Unanswered Questions
791 questions with no upvoted or accepted answers
20
votes
0answers
562 views
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 ...
17
votes
0answers
732 views
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 ...
16
votes
0answers
616 views
When did people know that all real polynomials of degree greater than 2 are reducible?
Admittedly, this may not be a research level question, but I am deeply curious about this.
Let $f(x) \in \mathbb{R}[x]$, and write $d = \deg f$. It is well known that if $\deg f > 2$, then $f$ is ...
15
votes
0answers
510 views
Conditionally convergent series
I am looking for the original reference discussing a specific, elementary example of a rearrangement of series converging to a value different from the original series. In what follows, I give some (...
14
votes
0answers
444 views
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/...
13
votes
0answers
134 views
Did Walter Pitts refuse to allow his name to be made publicly available?
I read on the Wikipedia page on Walter Pitts that :
Pitts was also described as an eccentric, refusing to allow his name
to be made publicly available. He refused all offers of advanced
...
12
votes
0answers
274 views
What was the typical format of a 16th century mathematical debate?
In The Equation that Couldn't be Solved, Mario Livio writes of academia in 16th century Bologna. Apparently, mathematicians would take part in public debates, sometimes involving solving problems. ...
11
votes
0answers
73 views
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 ...
10
votes
0answers
317 views
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 ...
9
votes
0answers
203 views
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 ...
9
votes
0answers
371 views
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” ...
9
votes
0answers
753 views
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 ...
9
votes
0answers
88 views
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 ...
9
votes
0answers
139 views
Contemporary reactions to the rise of axiomatization in the 19th/20th centuries
Starting somewhere in the 19th century, mathematics turned from the study of concrete objects to the study of objects satisfying enough properties to lead to interesting theorems. For example:
From ...
9
votes
1answer
261 views
Is Hermann Weyl's book “Space, Time, Matter” (1923) on General Relativity still relevant?
I really liked Hermann Weyl's mathematical books and would like to get accustomed to general relativity from his perspective, but wonder if it's still relevant after almost 100 (!) years?
Can this ...
