Say what you want of Stephen Wolfram, but he's an interesting person doing interesting things - and managing to finish a lot of them.

A bite-sized idea I liked from the long article: "the very act of exposition was a critical part of organizing and developing my ideas".

I've arrived to the same conclusion for myself (and this article, hopefully, will be the last straw for me to start writing in an organized manner).

My only moderately-successful writing so far has been my ADHD wiki[0], which, in the spirit of Stephen Wolfram, I will shamelessly promote here and now (I've gotten some marvelous feedback from HN in the past, and I believe it to be a useful resource to many).

FWIW Stephen not merely boasting about productivity; a fair bit of the article is dedicated to talking about techniques and tools that he believes help him with that.

While his article on Computational Essays[1] is mostly a Mathematica ad, Mathematica is a great system (which have influenced things like Jupyter notebooks a lot), and the idea of literal programming and interactive data/code/writing is a solid one.

We have yet to have a solid collection of resources like that even for teaching mathematics (where it's natural to play with code to experiment with ideas).

Another bit I liked: and yes, one seems to be able to see the essence of machine learning in systems vastly simpler than neural nets. Sure, we all know about that cellular automata are the Woflram's thing, so it's not surprising to see them pop up in his article about minimal learning computational models[2], but I feel an article like that has been way overdue.

We've been playing with neural nets long enough without having a solid idea what's really going on, and it's limiting to use them as legos of sorts. Why these blocks in particular? What else is out there?

The ChatGPT explainer that he mentioned[1] is still my go-to article for learning about it; I think I'll add another one of his to the list.

Finally, the bit one why history is important - and finding out his archive of writing on history of math and science[4] is great. I believe that history is the most underappreciate science itself, and learning science without its history leaves you without either context or deep understanding of it.

(Personally, I add etymology to history: I find resources like "Earliest Known Uses of Some Mathmatical Terms"[5] invaluable).

And, of course, it's great to see that he's diving into linking mathematics, computation, physics, biology. Great discoveries often lie on the interfaces of various fields.

As Vladimir Arnold wrote in his famous essay[6], divorcing mathematics from physics has been a phenomenal crime. I'm guilty of it too. I recently made a post on reddit[7] with a GIF showing the osculating circles and the evolute of an ellipse. It's pretty, but what is really hiding behind it is the shape of the gear tooth which nearly all gears have.

I learned (and taught!) the mathematics behind it without having any understanding how gears are designed and why they work. And people who make gears make them without understanding the math behind the equations. This came up at work (I'm working on implicit CAD modeling), and from a discussion a better understanding (...and a better product) emerged. There is no reason for narrow specialization that creates barriers in fields that aren't just related, but are necessary for each other - so I believe that the mere fact of Wolfram doing this work is important.

Maybe he'll find out something groundbreaking in those directions. Maybe not. But I can guarantee that he and people around him will stumble into fascinating things along the way that they wouldn't encounter otherwise.

Lord Kelvin thought that what makes atoms different is how they're tied into different knots. That turned out to not describe the reality of atoms at all - but gave rise to knot theory[8], which has since gained a fundamental ground in mathematics, particularly - topology (you can construct any 4-manifold by removing a tubular neighborhood of a knot in 3-sphere and gluing it back with some twists - see Dehn Surgery[9]). So, while Kelvin did not find what he was looking for there, the direction his effort has jump-started may, in fact, fundamentally describe our reality - as we have yet to learn what kind of manifold structure our universe has. And knot

Anyway. All in all, good, thought-provoking article (this comment, which contains some thought at least, is a testament to that); I'd recommend looking beyond the title and looking into the things Wolfram mentions. There's a ton of interesting tangents there.

[0] https://romankogan.net/adhd

[1] https://writings.stephenwolfram.com/2017/11/what-is-a-comput...

[2] https://writings.stephenwolfram.com/2024/08/whats-really-goi...

[3] https://writings.stephenwolfram.com/2023/02/what-is-chatgpt-...

[4] https://writings.stephenwolfram.com/category/historical-pers...

[5] https://mathshistory.st-andrews.ac.uk/Miller/mathword/m/

[6] https://www.math.fsu.edu/~wxm/Arnold.htm

[7] https://old.reddit.com/r/math/comments/1f1yblk/evolute_of_an...

[8] https://en.wikipedia.org/wiki/History_of_knot_theory

[9] https://ncatlab.org/nlab/show/Dehn+surgery