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Anonymous Thu 24 Dec 20:11:45 2020 No.12503783 View Reply Original Report

Quoted By: >>12505106 >>12505117 >>12505176 >>12505180 >>12505203

How do people typically prove things in math? What is the standard procedure for making a mathematical proof? What is considered an adequate "proof" in math?

Anonymous

Anonymous Fri 25 Dec 2020 00:09:47 No.12504585 Report

Quoted By:

Use the "laws of logic" together with axioms/proven theorems to show that another theorem must be true

Anonymous

Anonymous Fri 25 Dec 2020 03:11:00 No.12505093 Report

Quoted By:

For most undergrad results, rigorous arguments where each step is explained are the norm. The further you go, the less rigorous things can become.
This has been an issue in recent years (Wiles' first proof of Taniyama-Shimura is a good example) so some people are working on proof assistants to verify proofs programmatically.

Here's an example of one being used to construct the natural numbers:
https://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game/

Anonymous

Anonymous Fri 25 Dec 2020 03:17:01 No.12505106 Report

Quoted By: >>12505153

>>12503783
Before 20th century math it was simple
Just use definitions and theorems to make sense of some discovery you made which is generalizable to a certain set
Now it's literally shit
Idk if proofs even exist in this century anymore
Everything is fucking nonsense and has holes

Anonymous

Anonymous Fri 25 Dec 2020 03:22:01 No.12505117 Report

Quoted By: >>12505153 >>12505158

>>12503783
The special mathematical language used to make mathematical arguments. And this is the problem with many University programs today, they should teach proofs and my textbooks never went into it too in depth like they really should have imo. I never realized how much it really meant over the years and how much of a noob I really was when I first started the game

Anonymous

Anonymous Fri 25 Dec 2020 03:40:07 No.12505153 Report

Quoted By: >>12505158

>>12505106
> Idk if proofs even exist in this century anymore
I think that's a little extreme. There are definitely areas of maths that are on shaky ground, but we're nowhere close to the Italian school of Algebraic Geometry bad.
People have taken notice and are trying to fix things too, so I think it should be ok.

>>12505117
I'm really surprised that there are maths programs that don't at least cover some basic proof theory.

Anonymous

Anonymous Fri 25 Dec 2020 03:41:54 No.12505158 Report

Quoted By: >>12505167 >>12505180

>>12505117
>>12505153
What's good proof theory?
How do I relearn math with good proofs and unlearn all the stupid shit I learned

Anonymous

Anonymous Fri 25 Dec 2020 03:47:16 No.12505167 Report

Quoted By: >>12505173

>>12505158
If you want a really rigorous way of doing proofs I'd recommend looking into doing stuff alongside a proof assistant.
There are plenty to choose from, but the prof. behind the site I linked above is trying to write an entire undergrad syllabus using one, so it should cover some pretty basic stuff.
https://xenaproject.wordpress.com/what-is-the-xena-project/

Anonymous

Anonymous Fri 25 Dec 2020 03:49:31 No.12505173 Report

Quoted By:

>>12505167
Thanks anon!

Anonymous

Anonymous Fri 25 Dec 2020 03:51:06 No.12505176 Report

Quoted By:

>>12503783

You start from a list of statements who’s truth can be taken for granted (these include axioms, and results from other theorems), then you apply step-by-step reasoning to reach new true statements.

Some common proof templates include: proof by construction, proof by contradiction, proving the contrapositive, proof by mathematical induction, proof by the pidgenhole principle, proof by infinite descent, proof by definition.

Anonymous

Anonymous Fri 25 Dec 2020 03:53:11 No.12505180 Report

Quoted By:

>>12505158
Anon there is actually a thing called 'proof theory' look it up on YouTube http://symbolaris.com/course/constlog20-schedule.html

>>12503783
This is the standard procedure:
Look at the definitions. Can you get your 'proof' by rearranging things in order to match the definition? Then you can now substitute: if 1 = x then manipulate y until it's in the form of x, and now it's = 1.

There are entire strategies how to do this: https://www.youtube.com/watch?v=vGQZjITDft4

Anonymous

Anonymous Fri 25 Dec 2020 04:07:19 No.12505203 Report

Quoted By:

>>12503783
step by step proofs. Using whatever strategy you want. you go from step to step showing how you get from once place to another.

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