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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
5
votes
When did coordinate plane "as we know it" come into play?
I don't think there is a decisive answer to this question, because some
mathematicians accepted negative coordinates long before others did.
However, here is another landmark from the 1690s: Huygens' …
8
votes
At what times were people interested in prime numbers
In recent times it has been claimed that Bhaskara I (around 700) and
more definitely Ibn al-Haytham (965 - 1040) were aware of Wilson's
theorem. This is much earlier than Wilson's theorem was previous …
6
votes
Accepted
Jerome Franel's Chair at ETH
Franel was a number theorist who gave introductory calculus lectures in French
at the ETH. Maybe the ETH offered courses in different languages, because of its location in a multilingual country. Does …
18
votes
Mathematicians failing to solve problems despite having all methods required
Gödel 's failure to discover unsolvability of the decision problems for predicate logic and Peano arithmetic may be an example. Gödel had all necessary tools: arithmetization, diagonalization, and a …
8
votes
Accepted
History of the Lagrange Inversion Theorem
If you count any inversion of a power series as a predecessor of Lagrange
inversion, then I believe the earliest examples are Newton's inversion of the
log series to obtain the exponential series, and …
12
votes
1
answer
722
views
In search of an early picture of Max Dehn
I am trying to find a copy of a picture "Mathematische Gesellschaft:
Group Portrait, Faculty, University of Göttingen (1899)."
This picture was published by Springer-Verlag as a poster in 1985,
but …
8
votes
Which came first: the Fibonacci Numbers or the Golden Ratio?
As previous answers have pointed out, both the golden ratio and the Fibonacci numbers go back thousands of years. However, I believe the connection
between the two was discovered around 1730. At that …
5
votes
Accepted
Where can I find a translation of Caspar Wessel's "Om directionens analytiske betegning?"
There is an English translation of the first 10 sections of Wessel's paper in the anthology edited by Henrietta Midonick, The Treasury of Mathematics, volume 2 (Penguin Books 1968)
pp.321--329.
4
votes
Accepted
First Parameterized Subset of Primes that was Related to a Mathematical Result
An earlier example than the Fermat primes is the class of primes
of the form $2^n-1$, the so-called Mersenne primes. These occur in
Euclid's theorem that $2^{n-1}(2^n-1)$ is perfect when $2^n-1$ is
pr …
11
votes
A question regarding a claim of V. I. Arnold
I imagine that Newton et al would have no trouble solving this teaser because they would say: let x be infinitesimal, in which case both numerator and denominator equal x-x; quotient equals 1 :)
18
votes
What are some mathematical concepts that were (pretty much) created from scratch and do not ...
The solution of the cubic equation by Scipione del Ferro and Tartaglia
in the early 16th century. This was not only a great advance in algebra,
but it also forced mathematicians to confront complex nu …
8
votes
Earliest diagonal proof of the uncountability of the reals.
Cantor's diagonal argument first appears in his 1891 paper
"Über eine elementare Frage der Mannigfaltigkeitslehre", Jahresbericht der Deutschen
Mathematiker-Vereinigung 1: 75–78, in which he generali …
45
votes
Major mathematical advances past age fifty
P. S. Novikov was 54 when he gave the first proof (143 pages!) of the unsolvability of the word problem for groups in 1955, and 58 when he co-solved the Burnside problem with S. I. Adian.
57
votes
Major mathematical advances past age fifty
Since no one has mentioned A.N. Kolmogorov (born 1903), I hope I may be
forgiven for a second answer. The following is from Kolmogorov's
Wikipedia biography.
In classical mechanics, he is best known …
11
votes
Dehn's solution to Hilbert's 3rd: 1901 or 1902?
Another point to consider is whether "Über den Rauminhalt"
is in fact Dehn's first solution to Hilbert's 3rd Problem. I
believe his first solution was in the paper "Über raumgleiche
Polyeder" in the N …