Ask HN: I write mathematical essays. What do you want to read? | Hacker News Reader

Ask HN: I write mathematical essays. What do you want to read?

12 pointsjorgenveisdal8 comments

Hi

I have an ambition to write a book about "The Mechanics of Abstract Endeavors" in the next few years, as soon as I finish my Ph.D. To that end, over the last year or so, I've written about fourty or so essays on Medium about various math-related topics, to get into the rhythm and habit of writing daily.

Several of these essays have been featured on the front page of HN and relevant subreddits (except /r/math, they hate me), including:

1. "The Unparalleled Genius of John von Neumann"; 2. "Einstein and Hilbert's Race to Generalize Relativity"; 3. "Uncomputable Numbers"; 4. "The Mathematical Nomad, Paul Erdos"; 5. "The Math behind that Dick Joke in HBO's Silicon Valley"; 6. "The Black-Scholes Formula, explained"; and many more.

I still want to write more essays and have a bunch of ideas for topics. My next long essay will be a biography of Norbert Wiener, tentatively entitled "The Absent-Minded Father of Cybernetics, Norbert Wiener".

However, these take a fair while to write and of course are hit and miss with the HN audience, so I figured I'd head straight to the source, and ask:

- What math essay would you love to read that you still haven't read?

Thanks a bunch, you guys/girls are the best!

I think there's a ton of interesting cross over between machine learning, statistics, linear algebra, real analysis, topology etc. In the sense that there exists theorems and methods in different areas of math that are essentially the same, just different interpretations. It would be fascinating to see an exposition of this, for instance here is the geometrical interpretation of x,y,z, but actually this is the same as this theorem in calculus based statistics, except for this case...

I bring this up because there is already a ton of content about popular topics, but little that goes deep and draws parallels between disparate (not that those areas I outlined are really disparate) areas of math.

Even more interesting would be to choose common areas used in industry, like machine learning, and bring in some parallels and depth from fields that are not really studied outside an academic setting.

But then again your audience for this is rather small

A few suggestions:

— N vs NP Deconstructed and Explained.

— Prime Numbers. Patterns in Primes (like prime spirals); how prime sieves work; how mathematicians work with crazy large primes.

— Graph Isomorphism

— Topology and Topological Data Analysis

— Information Theory. Entropy. Relative entropy. etc.

Can’t wait to read your work.

I'd love to read some more optimization problems and techniques along with imaginary numbers and their applications

I would read a short article on how to read/translate complex mathematical formulas into plain English. Bonus points if you include a glossary for all the arcane symbols different sub-fields use in their formulas.

Those are some really good topics. Do you links to any of your essays?

I have been always fascinated by unsolved problems in mathematics. Have you written something before or maybe you could write an essay on one of those problems.

Google the titles and they should come up. I'm actually looking for suggestions, so didn't include links

To your question: Google "The Riemann Hypothesis, explained" and look for an older essay of mine from 2016. Still unsolved

Thanks, I will check it out.

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