Hacker News Reader

Comment by Onavo | Hacker News Reader

> Lysing action of the (1,2)b-carotene receptive encephalopathy pathway

High school biology is enough to get a vague idea of this though.

Right. With a college degree, I understand most of these words. I don’t have a clue about the impact of the research or how it fits into the corpus, but I understand the gist of the article title.

Despite my degree being in engineering, which involved 4 semesters of calculus, and 3 other semesters of math, (7 total) I have absolutely no fucking clue what’s going on in the Fields Medal description above. It’s only barely more intelligible than if it had been written in Chinese (which I truly cannot read at all).

I genuinely don’t understand it at all. Even words that I think I recognize like “harmonic” or “geometric” are useless to me because the actual terms are “harmonic analysis” and “geometric measure theory” and I have 0% clue what those are.

I don’t have to google any of the words in the example biology title.

Did your 7 semesters of calculus include any courses that a math major would take?

For example, a single upper-division undergrad level course on probability will expose you to measure theory.

Similarly, harmonic analysis is something that you can take as a reasonably good senior in mathematics.

I took multivariate calculus (I to III), differential equations, statistics, discrete math, and linear algebra.

I didn't take those courses you're talking about, but that's my point. I have a top <1% education in math in the nation, maybe top 2-3% of all college grads, and that's not enough to even scratch the surface of the summary.

Well, the snobby pure maths folks look down on applied engineering math ;)

if you took an engineering course that covered fourier transform, z transform, or laplace transform, then you have seen an introduction to harmonic analysis on the circle and the real number line.

typically when I see mentions of harmonic analysis together with differential geometry I start thinking of fourier transform on more fancy shapes (on the sphere, for example, the replacements for complex exponentials are called spherical harmonics)

my PhD was EE in signal processing and I took some extra math classes at the graduate level, and continue to read some of this for fun and profit.

I still cant understand most of the terminology in the fields medal citations. that probably requires a more thorough couple of years of graduate education in mathematics.

math is by far the furthest of the sciences in terms of depth of human discovery.

Harmonic analysis is "just" working with harmonic functions which you have enough background for: f(x,y) is harmonic if f_xx+f_yy=0 (f_xx=2nd partial derivative w/r/t/ x, and so on). Higher dimensions work the same: f_{x1x1} + f_{x2x2} + f_{x3x3}+.... = 0.

Every engineering student in the US takes those courses. I did too. That doesn’t make us top 2-3% of college grads.

The stuff you mentioned is first year business for most math undergraduates. You should not expect to know most things in senior level math after taking just first-year math.

It’s like expecting to know computational complexity theory, or distributed systems theory, after taking first year CS.

I think most undergrad level course on probability expose you to measure theory _without_ telling you they are measure theory.

Reply on news.ycombinator.com