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Comment by NhanH | Hacker News Reader

Tangentially to the topic at hand, but coming from the article:

> Mochizuki has estimated that it would take an expert in arithmetic geometry some 500 hours to understand his work, and a maths graduate student about ten years.

That's a 40x gap (500 hours assuming 40-hour work week is about 3 months-ish). Assuming that math grad student is active albeit junior researchers, that's a huge gap. I thought our notion of 10x programmer is already something considered extremely wildly stupid and doesn't exist? (I know the last sentence sounds a bit snarky, but it's too amusing to not point out).

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40x sounds pretty conservative to me. I did graduate school in math (did not get a Ph.D.) and my advisor indicated that he assigns problems assuming a 200x multiplier between his capability and the students'. That is, he'd assume that something he could see how to do and could execute inside of a week would be a good thesis problem to keep a Ph.D. student busy for two years.

As far as the 10x programmer stuff... Obviously there are 10x and probably even 100x programmers. They're the experts, and there are not many of them.

Out of curiosity, how old was your advisor at the time (ie is he in his mid career at his peak, toward the end or is he on the younger side etc.)? And is the gap in capability just because of his experience, or is he just a much better scientist than the average researchers?

My advisor at the time was 60-ish, and had tenure for 30 years or so. The gap in capability was (to my eye) mostly due to his experience.

Yep -- my advisor figured he could do my thesis problem in a week. It did take me only 1.5 years to find a counterexample and kill my own thesis, but these are estimates after all.

If he could have proven the theorem in a week despite its having a counterexample, that is impressive.

I'm guessing that he means that his work is closely related to arithmetic geometry (which I was once told was one of the hardest fields in pure math), and so someone with no background would have a lot of trouble getting it. Presumably it takes even longer to become an expert in arithmetic geometry (15 years?).

I also happen to believe in 10x programmers, in fact I think I am one. HN places a big emphasis on denying the importance of virtuosity or intelligence in programming, and characterizing it as a craft. It's very hard to argue against since nerds have had excessive modesty (often literally) beaten into them. At least you get the occasional boastful athlete who says "I'm just really talented".

It's plausible if by "maths graduate student" we understand "average maths graduate student". I.e. a different kind of student from that maths graduate student which the "expert in arithmetic geometry" once was.

We cannot interpret that as containing the claim that when any old randomly chosen maths graduate student becomes an expert in arithmetic geometry, they suddenly gain a 40X efficiency in understanding.

Think of it like this: Someone in Sacramento can get to Milwaukee in 3 days (driving). Someone in Chicago can get to Milwaukee in 3 hours (or less). That's a 24x factor.

When any old randomly chosen person Sacramento gets to Chicago, they do not gain a 24x efficiency in traveling. Rather, they've covered most of the distance to Milwaukee already.

Don't think of it as as 40x gap, think of it as a 10 year - 500 hours gap.

The expert has the 100 years - 500 hours study that are needed.

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