19
votes
Is GCH useful in proving theorems?
One surprising (at least to me) area where the GCH enters is the following piece of homological algebra. Let $k$ be a field of cardinality $\aleph_n$. Then Barbara Osofsky proved that the projective ...
- 9,561
17
votes
When has the scaffolding been more important than the completed building?
Ramsey Theory should count. Ramsey needed his theorem for a proof of a special case of the decision problem for first-order logic — which in the general case soon turned out to be unsolvable — but ...
13
votes
When has the scaffolding been more important than the completed building?
"examples where someone proved some (important?) theorem, then (much?) later, someone else rediscovered the insights that led to the proof and built a new theory that eclipsed the original ...
10
votes
How to tackle the smooth Poincaré conjecture
Fastforward $11+\frac12$ years, I thought I'd mention that I tried to do what my original post suggested, which is when I started my PhD and then when I completed my thesis it naturally spawned this ...
- 16.9k
8
votes
When has the scaffolding been more important than the completed building?
I see several different ways of interpreting the question.
The comic seems to be talking about mistakes (false starts, blind alleys, etc.) made along the way to a mathematical discovery. I think that ...
6
votes
Is GCH useful in proving theorems?
Dixmier traces are
easily constructed in ZFC and there is an extensive literature on the
topic. Connes pointed out that such a trace with particularly good
properties can be constructed in the ...
- 14.8k
2
votes
Video lectures of mathematics courses available online for free
A series of lectures on symmetric functions, Macdonald polynomials and double affine Hecke algebras (videos and notes) organised in 2021 by R Venkatesh of the Indian Institute of Science; see also its ...
2
votes
Video lectures of mathematics courses available online for free
I have recorded lecture series on
Random Matrices
Mathematical Aspects of Quantum Mechanics
High Dimensional Analysis: Random Matrices and Machine Learning
2
votes
Accepted
"On models of elementary elliptic geometry"
In the mentioned article, Schwabhäuser proves that all models of elementary elliptic geometry are isomorphic to elliptic Klein spaces over real closed fields. Actually, the paper only deals with the ...
- 1,364
1
vote
When has the scaffolding been more important than the completed building?
A classical example is the Riemann-Siegel formula, even though it hardly can be assumed to be more important than the building itself.
1
vote
History of limit point compact -/-> compact example
The earliest reference I can find is Dugundji's book Topology, published in 1966, where this result appears as Ex. 2 on page 239.
Here's how I found that. First, this result appears in Kelley's book ...
- 25.5k
1
vote
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
De Bruijn sequences are so named because Nicolaas Govert de Bruijn enumerated them in 1946, but he later acknowledged the priority of C. Flye Sainte-Marie, who enumerated them already in 1894.
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