Ciro Santilli @cirosantilli 37

Mordell's theorem guarantees that the rank (number of elements in the generating set of the group) is always well defined for an elliptic curve over the rational numbers. But as of 2023 there is no known algorithm which calculates the rank of any curve!

It is not even known if there are elliptic curves of every rank or not: Largest known ranks of an elliptic curve over the rational numbers, and it has proven extremely hard to find new ones over time.

TODO list of known values and algorithms? The Birch and Swinnerton-Dyer conjecture would immediately provide a stupid algorithm for it.

Magic software that allows you to write a single program that runs on a wide range of hardware.

TODO, come on, Internet!

Bibliography.

They come up a lot in many contexts, e.g.:

The big breakthrough of the vertebrates appears to be the ability to swim around in a straight line and eat smaller species that are floating about.

Bones appear to help that a lot!

It is likely the most efficient design to travel long distances. Be thin and wiggle your tail around.

Perhaps smaller animals can skip the bone thing. Maybe a notable example are the lancelets, which look a bit like small fish. But they only go up to 8 cm.

Things to do: