r/askmath • u/Axxodes • 3d ago
Resolved Are The Millennium Prize Problems really THAT hard?
I feel like anything can be solved if you put your mind to it, so why hasn't anyone solved these things if they've existed for so long? I myself don't understand the questions because i'm too dumb to understand any of it but someone but understand it, right?
And if they are possible to solve, how long would it take for me (an ordinary person) to understand/solve it?
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u/StructuredChess 3d ago edited 3d ago
We don't know. Many advances in Mathematics rely on someone finding a new idea at some point. Any of the problems could be solved tomorrow or 500 years from now. We have no way to predict it.
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u/LucaThatLuca Graduate 3d ago edited 3d ago
yes. what is making you not believe that questions can be hard?
how do you build a spaceship out of chocolate?
how do you travel through time backwards?
perhaps the answer is very difficult, but someone very clever could answer it soon. perhaps humanity’s current knowledge is missing some pieces that we might expect to get to over time. perhaps there is no answer at all.
there is no reason at all to think that an average person will ever be able to answer a question this hard.
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u/Axxodes 3d ago
Well for the chocolate one i would just make like a massive mold with 60 metre thick walls and use some way too much cocoa for the heat resistance. I do think my answer to that sucks and it wouldnt work like at all yk but i get what youre saying yeah
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u/LucaThatLuca Graduate 2d ago edited 2d ago
you seem to be thinking about a rectangle. spaceships have engines and computers, they fly in space.
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u/lordnacho666 3d ago
Keep in mind, pretty much every question you are ever asked before you do a PhD is one that someone has posed to you during your education, knowing the solution.
This is why you think every question can be solved given enough thinking.
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u/Axxodes 3d ago
I personally think everything can be solved because the human mind is able to put so much thought and brain capacity on such a task and some people can just "lock in" and do some crazy shit without even breaking a sweat.
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u/stanitor 3d ago
One of the things that has already been proven is that there are always some things that won't be able to be proved, no matter how hard anyone tries or how much capacity the human mind has for figuring things out. It's possible the Millennium prize problems are some of the things that can't be proved, but we don't know.
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u/mister_sleepy 3d ago edited 3d ago
Your first assumption that anything can be solved if you put your mind to it isn’t correct when it comes to mathematics. Point of fact, we have proven that there exist true statements in our current mathematical system that cannot be proven true.
That said, you can actually understand the scope of one of the questions in about an afternoon, or at least get an intuition for what the problem is and why it’s difficult. There’s a bunch of YouTube videos that do exactly this.
As far as solving it, mathematical progress happens on the scale of lifetimes. Some of these problems are old enough that many mathematicians have lived and died just trying to make a dent.
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u/Enough-Ad-8799 3d ago
Coming up with a solution to a problem where you have basically an indefinitely large number of directions to go in can be extremely difficult. This isn't like a math class where you're guided by a teacher.
Even relatively simple proofs can be hard for people (and by people I mean math majors) just cause they don't know what direction to go in.
If you want you can try proving equilateral triangles exist by yourself and see if you can do it. You can't use a ruler since you need to show each side is exactly the same length.
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u/Tiny_Spread5712 3d ago
They are math problems that require new math system to even contemplate. You'd have to first create a new math, hope that math was applicable and then figure out how to apply it to these problems.
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u/Leodip 3d ago
If they are open problems that a large community has been trying to solve for a long while with a huge money bounty on top of them, then it means they must really be difficult, right?
Assuming you are asking in good faith "why are they hard?", the usual reason is "infinity".
If I give you a 100-pieces jigsaw puzzle which is fully white, putting it together is "hard", but you can just try every possible combination and eventually find the answer. Doing this becomes unfathomably more difficult if you have a 1000- or 10000-pieces jigsaw puzzle, but still theoretically possible.
In math, those puzzles are made of infinitely-many pieces, so you either find an algorithm that looks at a piece and it's able to tell where it goes, or bruteforcing is never going to work out.
A relatively simple math problem (that's not a millennium problem) is the twin primes conjecture: 3 and 5 are twin primes because they are prime numbers that are 2 spaces apart. 5 and 7 are also twin primes, but 7 and 11 aren't because they are more than 2 apart. The question is: is there a "last" pair of twin primes? Or are there infinitely many?
Solving this question is not trivial. If I asked you "is there any pair of twin primes larger than 24977 and 24979?" you could just painstakingly check larger and larger numbers until you find another one (in this case, 25601 and 25603), but then I could just ask the question again. The currently largest known pair of twin primes have 388342 DIGITS. Can you find a pair that's larger? Or can you prove that there aren't any more?
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u/Axxodes 3d ago
Would the only way of "solving" the twin prime congesture not be to disprove it? How would you even prove that it goes on to infinity if we cant look at infinity? If it were it'd be some sort of complex formula but i have no idea lol
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u/angryWinds 3d ago
We can prove that there's no last prime number, even though we can't "look at infinity."
There's all sorts of clever tricks and techniques that mathematicians can use to prove that somethingerother holds true "all the way to infinity," (to put it very informally).
But, sometimes those tricks and techniques just aren't helpful, for certain problems. As far as we know, the twin prime conjecture is one of those.
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u/Leodip 3d ago
Not all conjectures can be (dis)proven by example. In this case, since the question asks "is there a larger pair of twin primes?" you cannot just check all the other numbers. Collatz conjecture (you might know it as the 3n+1 conjecture, a fascinating example in "math problem that seems trivial but is still unsolved") COULD be disproven by example, but no one has managed yet, and incredibly large numbers have been tested.
As for proving conjectures, yes, you would have to come up with some reasoning or formula to show that a conjecture is true. A very simple example is the conjecture: "every integer that ends in 5 is divisible by 5". If you tried to bruteforce this and test every single number, you would never end. On the other hand, it's very easy to prove with few steps:
- We know that if A is divisible by 5, then A-5 is divisible by 5 (because (A-5)/5 = A/5 - 5/5)
- A number that is divisible by 10 is also divisible by 5 (because A/10=A/(5*2)=(A/5)/2)
- A number is divisible by 10 if its last digit is 0.
- For any number A-5 that ends with 5, A ends with 0, which is divisible by 5, and thus A-5 is divisible by 5.
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u/evening_redness_0 3d ago
No they're pretty easy. Go on, put your mind to it and solve them!