The Four Colour Theorem: The first time machines mogged mathematicians (newsletter.pessimistsarchive.org)
15 points by list 3 hours ago
fhdkweig 2 hours ago
The problem of the proof was that we knew that FCT was true, but we had no idea why. A good/elegant proof teaches us something new about how that problem is related to other problems. It isn't just about getting a true/false answer to the conjecture.
omnicognate an hour ago
Indeed, and the computer aided proof discouraged research into the insightful proof a lot of mathematicians think is probably out there to find. "Proved but not insightfully" is a problem status some mathematicians are starting to think of as closer to "open" than "closed", which is a good thing IMO. (I am not a mathematician, though)
whatshisface an hour ago
Maybe the new heuristic auto tactics will lower the cost of finding the human proof of the four color theorem enough to be affordable in the current environment.
utopcell 40 minutes ago
> "The problem of the proof was that we knew that FCT was true"
Citation needed.
fhdkweig 34 minutes ago
That was terrible phrasing. I meant "The problem with the proof was that although it showed that FCT was true, the proof did not explain why".
dunham 12 minutes ago
jjtheblunt an hour ago
the title made me think of a much older machine that was used for calculating
wahern 32 minutes ago
> I would like to conclude by telling a cautionary tale. Let us try and place the Antikythera Mechanism within the global context of ancient Greek thought. Firstly came the astronomers observing the motions of the heavenly bodies and collecting data. Secondly came the mathematicians inventing mathematical notation to describe the motions and fit the data. Thirdly came the technicians making mechanical models to simulate those mathematical constructions, like the Antikythera Mechanism. Fourthly came generations of students who learned their astronomy from these machines. Fifthly came scientists whose imagination had been so blinkered by generations of such learning that they actually believed that this was how the heavens worked. Sixthly came the authorities who insisted upon the received dogma. And so the human race was fooled into accepting the Ptolemaic system for a thousand years.
> Today we are in danger of making the same mistake over computers. Our present generation is able to view them with an appropriate skepticism when necessary. But our children's children may be brought up within a society dominated by computers, that they may actually believe this is how our brains work. We do not want the human race to be fooled again for another thousand years.
-- E.C. Zeeman, Gears from the Greeks, January 1986, http://zakuski.utsa.edu/~gokhman/ecz/gears_from_the_greeks.p... (https://web.archive.org/web/20250502052226/http://zakuski.ut...)
jmount an hour ago
I think a lot of great ideas like tree-width were developed in hope of simplifying the proof.
layer8 2 hours ago
I didn’t know we had invented time machines yet. ;)
evekayser 3 hours ago
I think the same happens now with AI generating code. Nobody will read every line. that's part of the process from now on.
curt15 2 hours ago
The human who commits a bad change still takes the fall though. Automation doesn't absolve accountability.
Insanity an hour ago
But people think it does, and it’s annoying. The past months I’ve often found mistakes and then heard the response along the lines of “oh Claude wrote that”.
It’s used as an excuse, and then the conversation just moves on. I don’t see a lot of accountability being taken. If anything, senior leadership sees it as a sign of adoption and accepts a certain level of risk.