3 ms·

I liked their recent article on the Langlands program. https://www.quantamagazine.org/amazing-math-bridge-extended-beyond-fermats-last-theorem-20200406/ https:

I liked their recent article on the Langlands program. https://www.quantamagazine.org/amazing-math-bridge-extended-beyond-fermats-last-theorem-20200406/ https://www.quantamagazine.org/amazing-math-bridge-extended-...

dmix 7y ago
Quanta hires some great graphic design freelancers for the top headers as well (such as the one you linked to, less so the OPs). I like to click through their profiles and see their other work. Design + scientific papers hits a sweet spot for me for some reason.
twic 7y ago
The illustration there is great. But i think the article is pretty vacuous: it tells you that there is this bridge, but it doesn't explain what the bridge is. Which is understandable, because that's very complicated and deep, and this is a short article for a general audience. Take the explanation of automorphic forms: "On the other side of the bridge live objects called automorphic forms, which are akin to highly symmetric colorings of certain tilings. In the cases Wiles studied, the tiling might be something along the lines of M.C. Escher’s famous tessellations of a disk with fish or angels and devils that get smaller near the boundary. In the broader Langlands universe, the tiling might instead fill a three-dimensional ball or some other higher-dimensional space." Having read that, do you now actually know anything about automorphic forms? No. It goes on: "Namely, for both Diophantine equations and automorphic forms, there’s a natural way to generate an infinite sequence of numbers. [...] And for the kind of automorphic form that appears in the Langlands correspondence, you can compute an infinite list of numbers analogous to quantum energy levels." What on earth does that mean? This might well be the projection of the truth onto the low-dimensional space of ordinary language, but it ends up being word salad.
- ABeeSea 7y ago
  The idea of automorphic forms as analogous to symmetric colorings of a tesselation that shrinks on the boundary is a way more intuitive description than the mathematical definition of automorphic forms. So yes, I do feel like I know more about them from that definition versus the definition of invariance under subgroup action. And for the second quote, I took it to mean that the subset of automorphic forms that map to Diophantine equations can be used to generate an infinite sequence that maps to quantum energy levels which I believe means maps to the number of electrons in the orbit of the nucleus (2, 8, 18,...) etc.

dmix 7y ago

Quanta hires some great graphic design freelancers for the top headers as well (such as the one you linked to, less so the OPs). I like to click through their profiles and see their other work. Design + scientific papers hits a sweet spot for me for some reason.

twic 7y ago

The illustration there is great. But i think the article is pretty vacuous: it tells you that there is this bridge, but it doesn't explain what the bridge is. Which is understandable, because that's very complicated and deep, and this is a short article for a general audience. Take the explanation of automorphic forms: "On the other side of the bridge live objects called automorphic forms, which are akin to highly symmetric colorings of certain tilings. In the cases Wiles studied, the tiling might be something along the lines of M.C. Escher’s famous tessellations of a disk with fish or angels and devils that get smaller near the boundary. In the broader Langlands universe, the tiling might instead fill a three-dimensional ball or some other higher-dimensional space." Having read that, do you now actually know anything about automorphic forms? No. It goes on: "Namely, for both Diophantine equations and automorphic forms, there’s a natural way to generate an infinite sequence of numbers. [...] And for the kind of automorphic form that appears in the Langlands correspondence, you can compute an infinite list of numbers analogous to quantum energy levels." What on earth does that mean? This might well be the projection of the truth onto the low-dimensional space of ordinary language, but it ends up being word salad.

ABeeSea 7y ago
The idea of automorphic forms as analogous to symmetric colorings of a tesselation that shrinks on the boundary is a way more intuitive description than the mathematical definition of automorphic forms. So yes, I do feel like I know more about them from that definition versus the definition of invariance under subgroup action. And for the second quote, I took it to mean that the subset of automorphic forms that map to Diophantine equations can be used to generate an infinite sequence that maps to quantum energy levels which I believe means maps to the number of electrons in the orbit of the nucleus (2, 8, 18,...) etc.