He says geometric algebra was right about the problem, wrong about the fix

One movement, two very different claims

Alex Kritchevsky thinks Geometric Algebra diagnosed a genuine illness in math pedagogy and then prescribed the wrong drug. His whole argument turns on splitting GA into two claims that usually travel together.

Claim 1: the tools of exterior algebra — wedge products, multivectors, duality, contraction — are powerful and should be introduced far earlier than they are, rewriting how linear algebra and vector calculus get taught. He endorses this without reservation.

Claim 2: that David Hestenes' Geometric Product should be the fundamental operation everything else is built on. This he rejects, flatly, as "nonsense."

Why he calls the Geometric Product a costume

His technical objection is specific. The Geometric Product fuses a scalar (the dot product) and a bivector (the wedge product) into a single mixed-grade object that has no coherent general geometric meaning. To then recover ordinary linear algebra, GA has to bolt on pile after pile of auxiliary operations. What the product really is, he argues, is operator composition — genuinely useful, but in a narrow lane: rotations and reflections. He pairs this with a social critique, that GA drew a disproportionate share of cranks, which is why careful people retreat to the name "Clifford algebra" instead.

The table he is effectively drawing:

The thread sorted itself onto the same line

What is striking is that the people who showed up to argue mostly agreed with the split, and helped sharpen it. A mathematician took Claim 1 and ran with it, which is precisely the point: the fight is about the product, not the wedge.

"I support this claim, so I suppose I'm a proponent of geometric algebra. I think it's more or less been carried out for vector calculus by Spivak's 'classical' Calculus on Manifolds…" — a self-identified mathematician

The article's harshest line (that GA dressed up results that already existed) got first-hand corroboration from the review side of the table.

"I had the bad fortune of reviewing some GA research articles once upon a time. It was almost embarrassing. Everything of substance had been published in a conceptually cleaner bivector language previously." — a commenter who has reviewed GA research papers

Then the applied side confirmed exactly where the product does earn its keep, rotations, from someone who lives there.

"Maybe that's why I've found it so useful when doing rigging for animation—that's the entire job!" — the CTO of Xy Group, who does animation rigging

The one contested part was the crank remark, and the author came back to defend it as diagnosis rather than insult.

"I meant it more as an assessment of the state of affairs, not as an ad hominem … the crackpottery is impossible to ignore." — the post's author

Why the boundary holds

The usual shape of these arguments is a flame war between true believers and dismissers. This one inverted it: the dissenters mostly ratified the author's central distinction, each from their own vantage: a mathematician on the pedagogy, a reviewer on the literature, a rigging engineer on the one job where the product shines. The reason the consensus formed is that Kritchevsky didn't ask people to pick a side on GA. He handed them a scalpel that separated the part that works from the part that doesn't, and almost everyone, once they held it, cut in the same place.