Possible Proof of ABC Conjecture 102
submeta writes "Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely dense and difficult to understand, even for experts in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem."
Re:Won't really make for a simpler proof... (Score:3, Interesting)
A strong form of the abc conjecture (one providing an actual bound, not just showing there is a bound) combined with existing, relatively straightforward, proofs of the truth of FLT for small exponents would indeed prove FLT in general. However, I haven't heard anyone suggest just yet that an effective bound can be obtained from Mochizuki's work. At this early stage, certainly no one but Mochizuki would know, if even he does.
Re:Linking to Wikipedia to explain math (Score:4, Interesting)
Because if you look in all other commercial encyclopedias (encyclopediae?), you get a more english (well, natural language) translation of the concepts of a math article. But not even that, Wikipedia on this subject fails even at the post-secondary textbook level. I don't count myself among the dumbest of the population, but when I go to a Wikipedia page for something that is on my level for math, the articles on things like cycloids and such are much better explained by Machinery's Handbook or any other source, really, than there.
I am not saying that Wikipedia should dumb its articles down to the point where even the most innumerate among us would understand all of them, but the "spam equations on the wall with little explanation" model doesn't work very well unless you are immersed in the subject. For example, concepts covered in Algebra I and II in high school should be written for that level.^1 Also, this "write for the grad-student and mathemetician for everything" model does little to help people who use applied mathematics. Indeed, this whole focus on grad-student and up writing in the math articles is at odds with the rest of the Wikipedia.
As a result, anyone wishing to *learn* anything about math is better off using anything but Wikipedia.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
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BMO
Footnotes:
1. I had to explain to a high school student that she should not be using Wikipedia for help in her Algebra II class. Because all it did was confuse her. I mentioned that Wikipedia math pages are a "dick measuring contest for experts on the subject" and the light went on behind her eyes and she laughed and agreed. There are far better resources and I suggested she ask her teacher for them.
Re:Linking to Wikipedia to explain math (Score:5, Interesting)
Because if you look in all other commercial encyclopedias (encyclopediae?), you get a more english (well, natural language) translation of the concepts of a math article. But not even that, Wikipedia on this subject fails even at the post-secondary textbook level. I don't count myself among the dumbest of the population, but when I go to a Wikipedia page for something that is on my level for math, the articles on things like cycloids and such are much better explained by Machinery's Handbook or any other source, really, than there.
I am not saying that Wikipedia should dumb its articles down to the point where even the most innumerate among us would understand all of them, but the "spam equations on the wall with little explanation" model doesn't work very well unless you are immersed in the subject. For example, concepts covered in Algebra I and II in high school should be written for that level.^1 Also, this "write for the grad-student and mathemetician for everything" model does little to help people who use applied mathematics. Indeed, this whole focus on grad-student and up writing in the math articles is at odds with the rest of the Wikipedia.
As a result, anyone wishing to *learn* anything about math is better off using anything but Wikipedia.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
The problem is that these topics aren't what you'd see in high school algebra. In fact, upper level undergraduate courses would probably just touch on these. So yes, encyclopedias would have more easily understood articles but they almost certainly don't cover theorems like the ABC theorem or topology in any depth. In fact, most articles in encyclopedias will probably give you a very cursory explanation. To make an analogy it'd be like explaining people as living things with 2 legs, 2 arms and which breath air. It's not useful for any in depth topic and when you really want to understand, you'll need to go into details. And in math, those details come in the form of definitions and equations explaining how the definitions interact together.