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P.S. Reviews are still needed to check novelty etc.
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
Can you prove that?
I'd be interested in whether proofs like these will be formalized in proof assistants that can be checked with computer code, so that it removes doubt of error. It's something in math I'd like to see become more prevalent.
This does not remove doubt of error.
So who gets credit for proving it? Freedman, the original author from 1981; or the authors of this book? If Freedman's proof has so many gaps, should it be considered more of a proof outline, or a motivation for believing a conjecture, and the current book be considered the actual proof? Or does Freedman get the glory? In that case, there's not much incentive for people to do what these book authors did. Which I supp…
So who gets credit for proving it? Freedman, the original author from 1981; or the authors of this book? If Freedman's proof has so many gaps, should it be considered more of a proof outline, or a motivation for believing a conjecture, and the current book be considered the actual proof? Or does Freedman get the glory? In that case, there's not much incentive for people to do what these book authors did. Which I supp…
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
That's assuming you ascribe to viewing math as science.
> Why don't serious math journals require programmatically checked proofs for all publications
Presumably it has something to do with why formalized mathematics is rare: it's hard. Even relatively simple concepts become quite hard to deal with when fully formalized. I suspect that mathematics on this level is simply not amenable to the treatment that you envision (at least today).
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
> Math is the most formal science there is. Can you prove that?
So... it's a tautology. Math is the most mathy math. Biology or psychology are less mathy maths.
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
Having provablility holes in the formal system doesn't imply the existence of other systems that could be decomposed from currently known or unknown symbols. In this universe, information at the level of string theory seems to describe the limits, so math, as she is wrote, is as formal as it gets.
The map is not the territory, so math, as a map, will always be less "formal" than reality itself. It's pretty firmly in second place, though.
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
... Because that would take 2+ orders of magnitude more work, and nobody has the time/attention budget for it.
This is sort of like asking: why did you single person write this 10-page short story instead of making a Hollywood-style feature film?
Math is the most formal science there is. Why don't serious math journals require programmatically checked proofs for all publications, and instead rely on what essentially is a code review for a very large change request with extremely convoluted code to be vetted bug free by only a handful of experts? P.S. Reviews are still needed to check novelty etc.
Fully formalizing a proof with a tool like Coq or Isabelle is in and of itself a nontrivial problem.