The End of Mathematical Proofs by Humans?

vivin writes "I recall how I did a bunch of Mathematical Proofs when I was in high school. In fact, proofs were an important part of Math according to the CBSE curriculum in Indian Schools. We were taught how to analyze complex problems and then break them down into simple (atomic) steps. It is similar to the derivation of a Physics formula. Proofs form a significant part of what Mathematicians do. However, according to this article from the Economist, it seems that the use of computers to generate proofs is causing mathematicians to 're-examine the foundations of their discipline.' However, critics of computer-aided proofs say that the proofs are hard to verify due to the large number of steps and hence, may be inherently flawed. Defenders of the same point out that there are non computer-aided proofs that are also rather large and unverifiable, like the Classification of Simple Finite Groups. Computer-aided proofs have been instrumental in solving some vexing problems like the Four Color Theorem."

Does it really work?

[janek78]

Computer generated proofs really do seem like a real time saver. Provided that they work. Now, if we could only prove that... Let me think, how about building this atomic superpowered robotic monster to prove that computer generated proofs work? Or perhaps we could use those computers to prove it themselves!

Re:Creativity

[R.D.Olivaw]

especially when we already know the answer it's looking for. 42

Re:If computers could write proofs...

[Hideyoshi]

Computers can separate wheat from chaff. That's what AI is all about.

Which explains the glorious successes that subject has enjoyed in the last few decades ...

Re:The best math is always elegant.

[Craigj0]

Perhaps his proof was flawed and he realised it so he ripped the last page out?

Re:Godel/Turing/Cohen...

[g1t>>v]

That's what they said 50 years ago too ...

Re:Consider the source

[Trogre]

What does The Economist know? It's a right-wing rag.

What does Slashdot know? It's a left-wing rag.

"peer" review

[lucason]

How can the review of proof generated by computer by a human be considered "peer" review?

Why not have it verrified by other computers?

Re:Science by AI is flawed too

[Professor S. Brown]

Was that just an intentionally terrible example, or did you not actaully understand a good portion of the book?

Re:Critics Reaction...

[Sloppy]

Just write a program to check it. :-)

Motivation

[beacher]

Speaking of toys - I found this on Thinkgeek.com [thinkgeek.com] and it's a perfect for your favorite mathematician. " If A Pretty Poster And A Cute Saying Are All It Takes To Motivate You, You Probably Have A Very Easy Job. The Kind Robots Will Be Doing Soon.". Seems very apropos....

Can it prove the Riemann Hypothesis?

[alphadingo]

I'd pay $500,000 for a program that can prove the Riemann Hypothesis.

Re:I must be confused....the 4 color theorem....

[Anonymous Coward]

oh come on.

so if I have 30 countries all touching and one has borders with 7 of them, very simple to color it with only 4 colors, hell my 4 year old can figure that out.

lay off the hemp and booze.

Well, a lot of us are happy of this...

[DownloadTHIS]

The end of mathematical proofs by humans? I think I speak for the entire high school populus by saying "Thank God!"

Re:Science by AI

[Rune Berge]

Yeah, right. The great AI machine will be delivered in the same week as my flying car. Taking orders now, please form an orderly queue.

According to rumors it will be bundled with Duke Nukem Forever.

Re:Science by AI

[computational super]

On the flip side, according to my calculations, I lost e3 neurons, e1 synapses, and e0.5 operations per second to beer last weekend alone. That almost never happens to a computer.

Re:Science by AI

[jhobbs]

If this is right, then the 1e5 networked computers that are currently used by Google are a tenth of the way there.

Tommorrow's Headline: Googlebot declares self world ruler, buys Graceland

Re:Science by AI

[thuh Freak]

Computers replacing mathematicians completely is about as far-off as computers replacing poets or historians.

hey, don't ruin my hopes and dreams.

AI is total bunk!

[Anonymous Coward]

Which explains the glorious successes that subject has enjoyed in the last few decades ...

Yes, you're right. No one will ever build a chess-playing computer, computer controlled "braking systems", "automatic warehouses", and certainly, we'll just never accomplish the so called "computer controlled piloting system! "Autopilots", indeed!. They'll just never happen! AI will never work! Pie in the sky, the whole lot of it!

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AC