aquafox
Joined 4 years ago
Joined 4 years ago
From the expose in Terence Taos blog [1], it seems the difficulty of the Navier-Stokes counter example is a delicate balancing act between having a blow-up solution and a well behaved force field. And this involves a lot of technical arguments based on already existing ideas.
If this is true, then the achievement of the AI is rather to correctly navigating this balancing than inventing something completely new.
[1] https://terrytao.wordpress.com/2026/09/07/finite-time-blowup...
df.select(
pl.col("x"),
(pl.col("w")/pl.col("z")).alias("y")
)with
df |> select(x, y = w/z)
To see why \int_a^b f(x) dx = F(b) - F(a) with F'(x) = f(x),
we replace f with f' (and hence F with f) and get
\int_a^b f'(x) dx = f(b) - f(a).
Re-arranging terms, we get
f(b) = f(a) + \int_a^b f'(x) dx.
The last line just says: The value of function f at point b is is the value at point a plus the sum of all the infinitely many changes the function goes through on its path from a to b.
[1] https://www.zscaler.com/resources/security-terms-glossary/wh...