/sci/ - Science & Math » Thread #11564041

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Anonymous Tue 14 Apr 15:31:51 2020 No.11564041 View Reply Original Report

Quoted By: >>11564053 >>11564054 >>11564055 >>11564063 >>11565766 >>11565782 >>11566046 >>11566079

Why don’t mathematicians assume Riemann hypothesis or ABC conjecture or P=NP to be true (or false) and see what happens when you go down that reasoning. And if you hit another road block, you simply assume true or false again. Wouldn’t this be a much faster way of discovering more (possible) mathematics?

Anonymous

Anonymous Tue 14 Apr 2020 15:37:27 No.11564053 Report

Quoted By: >>11566046

>>11564041
>guys what if we did a massive proof by contradiction :DDDD
you lose decades of research if every result ends up being on a negative claim. Either way, this is both an unsettling and inefficient way to progress - why not tackle problems around and adjacent to this one in order to find a solution? You’ll get papers that actually prove something we know to be true, you develop tools to tackle later problems, and you diversify interests. This is exactly what happened with fernat’s last theorem and ring theory

Anonymous

Anonymous Tue 14 Apr 2020 15:37:30 No.11564054 Report

Quoted By:

>>11564041
What makes you think they don't already do this?

Anonymous

Anonymous Tue 14 Apr 2020 15:37:30 No.11564055 Report

Quoted By:

>>11564041
They do. Half the results of analytical number theory assume the Riemann hypothesis is true.

Anonymous

Anonymous Tue 14 Apr 2020 15:42:24 No.11564063 Report

Quoted By: >>11566075

>>11564041
You can find lots of papers that prove things implied by RH. From P != NP doesn't really follow much, since an algorithm for an NP-hard problem might still be much faster than an algorithm for some P problem, in practice. For P=NP, the only interesting thing would be an actual proof, because it would tell us what to do to solve problems in NP. We cannot just assume that doing something at random will work, we have to know an exact algorithm. Finally for ABC, there are also lots of papers that prove some of its implications.

Anonymous

Anonymous Wed 15 Apr 2020 00:04:12 No.11565562 Report

Quoted By: >>11566046

Because even if they do, it's still pretty difficult to prove it for certain

Anonymous

Anonymous Wed 15 Apr 2020 00:14:29 No.11565583 Report

Quoted By:

What you propose is essentially a proof by contradiction; that's how a ton of theorems are proved. Also there's a heap of papers in number theory exploring the consequences of RH or abc being true as some said

Anonymous

Anonymous Wed 15 Apr 2020 01:10:42 No.11565702 Report

Quoted By:

Consider Quantum loop gravity. It's easier in a bosonic setting. At least, I assume so.

Anonymous

Anonymous Wed 15 Apr 2020 01:32:06 No.11565766 Report

Quoted By:

>>11564041
Yes. You can't lightly make such choices, but being hampered by certainty is ludicrous. The very foundations of math--that it can in anyway directly tie with certainty to empirical reality--is not certain. But, and because of that, math is a logic puzzle for its own sake and takes it's internal logic as the sole rule seriously. Once you start thinking like you, you have left the computer brains behind. Take the risk and see where you go, because unlike them, you will go.

Anonymous

Anonymous Wed 15 Apr 2020 01:38:35 No.11565782 Report

Quoted By:

>>11564041
They do all the time

Anonymous

Anonymous Wed 15 Apr 2020 03:41:42 No.11566046 Report

Quoted By:

>>11564041
>>11564053
>>11565562
So i guess this is circumclampination.

Anonymous

Anonymous Wed 15 Apr 2020 03:49:04 No.11566075 Report

Quoted By:

>>11564063
>the only interesting thing would be an actual proof, because it would tell us what to do to solve problems in NP
It could easily be proven true without providing a method for constructing such algorithms.

Anonymous

Anonymous Wed 15 Apr 2020 03:50:08 No.11566079 Report

Quoted By:

>>11564041
Why don't we just reject everything. Nothing exists, mathematics doesn't exist, and see what happens.

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