- #1
Dragonfall
- 1,030
- 4
Can somebody give me a little-known unsolved problem that can be stated without differential equations?
Unsolved Problems Without Differential Equations
- Thread starter Dragonfall
- Start date
In summary, some little-known unsolved problems that can be stated without differential equations include problems in graph theory, the Gaussian correlation conjecture, and Guy's Unsolved Problems in Number Theory. These problems are not as well-known as others such as P vs NP and the Riemann hypothesis, but they still present interesting challenges and may have potential solutions using elementary methods.
- #2
Civilized
- 152
- 0
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
http://math.fau.edu/locke/Unsolved.htm
- #3
AUMathTutor
- 498
- 0
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.
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.
- #4
Civilized
- 152
- 0
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).
- #5
HallsofIvy
Science Advisor
Homework Helper
- 42,988
- 981
Woodchucks will be surprized to learn that!
(You may know them better as groundhogs.)
(You may know them better as groundhogs.)
- #6
CRGreathouse
Science Advisor
Homework Helper
- 2,845
- 0
Halls, do you have an axiomatization of woodchucks handy? 
- #7
AUMathTutor
- 498
- 0
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.
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.
- #8
AUMathTutor
- 498
- 0
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.
- #9
molinaro
- 19
- 0
AUMathTutor said:
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.
- #10
Aten
- 4
- 0
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.
- 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.
- #11
Petek
Gold Member
- 404
- 33
See here for a list of unsolved math problems, some of which can be described as little-known.
- #12
gel
- 533
- 5
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
[tex]
P(X\in A\cap B) \ge P(X\in A)P(X\in B).
[/tex]
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
[tex]
P(X\in A\cap B) \ge P(X\in A)P(X\in B).
[/tex]
- #13
Dragonfall
- 1,030
- 4
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.
Last edited:
- #14
Dragonfall
- 1,030
- 4
Civilized said:
Thanks for an actual reply. No angels dancing on pins here.
- #15
CRGreathouse
Science Advisor
Homework Helper
- 2,845
- 0
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).
- #16
Dragonfall
- 1,030
- 4
Yes! I had forgotten about that book. Thanks.
FAQ: Unsolved Problems Without Differential Equations
What is an unsolved problem without differential equations?
An unsolved problem without differential equations refers to a scientific or mathematical question that has not yet been solved using differential equations as a tool or method. These problems may involve complex systems, phenomena, or processes that cannot be accurately described or predicted using differential equations.
Why are some problems not solvable using differential equations?
Differential equations are a powerful tool for modeling and predicting many natural phenomena, but they are not suitable for all types of problems. Some problems may involve nonlinearities, chaotic behavior, or other complexities that cannot be accurately captured by differential equations. In these cases, alternative approaches must be used to solve the problem.
Can unsolved problems without differential equations ever be solved?
Yes, it is possible for unsolved problems without differential equations to be solved using other methods or tools. Scientists and mathematicians are constantly developing new techniques and approaches to tackle complex problems, and it is always possible that a breakthrough may lead to a solution for an unsolved problem.
Are there any famous unsolved problems without differential equations?
Yes, there are many famous unsolved problems that do not involve the use of differential equations. Some examples include the Navier-Stokes equations, the Riemann Hypothesis, and the P versus NP problem. These problems have puzzled scientists and mathematicians for decades and continue to be areas of active research.
What other methods can be used to solve unsolved problems without differential equations?
There are a variety of other mathematical and scientific methods that can be used to solve unsolved problems without differential equations. These include numerical simulations, statistical analysis, optimization techniques, and machine learning algorithms. Each problem may require a unique approach, and scientists often combine multiple methods to find a solution.