The culmination of ...
- 249
2
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1
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440
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Who was Hans J. Maehly?
During some recent work on the computation of the inverse Langevin function I ran into trouble trying to generate a highly-accurate minimax rational approximation with a variant of the Remez algorithm,...
- 5,801
2
votes
1
answer
127
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Who was the first to write proofs in this manner?
Who was the first to write proofs in this fashion?
By ``in this fashion'' I mean, using three columns, which go like:
Line number. Premise or assertion. Justification.
Line number. Premise or ...
- 81
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0
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83
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Arrow heads on coordinate axes
Where did arrow heads on coordinate axes appear for the first time?
I checked Descartes' "Discourse on Method, Optics, Geometry, and Meteorology"
but he does not use any arrow heads.
In ...
- 121
3
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1
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211
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Did any "classical era" physicist foresee that a theory such as Quantum Mechanics is logically inescapable?
I am interested in knowing if in the era preceding the observations that lead to the advent of Quantum Mechanics, anyone foresaw logically that a theory such as Quantum Mechanics is in a sense, "...
- 353
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1
answer
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What is the iodine fax process mentioned in Vannevar Bush's "As we may think"?
What is the iodine fax process mentioned in Vannevar Bush's "As we may think"?
Another process now in use is also slow, and more or less clumsy. For fifty years impregnated papers have been ...
0
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0
answers
131
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Did Archimedes know Archimedes' recurrence formula?
Archimedes used polygons inscribed and circumscribed to the circle to approximate pi in his "Measurement of a Circle".
However, I think Archimedes' recurrence formula is not used there.
Did ...
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