Beal's conjecture prize

[MattcAnderson]

Hi again everybody,

Matt here with some exciting (old) news.

The prize is US$1 million per problem.

There were 7 unsolved (very) hard mathematics problems
set out by the Clay Mathematics Institute around the year 2,000.

One of them was (sort of) recently solved.
Now, let's look at the Beal conjecture. It is a generalization of
Fermat's last theorem.

The Beal Conjecture is something like
a^x + b^y = c^z
where all variables are both positive and integers.

Wow!
What a problem.

see wikipedia.org
https://en.wikipedia.org/wiki/Millennium_Prize_Problems
and
https://en.wikipedia.org/wiki/Beal_conjecture

This is the sort of problem that definitely takes collaboration. One person cannot (yet) do it alone.
IMHO (In My Humble Opinion)

Have a nice day.

Matthew

[xilman]

Someone who wishes to remain anonymous has brought this to my attention, hence my careful parenthesization ot this post's title.

Attribution to Beal is in dispute. Both Zagier and Tijdeman mentioned the problem prior to
Beal. At an 1985 conference at Humboldt State Univ. John Tate gave a superb
talk on the recently discovered connection between FLT and the Taniyama Shimura conjecture.
(proved by Wiles). At the end of the talk a member of the audience (name unknown)
casually asked whether it could be applied to the case of unequal exponents.

Beal publicized the problem and offered money. It should be called the Beal Prize for
the Tijdeman-Zagier conjecture.

[storm5510]

Originally Posted by MattcAnderson

The Beal Conjecture is something like
a^x + b^y = c^z
where all variables are both positive and integers.

This very much resembles something I saw in a trade school class: a² + b² = c². Pythagorean Theorem, to be exact. The resolution was c = Sqrt(a² + b²), if memory serves. The length of the hypotenuse of a right triangle. It was a long time ago.

Originally Posted by xilman

Someone who wishes to remain anonymous has brought this to my attention, hence my careful parenthesization ot this post's title.

"Beal publicized the problem and offered money. It should be called the Beal Prize for the Tijdeman-Zagier conjecture."

If history is any guide...Farey...Haros (who the hell is Haros?)..Euler..Pell (what was it that Pell did again?)..equitable attribution in mathematics..there's more than enough precedent to lay waste to any claims of "fair and appropriate" attribution. Might as well name a planet Pluto and expect that to stick..

[xilman]

Originally Posted by MattcAnderson

There were 7 unsolved (very) hard mathematics problems
set out by the Clay Mathematics Institute around the year 2,000.

One of them was (sort of) recently solved.

Why, in your professional opinion, do you think the Poincaré conjecture is only "sort of" solved?

[storm5510]

Originally Posted by MattcAnderson

...This is the sort of problem that definitely takes collaboration. One person cannot (yet) do it alone.
IMHO (In My Humble Opinion)

Have a nice day.

Matthew

Someone here, with the ability, should write a program to do this, unless something already exists. There would need to be an ordered progression and not random numbers. The language platform would need to handle very large numbers. The only one I am familiar with can handle 64-bit unsigned integer types, 0 to 18,446,744,073,709,551,615, (FFFF FFFF FFFF FFFF). This might be large enough, then again, it may not.

[mathwiz]

Originally Posted by storm5510

Someone here, with the ability, should write a program to do this, unless something already exists.

Let me Google that for you.

[rogue]

Just don't bring up Don Blazys's proof. He was a crackpot who could not accept that his proof had flaws. You can search the forum for our debates with him on his proof. He tried passing off his proof in many places and just assumed it was correct if nobody disagreed. It doesn't mean that anyone agreed...

[storm5510]

This is most definitely over my head. Not a language I recognize.

[kriesel]

Originally Posted by storm5510

This is most definitely over my head. Not a language I recognize.

The linked article includes:

I ported it from Python 1.5 to 3.5

[chalsall]

Originally Posted by storm5510

This is most definitely over my head. Not a language I recognize.

Yeah...

In at least one case it has been well documented that if you're going to do an exhaustive search, it is best to use C. If not hand-crafted assembly, tuned to each processor...