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What I find interesting is that these proofs aren't one liners. To me, I intuitively presume that mathematical proofs should be one liners because they are expl

What I find interesting is that these proofs aren't one liners. To me, I intuitively presume that mathematical proofs should be one liners because they are explaining fundamental truths of nature; this universe and beyond. Having said that, it's quite possible that a more "elegant" proof will be discovered in the future. Maybe it requires further thinking outside the box -- it will more likely require new mathematics. If you want really non-elegant proofs, take a look at computer-assisted proofs (e.g. proof of the four color theorem). These make the subject of this thread seem extremely elegant!

anonymous 13y ago
It can be a one-liner, but you'll need more language. That is, you'll need terms that encode mathematical truths that currently can only be expressed as several pages. Think of this - I can use the number two and refer to it with just a single character - 2. However, properly stating all its properties and what it is starting from just the axioms of set theory, I'll need quite a lot of pages.
- VLM 13y ago
  Maybe a good way to resonate the situation with HN would be you wanna store the number 2. Well, if you only know and are permitted to use classic IEEE 754 floating point then this is going to be a really long story. But once someone "invents" binary integers and its widely accepted that you're "allowed" to assume everyone understands them, then to store the number 2, you just squirt out a 8-bit binary integer word 00000010 and call it good. And that's how "lets store the number 2" goes from 1000 pages and ten hours of lecture to explain to CS grads, to some 5 minute Kahn academy video that any goof off the street can more or less understand. There is no proof that any simpler explanation exists. Its quite possible no one will ever teach the proof of FLT to grade school kids. But if it ever happens it'll be like the analogy above.
dagw 13y ago
The proof is a one liner, if you take enough of the background theorems as given. The reason the proof is so long is that Wiles had to prove and build upon a bunch of other theorems to get to a point where proving FLT was possible. If for example you simply accept everything up to and including the Taniyama–Shimura–Weil conjecture as true, then the proof of FLT gets pretty close to one line.
VLM 13y ago
The best explanation I can give that will probably resonate with HN folks is I did a big data import this morning... was it a one-liner because "vlm@something:~$ submit.pbs.job.sh" is one line, or is it a ten or so lines of batch submission stuff, or is it one line running a perl script that rips apart one file format, cleans the data a bit, and shoves it into a DB or is it the one line of perl code, or one line of C, or one assembly line, or one byte/word machine language opcode, or one microcode operation, or one transistor? So someone Very familiar with the system is happy with one line of interactive shell running a trusted and well understood script. But if its weird, someone might demand to see the PBS batch script contents, or the innards of the perl, of if life and safety aerospace depended on it maybe they'd demand a down to the transistor formal proof of correctness (good luck with any non-trivial problem) Or put another way I could teach you the equation for the current flow thru a MOS transistor vs gate voltage, maybe even run a simple lab until you're happy, and then say, well, there you go, and thats why my batch script works, and I have an elegant proof of how it works, beginning with this transistor equation, but the margin of my HN comment is too narrow to contain it, so...

anonymous 13y ago

It can be a one-liner, but you'll need more language. That is, you'll need terms that encode mathematical truths that currently can only be expressed as several pages. Think of this - I can use the number two and refer to it with just a single character - 2. However, properly stating all its properties and what it is starting from just the axioms of set theory, I'll need quite a lot of pages.

VLM 13y ago
Maybe a good way to resonate the situation with HN would be you wanna store the number 2. Well, if you only know and are permitted to use classic IEEE 754 floating point then this is going to be a really long story. But once someone "invents" binary integers and its widely accepted that you're "allowed" to assume everyone understands them, then to store the number 2, you just squirt out a 8-bit binary integer word 00000010 and call it good. And that's how "lets store the number 2" goes from 1000 pages and ten hours of lecture to explain to CS grads, to some 5 minute Kahn academy video that any goof off the street can more or less understand. There is no proof that any simpler explanation exists. Its quite possible no one will ever teach the proof of FLT to grade school kids. But if it ever happens it'll be like the analogy above.

dagw 13y ago

The proof is a one liner, if you take enough of the background theorems as given. The reason the proof is so long is that Wiles had to prove and build upon a bunch of other theorems to get to a point where proving FLT was possible. If for example you simply accept everything up to and including the Taniyama–Shimura–Weil conjecture as true, then the proof of FLT gets pretty close to one line.

VLM 13y ago

The best explanation I can give that will probably resonate with HN folks is I did a big data import this morning... was it a one-liner because "vlm@something:~$ submit.pbs.job.sh" is one line, or is it a ten or so lines of batch submission stuff, or is it one line running a perl script that rips apart one file format, cleans the data a bit, and shoves it into a DB or is it the one line of perl code, or one line of C, or one assembly line, or one byte/word machine language opcode, or one microcode operation, or one transistor? So someone Very familiar with the system is happy with one line of interactive shell running a trusted and well understood script. But if its weird, someone might demand to see the PBS batch script contents, or the innards of the perl, of if life and safety aerospace depended on it maybe they'd demand a down to the transistor formal proof of correctness (good luck with any non-trivial problem) Or put another way I could teach you the equation for the current flow thru a MOS transistor vs gate voltage, maybe even run a simple lab until you're happy, and then say, well, there you go, and thats why my batch script works, and I have an elegant proof of how it works, beginning with this transistor equation, but the margin of my HN comment is too narrow to contain it, so...