5 Simple Math Problems No One Can Solve • Hacker News Board

Re: 5 Simple Math Problems No One Can Solve

#21

Post by iamcreasy » Sun, Oct 16, 2016, 11:17 PM UTC

cyphar wrote: post #17

iamcreasy wrote: post #4

How about the prime number problem. It's simple enough to understand. "A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers."

Finding primes is a P problem though, so I'd consider it a "solved problem". There's no equation that generates nothing but primes, is that what you meant?

Yes, kind of.

Re: 5 Simple Math Problems No One Can Solve

#22

Post by botw » Mon, Oct 17, 2016, 12:24 AM UTC

yayks wrote: post #14

The goal is to find a box where A² + B² + C² = G², and where all four numbers are integers: 3² + 4² + 12² = 13², except it is not the only goal.

"Mathematicians have tried many different possibilities and have yet to find a single one that works. But they also haven't been able to prove that such a box doesn't exist, so the hunt is on for a perfect cuboid." apparently, something wrong here.

Re: 5 Simple Math Problems No One Can Solve

#23

Post by SAI_Peregrinus » Mon, Oct 17, 2016, 1:12 AM UTC

tf2manu994 wrote: post #9

williamstein wrote: post #8

Earlier quoted context omitted.

What is a "simple formula"? I have no idea what "simple formula" means. In math reseacrch everything must be 100% precise and well defined.

I think they mean something a great deal faster than just dividing by each number to check.

AKS is a primality check in polynomial time, IE much faster than trial division. It's not "simple" for certain values of simple, but it's only 5 major steps.

Re: 5 Simple Math Problems No One Can Solve

#24

Post by StefanKarpinski » Mon, Oct 17, 2016, 1:42 AM UTC

ralusek wrote: post #10

I don't really know how to prove something, but for the first problem, it seems like any odd number multiplied by any other odd number (in the example, they choose 3) will always be odd. This can/has been proven. Then, any odd number, negative or positive, with 1 added or subtracted to it, becomes even. Finally, any even number divided by two is still even and approaches two. "Mathematicians have tried millions of nu…

If you're still within the edit timer, you should really replace this comment with "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." Maybe they'll rename the conjecture after you.

Re: 5 Simple Math Problems No One Can Solve

#25

Post by YomiK » Mon, Oct 17, 2016, 4:21 PM UTC

iamcreasy wrote: post #4

How about the prime number problem. It's simple enough to understand. "A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers."

There are many such formulas, such as Willan's 1964 simple formula for the nth prime. But they are basically all hiding a sieve, Wilson's theorem, the prime count function, or some other calculation. That is, none of them are at all practical, and most offer no insight.

I'd recommend perusing "Formulas for Primes" by Underwood Dudley, 1983. Free online link: http://www.maa.org/programs/faculty-and-departments/classroo...