Unsolved Problems Without Differential Equations

[Dragonfall]

Can somebody give me a little-known unsolved problem that can be stated without differential equations?

 

[Civilized]

There are a variety of unsolved problems in graph theory which may be susceptible to elementary methods. A quick google search turned up this page:

http://math.fau.edu/locke/Unsolved.htm

 

[AUMathTutor]

Does P = NP.

How many angels can dance on the head of a pin.

How much wood would a woodchuck chuck if a woodchuck could chuck wood.

How many grammatically correct English sentences are there containing at most n commas.

Etc.

 

[Civilized]

AUMathTutor, most of those unsolved problems are well-known (the OP asked for ones which are little known), and furthermore I believe that the last three are ill-posed (since english has no formal grammar and angels and woodchucks are afaik undefined).

 

[HallsofIvy]

Woodchucks will be surprized to learn that!
(You may know them better as groundhogs.)

 

[CRGreathouse]

Halls, do you have an axiomatization of woodchucks handy?

 

[AUMathTutor]

Actually, the P=NP problem is quite poorly known, if you look at how many people in the world have ever heard of it and divide by the number of people in the world.

Far more poorly known if you look at how many people understand what the question is actually asking.

Perhaps "well known" is a poorly-defined term.

 

[AUMathTutor]

And I think the English sentence one is actually not so ill-posed. You might have to make certain stipulations, but you do that all the time in any mathematical problem.

 

[molinaro]

How much wood would a woodchuck chuck if a woodchuck could chuck wood.

I first heard the answer to that question over 30 years ago:

A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood.

 

[Aten]

Well...

- Does an odd perfect number(s) exist?
- Prove the abc conjecture.
- Explain the role of modulus in Parrondo paradox.
- What is the probability that an infinitely small object would become finitely big?(well "big bang" theory :)...no comment..
- Prove the Riemann hypothesis.

I can give you many more - but those are OK for now :). The problem about the probability is more than obvious(0 probability for such thing to happen regardless of the fairytales about "singularity"!...) - it's interesting how it objects the big bang funny hypothesis of singularity. I believe in the bang - just don't believe in the idiotic religious assumptions about creation. Religion and dogmatic science(why not every science should be forbidden by law...including present day big bang assumptions.

Anyway... :)

The problems above can be formulated without a single differential equation and believe it or not - many people haven't heard of the Riemann hypothesis - including many math teachers in economically developed countries.

 

[Petek]

See here for a list of unsolved math problems, some of which can be described as little-known.

 

[gel]

The Gaussian correlation conjecture.

If X is a joint-normal random variable in Rⁿ, A,B are convex and symmetric (so A=-A, B=-B) sets in Rⁿ, then

<br /> P(X\in A\cap B) \ge P(X\in A)P(X\in B).<br />

 

[Dragonfall]

P vs NP and Riemann are both well known to anyone with a bit of math experience. I'm asking for something more esoteric. No god damn angels.

 

[Dragonfall]

There are a variety of unsolved problems in graph theory which may be susceptible to elementary methods. A quick google search turned up this page:

http://math.fau.edu/locke/Unsolved.htm

Thanks for an actual reply. No angels dancing on pins here.

 

[CRGreathouse]

Guy's Unsolved Problems in Number Theory has more if you're interested. I think he has at least one analog for (an)other field(s).

 

[Dragonfall]

Yes! I had forgotten about that book. Thanks.