alt Hacker NewsI spent 20 minutes trying to learn what this means as someone who hasn’t taken a ton of college math. Please feel free to correct me/treat this as a teaching opportunity. But I think this is just stuff that can be understood with just algebra, just the numbers are very very large.
It sounds like the big deal is you have at least 30 points in a graph that aren’t related and can be expressed as rational numbers (not necessarily integers so you get giant fractions). Being very humble here and invite people more advanced in mathematics to chime in where I’m wrong.
So like this is one of the x,y coordinate points that is two rational numbers.
x=30786757706172245427369935940751/4
y=58841476683002984849182029306774218124047405249/8
So there’s at least 30 points on the graph like this, which is a big deal because before there were only 29 independent points verified in any elliptic curve equation.
“Independent” seems to mean something precise here too but I’ll let someone else explain that because I’m not quite sure, somehow the points have to be unrelated to one another.
Bumping the rank from 28->29 previously took over ten years, so it’s a big deal in mathematics apparently.
Replies
As ducttapecrown said in their comment, you can define an addition on points on elliptic curves. (You can think of an elliptic curve as a cubic equation on the plane, so if you take a line that goes through two points, it will go through a third. There's more work to do to turn it into an addition, but that's the basic idea.)
There are different types of addition, though. A rank two addition would mean it looks like (x, y) + (x', y') = (x + x', y + y'). A rank three addition would mean it looks like (x, y, z) + (x', y', z') = (x + x', y + y', z + z'). Here they found the first example of an elliptic curve where the rank is 30.
You got nothing wrong. To expand, you can add points on elliptic curves together. To add P and Q, you draw the line between them, find the third point on the line, and reflect it over the x-axis [1]. Then the idea is to find a generating set S of points so that every rational point on the elliptic curve is a sum of points from S. The size of S is called the rank of the elliptic curve.
[1] There are some details: https://en.wikipedia.org/wiki/Elliptic_curve#Group_law