Is the problem explained in text anywhere? (TFA delegates to a video and afaict only discusses another video-suggested solution and a novel solution in text, I don't understand what we're solving.)

> Is the problem explained in text anywhere

the problem is that you want to cut up an onion in such a way as to minimize variation in the size and shape of the cut-up pieces

usually, so that the pieces will cook evenly

You would like to slice (half) an onion in a way that minimizes the variance in volume of the pieces. The problem is then simplified to slicing half an onion in a way that minimizes the variance in cross-sectional area of the pieces at the widest part of the onion.

The problem is "I have an onion that is spherical with even layers. How do I cut it into pieces with equal volume?"

It's more of a geometry thought experiment than a practical epicurean "problem".

> Is the problem explained in text anywhere?

Not very well. There are some snippets:

"to keep the pieces as similar as possible"

"The Jacobian r dr dθ gives a measure of how big the infinitely small pieces are relative to each other"

"The variance is a good measure of the uniformity of the pieces."

The problem is how to get roughly equal sized pieces from cutting an onion. If you cut towards the center the inner pieces are much smaller than the outer.