I'm not sure there is another profession in the world where it's impossible to explain to a layman on what the winners of their most prestigious award have worked on.
fwiw, I feel the same way about biology "Lysing action of the (1,2)b-carotene receptive encephalopathy pathway" type shit.
High school biology is enough to get a vague idea of this though.
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.
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 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.
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.
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.
https://www.quantamagazine.org/series/fields-and-abacus-meda...
I work in something related to Image Compression, so when the computer has to download the image from Internet it's smaller and use less data. Anyway, I study the mathematical part, not the programming part.
The idea is that images usually have big plain parts like the sky or the wall of a house, so you use big blobs of "ink" to paint them. For the border you use smaller blobs of "ink". And very close to the border you use smaller and smaller blobs of "ink". In this method, all the blobs of "ink" has the same shape, the only difference is the size. Also, the plain parts are not perfectly plain, so you use some small blobs of "ink" there.
In a typical image, you need very few blobs of "ink" if you pick the shape of the blobs of "ink" correctly. So you can only send the position and size of the blobs of "ink", that is much smaller than sending all the information of the image. The hard part is choosing a shape of the blobs of "ink" to make this conversion automatically and very fast, without asking the computer to do something smart to select the positions.
If the listener has more technical background:
The blobs of "ink" have white "ink" in some parts and black "ink" in other parts. This correspond to positive and negative values and actually all the blobs of "ink" are an orthonormal base so the calculation is only a orthonormal base change, that is super easy and fast. There is no smart selection of the position of the blobs of "ink" positions, just a boring orthonormal base change.
If the listener has even more technical background:
Something something Fourier Transform.
I don't want to count how many lies that description has. Also, all the parts in this description were done by other persons perhaps 10 year before me. I think I only once compressed an image, just for fun, and got a tiny compression because it was a toy method (¿Haar base?).
The main problem is that research is mostly about very specific details. Let's imagine the rounding of metallic nuts for screws, in a society where nobody has seen a nut or a screw. So when people ask, you have to say something like "I make bridges, actually a small part that keep them tight, actually I don't make them but I study how they are more resistant for exaple to corrosion. You are asking what is corrosion? Corrosion changes the color of bridges and they get weak an may fall apart." Notice that I never mention "rounding"! I probably need like half an hour to explain the relation between the rounding of the nut, the alloy, the salt in the sea breeze, the daily heat and cold cycle, and perhaps other things that may be relevant in my totally fictional example.
> Still I think honesty is a better policy, even if it's not as satisfying, and if departed from at least making sure both sides know there are convenient lies and oversimplifications.
Yes, you can call my description an oversimplification. It's hard to keep a balance and make a nice explanation that last less than 30 seconds before people get bored.
Dating or maybe a significant other, parents, siblings, any BBQ event IE any social event outside academia where someone asks "So what do you do?"
Yes we do have plenty of practice adjusting our explanations to the audience.
Other fields do it, but it is almost systematic in math, and arguably, it makes things even harder to understand as people names are not descriptive.
Omitting the human history of a field does not automatically make it easier.
Same with their ability to summarize and explain things
And their ability to create mathematical objects that are similar, but weird in a funky way, to the actual real objects.