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Comment by ajarmst | Hacker News Reader

The author could have benefitted significantly from some exposure to Abstract Algebra, as he seems completely unaware of pretty rudimentary things in Field and Group Theory. The author might also benefit from some exposure to an actual mathematician, judging by the laughable canards he levels at mathematicians and their lack of "rigour" in his abstract. Finally, the author would benefit from some exposure to actual published papers, judging by his apparent unfamiliarity with what abstracts are for.

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His fundamental conceit, namely that mathematics sometimes suffers from ambiguous or sloppily used notation, is a valid one, and this fact has caused a great deal of confusion for a great number of people.

That's a reasonable point, but I wonder if that problem is usually encountered when mathematicians from a particular branch of study read works from a different one whose usages and assumptions differ. I've bounced of it in even very simple areas, like whether 0 is a natural number, whether is is positive or negative (or other), whether 1 is prime, etc. Within the context of a particular community, such ambiguities aren't present.

"This works perfectly well for communication between researchers in the same field, but may be an obstacle for communication between researchers from different fields or for newcomers such as students"

It appears you did not read the abstract after all.

> the author would benefit from some exposure to actual published papers

http://www.diku.dk/~grue/

Looking at his CV, he might even have had taken a few classes in Abstract Algebra.

I usually give the benefit of the doubt and assume ignorance, not incompetence. If he was familiar with Abstract Algebra, then the omission of any reference to groups and fields in the examples he gives seems bizarre, as are the pompous declarations in the "abstract" that doesn't abstract his arguments or findings.

On page 4 he does make a reference to the abelian group (Z, +). Though he just calls it "a structure" (which is not wrong), I agree that this paper is somewhat unusual. It even includes some typos ("yeild," page 4), yet it is readable and exposes an interesting topic; the ambiguity of mathematical notation.

Pooh-pooh.

https://en.wikipedia.org/wiki/Pooh-pooh

Also, ad hominem.

The critique that mathematics is far too forgiving of ambiguity and lack of rigour is, however, quite entertaining.

Leslie Lamport has also leveled this criticism against mathematicians.

http://research.microsoft.com/en-us/um/people/lamport/pubs/p...

Fair enough, and thanks for reminding me of that paper, which is a gem. I'd argue that Lamport makes a convincing case with evidence and proposes changes that would rectify the evidenced issues. This author simply asserts it as a fact and then introduces an odd notation with little concrete justification. I also think Lamport's critique is less of the abstract symbolic systems used in mathematical proofs, but a lamentable tendency to use prose.

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