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akalin

akalin on Hacker News

Re:Claude Fable produced a counterexample to the Jacobian Conjecture on Wednesday July 22, 2026 @06:25AM (#49004470)
In this case, the same way I would -- calling out to SymPy.

Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.

Re:Multiplicative Infinitesimals on Thursday January 09, 2025 @01:23AM (#42642177)
I'm partial to Caratheodory's definition of the derivative, which avoid limits like the infinitesimal approach, but doesn't pull in all the extra baggage that come with infinitesimals (if you do it rigorously).

djb (yes, that one) has a pretty good primer on it: https://cr.yp.to/papers/calculus-19970403-retypeset20220326....

Re:Getting the Lorentz transformations without requiring an invariant ... on Saturday November 11, 2023 @04:37PM (#38234805)
I think what's left unsaid in the paper is that if a Lorentz-invariant speed exists, then it is unique. (This is easy enough to show.)

Therefore, once you show that the speed of light in a vacuum is Lorentz-invariant, then it has to be the unique Lorentz-invariant speed (i.e., the universal speed limit).

Re:Ask HN: Could you share your personal blog here? on Tuesday July 04, 2023 @03:32PM (#36591540)
https://akalin.com

I write very infrequently, but my favorite posts are:

- Why is the Quintic Unsolvable? - https://www.akalin.com/quintic-unsolvability

- A Gentle Introduction to Erasure Codes - https://www.akalin.com/intro-erasure-codes

Re:Examples of common false beliefs in mathematics on Monday January 31, 2022 @03:47AM (#30145906)
It's just unfortunate terminology -- a closed set is one whose complement is open, not one which is not open.

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