Unanswered Questions
1,289 questions with no upvoted or accepted answers
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What is the modern significance of Theaetetus's classification of quadratic irrationals?
Before Eudoxus's theory of proportion there was a theory of irrationals based on continued fraction expansions, which Fowler calls anthyphairesis. Theaetetus is said to develop a classification of ...
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19
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A basic mistake by Cayley
Arthur Cayley's first paper on abstract groups, in 1854, can be found in his Collected Papers on the Internet Archive, starting at https://archive.org/stream/collectedmathema02cayluoft#page/122/mode/...
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17
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Did Kontsevich start a lecture with "one I will not define, the other nobody knows how to define, and we will be proving that they are equivalent"?
The story was circulating in early 2000s, so presumably it happened in 1990s. Kontsevich, it goes, opened a lecture course on mirror symmetry with:"This course is about two categories. One I will not ...
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Did Kronecker say that set theory is not mathematics?
I have frequently come across Kronecker's statement about set theory:
I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there.
It ...
12
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Origin of the special Finnish notation for difference of antiderivative
Apologies for a question that is specific to one country (but perhaps others find it a curious example of how mathematical notation can vary between countries).
In Finnish calculus texts, if $F$ is an ...
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Why are the classic statistical approaches to NLP mostly generative models while the most recent ones are mostly discriminative?
Looking at the classic statistical approaches to natural language processing (e.g. tagging, parsing, etc.), I see that they are mostly generative models: n-gram models, Naive Bayes classifiers, hidden ...
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How were contour plots of complex functions produced in the days of mechanical differential analyzers?
I was reading an old paper (specifically, the first appearance of the Pearcey function, here) and I was struck by the beauty of the plots it contains, particularly for a paper from 1945-46:
Pearcey ...
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11
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Chronology of proofs of cubic and biquadratic reciprocity laws
I just want to check if anybody knows a website where one can find a chronology of proofs of more difficult reciprocity theorems (such as the cubic and biquadratic cases) similar to the (already ...
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Ramanujan's Method for solving cubic, quartic, quintic
In Ramanujan's Notebooks Volume IV pg. 31 by Bruce C. Berndt, he describes an easy way to solve the general quartic by starting with the system$$x^2+ay=b\\y^2+cx=d\tag1$$
And solving for $x$; which ...
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First use of term "Hilbert's Nullstellensatz"
This year (2021) marks the 100th anniversary of Emmy Noether's 1921 paper in which she introduced Noetherian rings and proved the primary ideal decomposition for them. The original version of her ...
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Apéry’s mysterious recurrence relation
A fairly detailed (14 page) account of Apéry’s original proof of the irrationality of $\zeta(3)$ is given in Julian Havil’s book The Irrationals which states that Apéry’s starting point is the ...
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Books on elliptic functions
In the end of his address to Annual Meeting of the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", the Association president G. N. ...
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9
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Who was the first to use the "does not exist" sign ∄?
Who was the first to use the "does not exist" sign ∄? I'm aware that Giuseppe Peano originated serifed ∃ and, moreover that Whitehead and Russell repurposed Peano's serifed ∃; I'm also aware that ...
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Whence “homomorphism”, “homomorphic”?
The kernel question leads to another : Today, homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen?
“Homomorphic” ...
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On the history of population dynamics of territorial species
I am interested in the historical priority in population biology, essays or monographs, discussing the concept of territoriality prior to 1950.
What is it? In the early 18th century discussions of ...
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