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Results tagged with big-list
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user 6153
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
3
votes
Fundamental theorems
To add to the Gowers examples: the fundamental theorem on finitely-generated abelian groups. It seems at least a mildly interesting linguistic point. German discriminates between Hauptsatz and Fundame …
6
votes
If you went into a coma now and woke in twenty years time what would be your first post on MO?
Can't decide between "update me on the Millennium Problems" and "Is Wikipedia still there?"
5
votes
Mathematics for ebook readers
It is not perhaps generally known that Wikipedia has a book creator, than can export any compilation of articles as PDFs. It is there on the left-hand sidebar:
http://en.wikipedia.org/w/index.php?tit …
6
votes
Consolidation: Aftermathematics of fads
One thing that comes directly to mind is the calculus of variations, in the classical sense, where the point is to get rigorous results by mathematical analysis.
Now, there are probably several typi …
11
votes
Statements reliant on conjectures
The standard conjectures (http://en.wikipedia.org/wiki/Standard_conjectures_on_algebraic_cycles) were pretty much designed to be used in this way (and then proved); but proofs are lacking, and some of …
12
votes
Approaches to Riemann hypothesis using methods outside number theory
I think, tautologously, any method proving the Riemann Hypothesis (or even seriously improving our knowledge on the zeroes) becomes "number theory" immediately. That said, I know what the question mea …
- 12.6k
2
votes
Looking for a mathematically rigorous introduction to game theory
I would look for introductions to combinatorial game theory by Elwyn Berlekamp alone. Not that the mathematics is any different from other treatments, but it probably stands clearer of the "recreation …
13
votes
What is your favorite isomorphism?
I nominate the Chinese Remainder Theorem, in the form of an isomorphism of a ring of residues with a cartesian product ring. This isn't "profound" mathematics, but simply unpacking it (with constructi …
24
votes
What elementary problems can you solve with schemes?
The "classical" example is surely duality of abelian varieties. If you want this duality to work over finite fields (or in characteristic p generally), it becomes apparent that you can't work with var …
4
votes
What would be good to know before starting my undergraduate studies to become a good mathema...
The answers surely depend on what kind of mathematics course, and where (you give no clues at all). But here's one traditional point: make sure you are absolutely solid on the difference between neces …
10
votes
Why are modular forms interesting?
Bryan Birch's view is that they form a bottomless area for research problems. All answers to the question fall into two types: showing examples of why this is true, and asking why it should be true. G …
17
votes
When have we lost a body of mathematics because errors were found?
I feel the answer is obviously "yes", and indeed that much of 19th century mathematics was lost, in a serious sense, for much of the 20th century. I was struck recently by discovering that Henry Fox T …
4
votes
The resolution of which conjecture/problem would advance Mathematics the most?
I conjecture the question to be premature ...
I would nominate the Riemann Hypothesis, since it is clear that something occurs that we fundamentally don't understand. But folding other things in with …
4
votes
Can a mathematical definition be wrong?
If a definition can be tentative, it can also be wrong. Lakatos has been mentioned already. This is actually a fairly basic issue in understanding how "formal" mathematics advances. Something as funda …