Tracking the World's Great Unsolved Math Mysteries

coondoggie writes "Some math problems are as old as the wind, experts say, and many remain truly unsolved. But a new open source-based site from the American Institute of Mathematics looks to help track work done and solve long-standing and difficult math problems. The Institute, along with the National Science Foundation, has opened the AIM Problem Lists site to offer an organized and annotated collection of unsolved problems, and previously unsolved problems, in a specialized area of mathematics research. The problem list provides a snapshot of the current state of research in a particular research area, letting experts track new developments, and newcomers gain a perspective on the subject."

Comments

Check out the Collatz Conjecture...

[Oxford_Comma_Lover]

http://en.wikipedia.org/wiki/Collatz_conjecture Speaking of unsolved math mysteries, the 3n+1 problem is a fabulous way to spend days and days of your life. It's particularly fun if you think about it in binary. Whatever the answer is, it's either simple and elegant or complex beyond imagination.

I have this proof.

[140Mandak262Jamuna]

I have this wonderful proof for this conjecture, but unfortunately the 80 char limit for sig in slashdot is too small for it.

Sadly...

[cosm]

their servers will explode when they take a stab at Navier-Stokes. I asked Wolfram-Alpha, but it simply returned the exact solution of a degenerate case, the solution being 'Fuck you.'

Massively collaborative "Polymath" efforts

[Anonymous Coward]

As of about a year ago, a new kind of collaborative math project known as "polymath" is emerging. These research projects are completely open for any interested scholar to drop in and make contributions to the problem at hand. The technical infrastructure is based on well-known tools such as wikis and forum discussions

The very first such project successfully explored a new approach to the density Hales-Jewett thorem--a significant problem in combinatorics--in about six weeks of effort, with a fully preserved record of about a thousand contributions from dozens of participants.

See Polymath Wiki for the details. This new contribution from the AIM will provide a focus point for such efforts and encourage similar massively collaborative projects.

And of course, the emerging field of computer-verified mathematics is also dependent on massive collaboration, in order to translate existing results into a fully-formalized form that computes will understand and verify as correct. A wiki-based project could be a great help there as well.

Re:Math cannot exist before wind.

[jd]

I would claim that the ratio of a circle to its diameter is independent of being observed, or indeed there being an observer. I would also claim that the laws of geometry, probability and topology are universal and also do not depend on the existence of observers, let alone their ability to perform maths.

Radioactive decay follows an exponential decay curve. It will have done so long before anyone could add, let alone handle irrational numbers like e.

This puts me firmly in the category of maths being discovered, not invented. Mathematical tools, however, are invented and not discovered. I consider these to be quite different. If you were to imagine an alien lifeform on some distant world, they'll have an identical math but their experience of it, the way they treat it, the systems they use, those will all be unique to them because those are inventions and not anything fundamental to maths itself.

In a simpler example of the same concept, we can use ancient Greek maths today even though they didn't have a concept of zero and had (to modern eyes) very alien views on the way maths worked. We can use ancient Greek maths because the results don't depend on any of that.

We can use Roman results, too, despite the fact that their numbering system doesn't really follow a number base in any way we'd understand. It doesn't matter, though, because the important stuff all takes place below such superficial details. Even more remarkable, we can read many of the numbers written in Linear A, even though we can't read the language itself and know very little about the culture or people.

None of this would be possible if what lay under maths was invented. It's very hard to rediscover lost inventions, as there's many ways of producing similar results. But when you can rediscover lost number systems with comparative ease - well, doesn't that tell you there has to be something a bit more universal to it?

(I won't get into parrots being able to discover the notion of zero, but it's again pertinent as it's an example of a universality that transcends the invented language it's described in.)