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Definition of ordinal multiplication
The ordinal multiplication $\cdot$ can be defined recursively via ordinal addition $+$ for any ordinal $\alpha$ as follows:
$\alpha\cdot 0=0$.
$\alpha\cdot (\beta+1)=\alpha\cdot \beta+\alpha$ for any ordinal $\beta$.
$\alpha\cdot \lambda=\bigcup…
modnar
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What is the source of Donald Knuth's remark about naming programming languages?
(This question toes the line between belonging here and belonging on the Retrocomputing Stack Exchange.)
Here is the quote; sometimes the first sentence is omitted:
The most important thing in a programming language is the name. A language will not…
texdr.aft
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6
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How did Meyer know atomic volumes to plot them just before Mendeleev's periodic table?
Back to 1868, Mendeleev's periodic table has not been published yet, but we are quite there.
As a scientist, you're still struggling to identify very clearly these elements with limited means.
Especially, you feel and observe that there are some…
user1556814
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6
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2 answers
Who first proposed the theory of tidal locking?
I'm interested in the history of the concept of tidal locking but haven't been able to find any articles presenting a timeline of its development. I'm hoping to have a look at the first published paper on the subject, if possible.
Any leads would be…
numbynumb
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2 answers
A branch of mathematics which refused to be rigorous?
I'm currently in a class on formal mathematics/formal logic/axiomatic set theory. Someone asked, "At the end of the day, as mathematicians, why do we care about rigor?" My professor gave an example of a mathematician who did not believe in the…
The Ledge
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6
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Was the sun assumed to be at rest aether frame?
Back in the past, was the sun assumed to be at rest in the luminous aether frame?
Kashmiri
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6
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How did Dyck originally state and prove his theorem in topology about the connected sum of a torus and projective plane?
Dyck's theorem in topology is sometimes stated as follows: the connected sum of a torus and projective plane is homeomorphic to the connected sum of three projective planes.
Certainly, this is the modern formulation of his theorem, given that Dyck…
user13915
6
votes
2 answers
History of generating functions
I've seen that there is some information in the first volume of Polya's "Mathematics and Plausible Reasoning". Also, the following paper deals with the usage in probability - "The historical development of the use of generating functions in…
frgt
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6
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What is the source of Hermann Weyl's remark about "near-sighted policemen" with respect to compact spaces?
Hermann Weyl is widely reported as making the following observation about a compact space:
"If a city is compact, it can be guarded by a finite number of arbitrarily near-sighted policemen."
This was reported in a paper by Edwin Hewitt in a 1960…
Prime Mover
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What is the origin in the discrepancy between engineers' and physicists' notation of waves?
my question is very simple. Physicists use this notation in order to write a (for example) plane wave:
$$
\xi(z) = \xi^+ \mathrm{e}^{+\mathrm{i}kz} + \xi^- \mathrm{e}^{-\mathrm{i}kz},
$$
where $\xi^+$ is the progressive wave and $\xi^-$ is the…
gunix12
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What was the content of Emmy Noether's 'two-line' note on Homology?
I was surprised to learn that the note published by Emmy Noether in 1925 that suggested that Homology was better thought through as actual groups rather than numerically as Betti numbers consisted of fourteen lines. This is mentioned in Weibels…
Mozibur Ullah
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Can anyone find Newton's calculation error in Principia, Book III, Proposition XIX?
Musing about the historical evolution of the notation for the gravitational constant ($f$, $G$, $\kappa$, $\kappa^2$), I found myself digging for the first time in my life into Newton's Principia, looking for the data he could have used (had he…
mmanu F
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6
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1 answer
Who is the Göbel who is the eponym of Göbel's Sequence?
Richard K. Guy refers to him as "F. Göbel" in his Unsolved Problems of Number Theory but that's as close as I can get.
For reference:
https://mathworld.wolfram.com/GoebelsSequence.html
Prime Mover
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1 answer
What did Delaunay invent Delaunay triangulations for before computers were developed?
I was teaching my students about Delaunay Triangulation which is a method for dividing a surface into triangles. This triangulation method is the basis of most computer calculations that require a surface to be approximated as small elements. Here…
Hugh
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6
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1 answer
Some references for Vladimir Arnold's thesis "Mathematics is a part of physics"?
The mathematician Vladimir Arnold claimed that mathematics is a part of physics.
I am aware of Arnold's On Teaching Mathematics where he stated this view, but is there any piece of writing where Arnold, or someone else, elaborated on it?
Ansonī Bōdo
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