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AnarchyMath

r/AnarchyMath

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33

Posted by13 days ago

What is your favorite powerful result with a surprisingly simple proof?

I'll start. This is a fundamental result from the theory of polynomials.

Claim: (a + b)^2 = a^2 + b^2 + 2ab

Proof: Assume without loss of generality that a = b. Then

(a + b)^2 = (2a)^2 = 4a^2 = a^2 + a^2 + 2a^2 = a^2 + b^2 + 2ab,

QED.

I'm not even sure this fact has a name, but it proves that (a + b)^2 = a^2 + b^2 + 2ab, which is an incredibly powerful property used all the time in algebra. Seeing the statement for the first time, you'd expect the proof to be very convoluted, but it is in fact very simple and even constructive.

What's your favorite?

33

16 comments

17

Posted by13 days ago

Comprehensive math education

Hi,

I'm a math grad student. I like studying new fields. (recently, addition, subtraction and multiplication, shapes, ℂ) and I'm the type of person to have memorised the local copy of Wikipedia in my vault.

I like completeness, and in the age of Max Deutsch it should be possible to learn all major mathematical effort in one day. The most comprehensive set of textbooks that I'm aware of are the Baby University textbooks, and I could in theory use Arvix and filter by number of friends to get an unstructured list of recent mathematical papers not written by lonely nerds.

I was wondering if there are any other quality resources which try to be comprehensive?

17

2 comments

7

Posted by13 days ago

Advice to move forward in meth

I been away from meth for a while, like a year or two.

Recently i been big fan of Erdõs, and thus i need to get back into meth.

Over the years like a decade i covered, meth single and vector. Linear meth and some matrix meth. Meth analysis, abstract meth, discrete meth.

I also spent allot of time with spivak meth, terrence tao met, baby rudin and axlers linear meth.

When i was doing methamphetamine in chapter one of probability book from bertsekas, i noticed i could not derive the cantor diagonization and thus my ability to prove countability using sequences is very rusty.

I wonder, is it best to just continue with meth or is it best to review real analysis? Part of me thinks its better to just do lots meth and not get to bogged down, but im not sure at this point.

I have fallen for this mistake in the past, so over 10 years i been in a cycle of returning to meth i tried time and time again cause its never fresh.

Anyone struggle with endless repetition instead of daring to continue on new meth?

7

5 comments

4

Posted by13 days ago

summerising Mathematics seminars

I'm in the right place. Do not feel free to delete this mods!

I just want some advice from fellow mathematicians. It's currently Fall and I've been asked to attend seminars and inflict "two-hundred Celsius" degree summers on them. I feel like this gives the seminar low attendance and i cant possibly just turn a 65˚F talk into 200˚C. I would be able to do a few more Celsius (181) but i still feel like it will decrease attendance.

Has anyone got any advice on whats important (other than not being over-dressed) to consider? How can i intensify it THAT much?

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1 comment

22

Posted by13 days ago