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I don't have any post graduate education. I'm ok at math, but not exceptional. I managed to publish a paper a few years ago that is mostly a math paper that I'm really proud of. https://arxiv.org/abs/1809.04052 (It's a useful algorithm for big-data work, but it's also a bit of math about how to align probability distributions so they collide as much as possible. I tell my kids that daddy discovered something new about how triangles fit together.)

There are lots of useful corners of math out there, lots of things that are worth thinking about that no one has thought about just because there are so many things to think. There are plenty of things worth poking at that aren't The Big Problems.

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You like math? You do math? Guess what? You're a mathematician, regardless of post-graduate education or self-assessment of your ability!

(I love to see 'amateur' mathematics, not in the derisive sense of the word but in the formal sense of "not done by a professional mathematician". Good on you!)

I love this quote from a follow up paper:

> Interestingly, hash algorithms with collision probabilities equal to JP have already been unintentionally presented before JP was actually discovered and thoroughly analyzed in [8]. In [7] a data structure called HistoSketch was proposed to calculate signatures for JN ... after some simplifications and thanks to a nonequivalent transformation that eliminated the scale dependence, the final HistoSketch algorithm had a collision probability equal to JP instead of the originally desired JN.

It's none the less a very interesting measure. Thanks for sharing!

I recently worked on a project trying to determine "the best" locality sensitive hashing amoung all measures of similarity for sets: https://arxiv.org/abs/1904.04045 I wonder if something similar could be done for probability distributions. It seems hard.

Your paper is lovely and your work is valuable. Thank you for pushing the envelope just a little bit. Our modern world is built by as much of things like this - that push out science but by bit, as it is by advanced measured in monumental leaps and bounds.