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Results tagged with big-list
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user 9896
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.
-1
votes
What are some correct results discovered with incorrect (or no) proofs?
Results in complexity theory such as $P \neq NP$.
Philosophically, it makes sense that there is a difference between verification and search, and no-one has discovered a counterexample.
(Note, tha …
2
votes
Random versions of deterministic problems
While it is not known that $P \neq NP$, it is known that for most oracles $A \subseteq \omega$ we have $P^A \neq NP^A$. This might be interpreted as "evidence" for the conjecture when $A = \emptyset$. …
4
votes
Blackbox Theorems
The Lovasz Local Lemma gives a very simple criterion for when certain random events have positive probability. Almost all applications of the Lemma automatically have an algorithm to find such events. …
15
votes
Why are so few operations with arity bigger than 2?
Any $k$-ary relation can be expressed in terms of binary relations by means of projection maps, i.e. introduce new objects which correspond to $n$-tuples of the original objects ($n \leq k$), and intr …
33
votes
18
answers
6k
views
Non-rigorous reasoning in rigorous mathematics
I was wondering what role non-rigorous, heuristic type arguments play in rigorous math. Are there examples of rigorous, formal proofs in which a non-rigorous reasoning still plays a central part?
Her …
9
votes
What notions are used but not clearly defined in modern mathematics?
Infinitesimals are almost in this category.
Technically, calculus generally uses limits instead of infinitesimals. And there are logical systems (e.g. nonstandard analysis) in which genuine infinites …