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Results tagged with ho.history-overview
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user 25510
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
10
votes
Recent breakthroughs with applied origins
If you include mathematical physics (string theory, QFT) to "applied mathematics", the breakthroughs are too numerous to list them here. Statistical mechanics is especially productive in its influence …
53
votes
Has the mathematics research community ever been led astray by a dumb mistake?
In 1970, Irwing Noel Baker "proved" that a transcendental entire function of one complex variable can have at most one completely invariant component of the set of normality. In fact he "proved" a mor …
26
votes
Has the mathematics research community ever been led astray by a dumb mistake?
Hilbert problem 16, second part asks for an upper estimate of
the number of limit cycles of a polynomial system of
differential equations in dimension 2. For long time
it was believed that Henri Dulac …
-3
votes
Etymology of “real numbers"
An excellent explanation is given in the short paper of
N. J. Wildberger, Real fish, real numbers, real jobs, The Mathematical Intelligencer 21 (1999) pp 4–7. https://doi.org/10.1007/BF03024838 (Rese …
- 91.8k
3
votes
History of Gauss theorems that say "it clearly follows that" but it did not clearly follow
This could be related to the "Gauss problem" on the limit distribution of remainders of partial fractions. Gauss found this distribution, and in a letter to Laplace, claimed that he proved it. The fir …
- 91.8k
20
votes
(Obscure) areas of mathematics that are largely inactive or forgotten today?
The most difficult condition to satisfy is 1, since Google book "knows" most of books. All other conditions are easy to satisfy, and many examples can be given, but I will give only one.
Princeton Com …
- 91.8k
9
votes
What is an important mathematical question?
It is indeed somewhat subjective. A discussion of this, with examples, is contained in Hardy's book Mathematician's Apology. But mathematicians frequently disagree on many questions whether they are i …
15
votes
What is the origin/history of the following very short definition of the Lebesgue integral?
This approach was used in the German Analysis (Calculus) textbook
MR0222221
Hans Grauert and Ingo Lieb,
Differential- und Integralrechnung. Band I: Funktionen einer reellen Veränderlichen,
Heidelberge …
- 91.8k
15
votes
Papers of the masters translated to English in one location
Most of the famous 19th century mathematicians have their collected works published and some of them have been digitized. But they are all in the original language. Translations into English are rare. …
29
votes
Algebraic geometry over the complex numbers, and beyond
Algebraic geometry began over the field of reals. What Apollonius of Perga did would be certainly qualified today as algebraic geometry: he classified real plane curves of second order and studied the …
- 91.8k
62
votes
Accepted
Is spherical trigonometry a dead research area?
It is not. As a proof, I will mention three relatively recent papers where I am a co-author:
M. Bonk and A. Eremenko, Covering properties of meromorphic functions, negative curvature and spherical geo …
- 91.8k
4
votes
Can the theory of elliptic functions developed from purely geometric considerations?
Some elementary parts of the theory of elliptic functions can indeed be developed in this way. To those books listed by Alexey Ustinov I can add a large treatise by G. Halphen, Traité des fonctions el …
- 91.8k
1
vote
Nicely motivated papers or book chapters on the formula for the sum of the $k$-th powers of ...
G. Polya, Mathematical discovery.
- 91.8k
20
votes
Who was H. Vogt?
According to Zentralblatt (which is freely accessible on Internet, since Jan 1, 2021, btw) Henri Gustave Vogt was a mathematician, apparently French, since he wrote in French, published in French jour …
14
votes
Nontrivially fillable gaps in published proofs of major theorems
Since some answers include the results published before 1950, let me include the famous story of Hilbert's Problem on finiteness of the number of limit cycles of a polynomial vector field in the plane …