- #36
Maths Lover
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micromass said:Sorry for hijacking your thread here anyway
I didn't understand what you really want to say !
how can you Hijack my thread ?! is it a puzzle ?
explain please ?!
micromass said:Sorry for hijacking your thread here anyway
Jimmy Snyder said:Original poster, or original post according to context.
Maths Lover said:I didn't understand what you really want to say !
how can you Hijack my thread ?! is it a puzzle ?
explain please ?!
micromass said:Hijacking a thread is when you start a pedantic argument about something useless that is not really what the OP wants to talk about.
Maths Lover said:@micromass
so , any new proof for any theorem will be treated with the same way ?
or some theorems is diffrent from others ?
what about main theorms in calculus ?
micromass said:No, I wouldn't say that they will all be treated the same way. I guess it depends on the proof itself. If the proof is really novel and provides some kind of idea that can be generalized, then it might be interesting to professionals. Or when the proof illustrates some kind of abstract theory.
A famous example is the insolvability of the quintic. This was originally proven by Abel and Ruffini. But later, Galois proved it using the methods of (what is now called) Galois theory. From a certain point of view, the theorem was already proven. But the proof Galois gave is very intricate and beautiful. Furthermore, it gives exactly a criterium of when a polynomial can be solved or not. And the same method can be generalized to other settings as well (such as integration theory). Finally, Galois theory is one of the most elegant mathematics known to man! Despite Galois theory not really proving anything novel, it is still one of the most important theories in mathematics out there.
If you are interested in Abel's theorem, then I highly recommend the following book: https://www.amazon.com/dp/1402021860/?tag=pfamazon01-20
It is suitable for high school students who are interested in higher level math. It introduces elegant theories such as groups and Riemann surfaces and it culminates with Abel's theorem.
Maths Lover said:I heared about Galois theory for 2 years .
as you know " I think that you know " that I study Abstract Algebra nowdays from Dummit and foote , and Galois theory is the topic of 14th chapter , and I'm very excited to reach this chapter but I still in the second one ,
Jimmy Snyder said:I was told that the original proof of the Riesz Representation theorem was 300 pages long. I don't know if it's true.
micromass said:Ah, yes, I should have remembered! But yes, Galois theory is very exciting. I just hope Dummit and Foote cover it the right way and don't try to obfusciate things. A lot of textbooks on Galois theory seem to have this problem.
Maths Lover said:I hope the same :)
if he did , does artin cover it well ? or he obfuscated it ! ?
jedishrfu said:Speaking of proofs don't forget the book: Proofs from The Book
http://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
micromass said:I don't really remember his treatment well. But I really like Artin, so I guess he did a good job.
If you're looking for beautiful treatments of Galois theory, then the following books are exellent:
https://www.amazon.com/dp/0486623424/?tag=pfamazon01-20 (this is not the same Artin as the one who wrote the algebra book)
https://www.amazon.com/dp/1402021860/?tag=pfamazon01-20
Galteeth said:Hey Maths lover, just out of curiosity what is your native language?