Unanswered Questions

446 questions with no upvoted or accepted answers
18
votes
1answer
449 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 ...
16
votes
0answers
645 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 ...
14
votes
0answers
362 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 ...
13
votes
0answers
311 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/...
12
votes
0answers
20k views

Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \...
12
votes
0answers
248 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. ...
12
votes
0answers
311 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 (...
10
votes
0answers
2k views

How did Jun John Sakurai die?

How did theoretical physicist Jun John Sakurai die? The only result from extensive googling is that he died "suddenly" while working at CERN. Does anyone know anything more specific?
10
votes
0answers
69 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
115 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 ...
9
votes
0answers
341 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” ...
8
votes
0answers
639 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 ...
8
votes
0answers
213 views

How did Weyl's 1918 paper; Gravitation and Electricity, influence classical physics?

The main-stream view seems to be that Weyl's 1918 paper Gravitation and Electricity was initially considered a failure for reasons first pointed out by Einstein. But these initial ideas were reapplied ...
8
votes
0answers
85 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 ...
8
votes
0answers
127 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 ...

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