Unanswered Questions

1,052 questions with no upvoted or accepted answers
21 votes
0 answers

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
0 answers

When did people know that all real polynomials of degree greater than 2 were 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 ...
17 votes
0 answers

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 ...
15 votes
1 answer

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/...
14 votes
0 answers

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 ...
13 votes
0 answers

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
0 answers

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
0 answers

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 ...
11 votes
0 answers

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
0 answers

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 ...
9 votes
0 answers

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
0 answers

Did John Von Neumann hate pure mathematics that became too abstract?

John von Neumann wrote the following in his essay The Mathematician: As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only ...
9 votes
0 answers

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 ...
9 votes
0 answers

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 ...
9 votes
0 answers

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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