when matematicians solve some problem that has’nt ever been solved how do they know they got the right answer and they did the right steps ?
In: 0
A lot of the time it isn’t about solving something, but proving something, but anytime a new thing is proposed it is always checked by other mathematicians before going public.
They recheck their work. And other mathematicians check their work to verify that it’s correct.
A lot of the time it isn’t about solving something, but proving something, but anytime a new thing is proposed it is always checked by other mathematicians before going public.
They recheck their work. And other mathematicians check their work to verify that it’s correct.
Other mathematicians check their work.
By “check their work” what I mean is that other mathematicians read through the proof and make sure that each step follows logically from the last. At the frontiers of math, subfields get so specific that there are only a handful of people in the world who can actually peer review the proof. This means the peer review process can take years.
Still, mistakes do occasionally slip through the cracks. This doesn’t really happen with well established results that have been proven in multiple ways, and it doesn’t happen with big results that a lot of people care about, but it can happen.
Edit: I should probably expand on what “each step follows logically from the last” means. Say I’m trying to prove that 1=2 step by step:
1) let x = y be nonzero
2) then x^2 = xy
3) and so x^2 – y^2 = xy – y^2
4) this implies (x+y)(x-y) = y(x-y)
5) divide through by (x-y) to get x+y = y
6) but x=y, so that means 2x = x
7) therefore 2=1
Now, my result is obviously incorrect. That means one of those steps was wrong, or in other words, there’s one step which does not imply the truth of the next step. Which is it?
Other mathematicians check their work.
By “check their work” what I mean is that other mathematicians read through the proof and make sure that each step follows logically from the last. At the frontiers of math, subfields get so specific that there are only a handful of people in the world who can actually peer review the proof. This means the peer review process can take years.
Still, mistakes do occasionally slip through the cracks. This doesn’t really happen with well established results that have been proven in multiple ways, and it doesn’t happen with big results that a lot of people care about, but it can happen.
Edit: I should probably expand on what “each step follows logically from the last” means. Say I’m trying to prove that 1=2 step by step:
1) let x = y be nonzero
2) then x^2 = xy
3) and so x^2 – y^2 = xy – y^2
4) this implies (x+y)(x-y) = y(x-y)
5) divide through by (x-y) to get x+y = y
6) but x=y, so that means 2x = x
7) therefore 2=1
Now, my result is obviously incorrect. That means one of those steps was wrong, or in other words, there’s one step which does not imply the truth of the next step. Which is it?
Usually what we need are proofs.
You state something lets call it a conjecture and if mathematics is consistent that conjecture is either true ore false.
Ok but how do you prove it that is the question. It depends but there are general ways statements can be proven. In theory the easiest way to think about it is that if the statement is in fact true assuming the opposite leads to a contradiction. If you can show that, then you have proven your statement. When mathematicians do this its called an indirect proof. Its not always the best approach but thats the core idea.
But to answer your question exactly, we know we got the right answer because we knew what the answer had to be and we had started from solid proven ground, taken logical steps and got what we were looking for.
Finding the steps that lead you towards the solution is the job. You can make an incorrect step which is a mistake, your step either makes or doesn’t make sense in math thats obvious. You can make a correct but unnecessary step, you didn’t get cloaser to the solution or you did the right step.
They’ll publish their proof in a mathematical journal so that other mathematicians can examine it and look for errors.
Usually what we need are proofs.
You state something lets call it a conjecture and if mathematics is consistent that conjecture is either true ore false.
Ok but how do you prove it that is the question. It depends but there are general ways statements can be proven. In theory the easiest way to think about it is that if the statement is in fact true assuming the opposite leads to a contradiction. If you can show that, then you have proven your statement. When mathematicians do this its called an indirect proof. Its not always the best approach but thats the core idea.
But to answer your question exactly, we know we got the right answer because we knew what the answer had to be and we had started from solid proven ground, taken logical steps and got what we were looking for.
Finding the steps that lead you towards the solution is the job. You can make an incorrect step which is a mistake, your step either makes or doesn’t make sense in math thats obvious. You can make a correct but unnecessary step, you didn’t get cloaser to the solution or you did the right step.
They’ll publish their proof in a mathematical journal so that other mathematicians can examine it and look for errors.
Latest Answers