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1500 questions
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Origin of Q for the set of rational numbers?
It seems many sources$^1$ attribute the use of the letter "Q" to represent the rationals to the N. Bourbaki group (in the 1930's); however, the Wikipedia entry on rational numbers claims that Giuseppe Peano introduced the notation in 1895…
Rax Adaam
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Who predicted the existence of the muon neutrino?
The Wikipedia article on the muon neutrino says:
The muon neutrino is a lepton, an elementary subatomic particle which has the symbol $\nu_\mu$ and no net electric charge. Together with the muon it forms the second generation of leptons, hence the…
John Baez
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Who introduced the divisibility symbol $a\vert b$ ("$a$ divides $b$") and when?
I have just stumbled across this post and became curious about the same question, namely the part regarding the origin/history of the vertical bar symbol $a\vert b$ that we use to denote "a divides b" (I don't care at all about why it is written…
BigbearZzz
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Does Blum's speedup theorem have any conceptual predecessors?
Blum's speedup theorem seems to me that bears at least some superficial resemblance to Gödel's research on the length of proofs under certain axiomatic systems.
Does Blum's speedup theorem have any conceptual predecessors?
GEP
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Why were equivalence classes named classes rather than sets?
If $R\subseteq A\times A$ is an equivalence relation (i.e., a relation that is reflexive on $A$, symmetric, and transitive), then for each element $x\in A$, the subset $[x]_R=\{y\in A: \langle x,y\rangle\in R\}$ of $A$ is called an equivalence class…
evenodd
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11
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Who discovered pigeonhole principle in mathematics?
The principle was used as early as late 1760s by Lagrange but are there any earlier uses of it in math?
GEP
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Where are Pierre Samuel's videos of Bourbaki proceedings available?
Wikipedia's article on Pierre Samuel claims (uncitedly):
He was a member of the Bourbaki group, and filmed some of their meetings. A French television documentary on Bourbaki broadcast some of this footage in 2000.
Does anyone know the name of…
user514014
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10
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Did Descartes leave solving the quintic as an exercise to his readers?
In this document by Jim Brown it is claimed (on Section 3, pg 5) that:
[Descartes] believed that all polynomials of degree $>4$ could be solved with the same methods as had been applied to the quadratic, the cubic, and the quartic. In fact, he left…
ZKG
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Was the continuum hypothesis commonly believed to be independent before Cohen's proof?
Someone drew my attention to the Russian translation of Rademacher and Toeplitz's Von Zahlen und Figuren (The Enjoyment of Mathematics in the English translation). In the chapter on set theory the Russian editor, Isaak Yaglom, added a footnote…
AnatolyVorobey
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What are the references for Riemann's discussion of gravity?
I've heard anecdotally that Bernhard Riemann was interested in applying his discovery/invention of Riemannian geometry to model gravitation about 50 years before Einstein managed to do so.
In this video, we hear Edward Witten say,
Riemann almost…
Maximal Ideal
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How did the obelus ÷ come to stand for division?
The obelus ÷ represents division on calculator keyboards, and sometimes in elementary education.
It has a long non-mathematical history starting before 200 BC. Its earliest use as a symbol for division is in Johann Rahn's 1659 Teutsche Algebra.
Is…
Leopold says Reinstate Monica
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What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?
In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this theorem, or one that discusses it?
harpersferry
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10
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Why didn't Lorentz conclude that no object can go faster than light?
Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, as far as I understand this equation was known…
Rob
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What was the scientific explanation of earthquakes in the 18th century?
I'd like to know what western scientists thought about the causes of earthquakes in the mid to late 18th century (especially pertaining to the one in Lisbon in 1755). I've read that the ancient Greeks thought that they were caused by rocking of the…
swit
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Did Einstein say "We cannot solve our problems with the same thinking we used to create them"?
According to various sources on the Web, Albert Einstein is likely to have said or written one of the following:
Probleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden sind.
(German)
We cannot solve our problems with…
user7921