Re:Number theorist fears many proofs widely considered to be...
by Silhouette on Sunday September 29, 2019 @04:30PM
(#21109440)
IMO the final paper had too much technical jargon which was convoluting some simple concepts.
This is symptomatic of IMHO the biggest single problem with the world of mathematics today. This discipline should be about developing ideas based on rigorous foundations and logic, which is a useful and important purpose. Once you have understood those ideas, even "advanced" results often seem quite simple and intuitive, and we can take that understanding and apply it to other work if helps us to make useful progress. However, the amount of needlessly obscure terminology, poor notation and just plain bad writing in formal papers make the whole field absurdly inaccessible, even to many who might have no trouble understanding the underlying concepts and important results.
Just imagine what would happen if we tried to write engineering specs or software the way postgraduate mathematics research is done. We'd be trying to debug source code where every identifier was a single character, taken from one of three or four different alphabets, with several of them looking similar enough to mistake one for another, with a bunch of combining accent modifiers on top that were used to fundamentally change the semantics of the program, interspersed with comments by someone who needs a remedial class in basic writing skills, full of technical terminology that is defined in terms of other technical terminology from other software packages, except that sometimes the meaning is subtly different in this context but that isn't noted anywhere on the screen at the time, resulting in needing to spend half an hour doing a depth-first-search of all the definitions only to find that a function whose only identifier is the name of the developer who wrote the second version (because the first person to work on it already has another function bearing their name) is actually equivalent to what a programmer would write as
const DAYS_IN_WEEK := 7
I write this as someone who studied mathematics to a high level and has touched on the field many times since in connection with heavily mathematical software development. It's the worst sort of closed-world gate-keeping, and we could do so much better, but sadly inertia and vested interests are not our friends in this matter.
This is symptomatic of IMHO the biggest single problem with the world of mathematics today. This discipline should be about developing ideas based on rigorous foundations and logic, which is a useful and important purpose. Once you have understood those ideas, even "advanced" results often seem quite simple and intuitive, and we can take that understanding and apply it to other work if helps us to make useful progress. However, the amount of needlessly obscure terminology, poor notation and just plain bad writing in formal papers make the whole field absurdly inaccessible, even to many who might have no trouble understanding the underlying concepts and important results.
Just imagine what would happen if we tried to write engineering specs or software the way postgraduate mathematics research is done. We'd be trying to debug source code where every identifier was a single character, taken from one of three or four different alphabets, with several of them looking similar enough to mistake one for another, with a bunch of combining accent modifiers on top that were used to fundamentally change the semantics of the program, interspersed with comments by someone who needs a remedial class in basic writing skills, full of technical terminology that is defined in terms of other technical terminology from other software packages, except that sometimes the meaning is subtly different in this context but that isn't noted anywhere on the screen at the time, resulting in needing to spend half an hour doing a depth-first-search of all the definitions only to find that a function whose only identifier is the name of the developer who wrote the second version (because the first person to work on it already has another function bearing their name) is actually equivalent to what a programmer would write as
I write this as someone who studied mathematics to a high level and has touched on the field many times since in connection with heavily mathematical software development. It's the worst sort of closed-world gate-keeping, and we could do so much better, but sadly inertia and vested interests are not our friends in this matter.