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/sci/ - Science & Math

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9283242 No.9283242 [Reply] [Original]

How do I create a new theorem in mathematics?

>> No.9283254

>>9283242
Easy mode: Study a new object and start finding its properties

Regular mode: Find some already established object and then find a variation or generalization of the same object and see how many of the theorems that are valid for the original object also apply to your variation/generalization. (Think of the real numbers and metric spaces)

Hard mode: Study a well known and famous object and try to see if you can prove something new about it.

>> No.9283281

Literally just invent a problem and solve it.

>> No.9283289

>>9283281
This, but remember that it is not cool to be known as "that guy who solves his own problems". If you are a student and you need something for your first paper or maybe even your thesis then it's fine. You are newbie. It is not like anyone expects to solve bigger problems. Just pose your own problem and solve it yourself. This is pretty common, actually.

But after you are a doctor and have a couple of years in the biz you should start to look into diversifying and see if you can do research on problems other people have proposed. And it is fine if from time to time you come up with your own problem and publish something about it, but just don't be known as "that guy".

>> No.9283712

>>9283254
This. Also, connect techniques many would commonly shy away from and make a connection to each. Once this is done, prove your observation.

>> No.9283713

It has to be something no-one else has already done so good luck.

>> No.9283735

is there a way to connect all these algebras together:

https://en.wikipedia.org/wiki/Category:Algebras

>> No.9283864

>>9283242
Add up all the old theorems and divide reality by it. Whatever's left over can be your new theorem.

>> No.9284745

>>9283242

Take two established, but scantly related theorems. Take conjunction of their hypotheses and conclusions. Publish on viXra.