Comment by doonesbury | Hacker News Reader

Comment by doonesbury | Hacker News Reader

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Thank you for bringing smarter, better information. I stand corrected then.

>a^4 = b^2 = 1, a^3 b = ba >has exactly eight elements

I suppose the missing issue (or at least the one I feel could have had more sunshine on it) is how and why elements of the monster groups are represented as this would more subtly capture the symmetry that keeps the group finite. It's not so much symmetry as a subject unto itself, as the subtle interplay between group operations on the form of elements with symmetry that keeps the group finite.

Your term "a^4=1" has exactly that missing emphasis: take element 'a' (i.e. a square) and rotate it four times and it's the same as multiplying a by 1, which is the identity element. Ditto b^2: perform the mirror operation twice and again it's the same as doing b*1 etc.

“Thank you for bringing smarter, better information.”

Thank you for being modest, but the information isn’t “better” than yours, just more precise and more “messages from the front”. Both are equally valuable.

There has been an ongoing issue in mathematics between documentation and communications.

Documentation is rampant. It is a necessary part of the process of determining whether something is correct, rather than almost correct. It’s a technical requirement of the process, much like desks and chairs.

Communications is almost an afterthought to the community, but is math’s basic value to society. Here I define “communications” as imparting the basic insights to anyone who isn’t either developing the proof or reviewing the proof for correctness, I.e. the entire planet minus 10 or 20 people.

Communications has relatively little to do with documentation, although documentation can and has masqueraded as communications. The current mathematical enterprise has put 95% (99%?) of the effort on proofs to expand the mathematical universe, and precious little on communications.

I’d argue that should be reversed at this stage in the development of mathematics. But, as a nod to the established order, I’d propose that 50% of the effort of professional mathematicians be spent in the development and improvement of the communications side of mathematics. No better time, given the maturity of media technologies.

My two cents...

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