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Results tagged with soft-question
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user 4600
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
19
votes
Accepted
Is Turing degree actually useful in real life?
Application to everyday life
Any time you watch the "spinning beach ball" or "hour glass" on your computer, trying to decide whether it's time to reboot or just wait a little longer, you are doing som …
13
votes
Why would one number theorems, propositions and lemmas separately?
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis …
12
votes
Why do we need random variables?
Let $\Omega_n$ be the set of equivalence relations on $\{0,1,2,\dots,n-1\}$, each eq. rel. being equally likely. Let $X$ be the number of classes, and $Y$ the size of the largest class.
Note that whe …
- 24.8k
10
votes
The use of the word "model" in Mathematical Logic vs the same word in Natural Sciences
It may seem a bit backwards, but one could try to look at it the other way around: pretend the axioms and theorems are the things that we observe. We don't really observe the field $\mathbb R$ of all …
- 24.8k
10
votes
Still Difficult After All These Years
I would like to believe that by 2110 the Langland's program would be reduced to a 10-page pamphlet (with complete proofs) that I could read over breakfast. Is this belief plausible?
In a way, no …
6
votes
Toy Models of Quantum Mechanics
One problem with non-"regular" fields in quantum mechanics is that the Spectral Theorem may fail. For example, if I recall correctly there is a $3\times 3$ symmetric matrix with entries in $\mathbb Z_ …
- 24.8k
5
votes
Graduate program applications that require questionnaires and other non-letter material
University of Minnesota
Not bad -- I was Driven to Discover (SM) that I have to create a password just for using the system that one time. But was able to bypass the survey completely.
5
votes
What was Hilbert's view of Gödel's Incompleteness Theorems?
Here's the Logicomix account of Hilbert's reaction.
Perhaps a reference to Hilbert's Hotel?
- 24.8k
3
votes
Are there nonequivalent randomnesses?
Although as the OP admits it's not clear what the question is here, there is a sense in which no, there do not exist nonequivalent randomnesses (for a fixed probability distribution $\mathbb P$), rath …
- 24.8k
3
votes
You pass X people and Y people pass you: how relatively fast are you?
A much simplified model
Assume there are $k$ runners whose speed is independently uniformly distributed on $[0,1]$, where 1 means one loop per hour. They all start at the same place at the same time …
- 24.8k
2
votes
Recent trends in effective analysis
The references you mention are all monographs (Abert, Pour-El and Richards, Simpson, Weihrauch). Here are some more recent (at most 5 years old) monographs which border on computable analysis:
Kohle …
- 24.8k
2
votes
Is modern computability theory "really" about algorithms?
The main motivation is Church's thesis: a subset of $\mathbb N$ is computable (using an idealized computer, mechanical device or diligent clerk) if and only if computable by a Turing machine.
Being …
- 24.8k
1
vote
Are there any organized websites for seminar/conference videos?
You can subscribe to tags on Vimeo, and in principle arXiv tags like pr.probability could be used
http://vimeopro.com/staff/tutorials/video/741488
0
votes
Examples of "unsuccessful" theories with afterlives
The typical oracle methods of Computability theory AKA Recursion theory were shown to be insufficient to settle the P vs. NP problem by Baker, Gill and Solovay 1975.
Thus recursion theory became divo …