kkylin

Related & of interest: https://xenaproject.wordpress.com/2026/07/20/human-mathemati...

Actually we weren't (& aren't) able to afford this kind of thing. Dad worked for the airline & somehow got this perk, just once.

We got front lower deck seats once when I was a kid. My sister and I had extra open floor space for playing. It was great.

Bott is often quoted as saying "Evrey mathematician has a secret weapon. Mine is Morse theory." Every time I see his name I've tried to look up a source. Finally found one:

https://mathoverflow.net/questions/100316/raoul-botts-quote-...

Anyway if you enjoyed this you might also enjoy

https://www.numdam.org/item/10.1007/BF02698544.pdf

Slightly off topic (since there's already been so many better answers than I can write), but our knowledge of the dino-slaying asteroid came much later: https://en.wikipedia.org/wiki/Alvarez_hypothesis

I really do think the incompleteness theorems deserve the attention they get, not just because of what they say about efforts to formalize mathematics and because of the historical context -- remember Gödel numbers came (just) before Turing and the first recognizably modern electronic computers. That numbers can represent things that are not numbers was (IMO) a revolutionary idea.

Having said all that, I'd taken mathematical logic in college to learn about incompletenss, but the most interesting things I got out of it were completeness and compactness. Non-standard models really can be quite interesting.

In addition to the above links on quasicrystals etc, it may help to have a bit of context on periodic tilings, which have very precise mathematical properties: https://en.wikipedia.org/wiki/Lattice_(group).

The structure of the periodic table itself can also be understood, to leading order anyway, in symmetry terms. See for example https://mathstodon.xyz/@johncarlosbaez/112540366778806757 and references there.

Of course one reads a (nice) post like this and must add one's favorite not on the list. Here's mine: https://en.wikipedia.org/wiki/Fouquieria_columnaris

I had an even older iPad I was happily using for similar use cases. Until one day a family member bricked it and I needed to factory reset. No big deal, I thought -- nothing important on it. Turns out it needed to phone home to do the factory reset, and since the server it wanted to talk to was no longer up (or perhaps the address changed?) I couldn't factory reset the iPad.

If someone has a work-around I'd love to hear it. Until then, or until Apple changes this design, I think I'm done with iPads. I don't want to pay that much to "own" something that Apple can simply make obsolete by reconfiguring or turning off a server somewhere.

Edit: fix typo

In my couple decades as an academic mathematician I've only ever met one. He was a strong advocate, and got me to install & try it, but I could never convert to using it fulltime.

I've had the same dream! thanks for the pointer.

Yes, 1.00 was popular with Course 6ers who wanted easy units.

Not just bears it seems: https://www.scientificamerican.com/article/raccoons-are-show...

Came here to say this -- looks like the data assimilation is still done the "old fashioned" way. I wonder how long that will last?

Yup. Back in my day there was 1.00, a Civil Engineering course, a pretty standard intro to programming in plain old C. I don't know if it still exists. There was nothing of that sort in EECS, though there are lots of IAP courses (which take place in January, before spring semester starts). IMO a month is about right to spend on (leisurely) picking up a programming language for fun. A friend and I learned APL that way.

We've still got this:

https://en.wikipedia.org/wiki/Eunice_aphroditois

Thankfully they don't live on land.

I have been using mu4e for years, and am generally happy with it, and yet... I've never recommended it to anyone else. Unlike, say, org-mode or magit, which I'd happily evangelize.

The pain points are what other commenters have said:

- I don't find the default config a good fit for me, and run it heavily customized. As someone said everything in Emacs turns into a project...

- Performance can be an issue, especially indexing new mail (and especially if you like to lug around a copy of most of your emails locally as I do). On a laptop while traveling this used to be more of a problem, but newer versions are notieably quicker and newer laptops have better battery life.

- HTML rendering isn't great. Thankfully I don't get too many important messages that isn't just plain text. This might be a reasonable use case for xwidget-webkit though I'd imagine there are security/privacy issues to work out. (Another Emacs project -- yay!)

When I started I thought it would be an efficient way to get through lots of emails, and it has been for the most part. I'm just not sure I've saved time overall unless one counts the hours configuring it as "entertainment / hobby" rather than "work".

:-)

I don't question this decision is sometimes (often) driven by the need to increase publication count. (Which, in turn, happens because people find it esaier to count papers than read them.) But there is a counterpoint here, which is that if you write say a 50-pager (not super common but also not unusual in my area, applied math) and spread several interesting results throughout, odds are good many things in the middle will never see the light of day. Of course one can organize the paper in a way to try to mitigate the effects of this, but sometimes it is better and cleaner to break a long paper into shorter pieces that people can actually digest.

That's exactly right. A couple more things:

- Differenting a function composed of simpler pieces always "converges" (the process terminates). One just applies the chain rule. Among other things, this is why automatic differentiation is a thing.

- If you have an analytic function (a function expressible locally as a power series), a surprisingly useful trick is to turn differentiation into integration via the Cauchy integral formula. Provided a good contour can be found, this gives a nice way to evaluate derivatives numerically.

Thank you so much for all this detail. This is very interesting & quite helpful, and it's great you were able to communicate all this with your friend.

For anyone else interested: I wanted to be able to typeset mathematics (actual formulas) for the students that's as automated as possible. There are 1 or 2 commercial products that can typeset math in Braille (I can't remember the names but can look them up) but not priced for individual use. My university had a license to one of them but only for their own use (duh) and they did not have the staff to dedicate to my students (double duh).

My eventual solution was to compile latex to html, which the students could use with a screen reader. But screen readers were not fully reliable, and very, very slow to use (compared to Braille), making homework and exams take much longer than they need to. I also couldn't include figures this way. I looked around but did not find an easy open source solution for converting documents to Braille. It would be fantastic to be able to do this, formulas and figures included, but I would've been very happy with just the formulas. (This was single variable calculus; I shudder to think what teaching vector calc would have been like.)

FYI Our external vendor was able to convert figures to printed Braille, but I imagine that's a labor intensive process.

Partway through the term we found funding for dedicated "learning assistants" (an undergraduate student who came to class and helped explain what's going on, and also met with the students outside of class). This, as much or more than any tech, was probably the single most imapctful thing.

Thanks! Did you communicate in "raw" TeX, or was it compiled / encoded for braille? Can you point me at the software you used?

Like many others, I too would very much like to hear about this.

I taught our entry-level calculus course a few years ago and had two blind students in the class. The technology available for supporting them was abysmal then -- the toolchain for typesetting math for screen readers was unreliable (and anyway very slow), for braille was non-existent, and translating figures into braille involved sending material out to a vendor and waiting weeks. I would love to hear how we may better support our students in subjects like math, chemistry, physics, etc, that depend so much on visualization.

Question for all of you more knowledgeble than I: can SMART data be tampered with? When I get, say, a refurbished Mac from Apple, I'm trusting Apple won't stoop to that. But a SSD vendor I've never heard of?

MIT Scheme (and ScmUtils) are unfortunately not getting enough maintainence, but they still work with a little effort. Probably better on Linux than any other environment. If you have a Mac you may try this:

https://github.com/kkylin/mit-scheme-intel-mac-patch?tab=rea...

Works well on Intel Macs and (with effort) mostly works on Apple Silicon.

Published paper:

https://www.nature.com/articles/s41593-025-02055-5

Preprint on biorxiv:

https://www.biorxiv.org/content/10.1101/2023.06.05.543698v1

Also, new stuff just isn't designed to be opened up.

I took an old monitor that started failing to a local makerspace (which has a very popular monthly repair cafe), and it took some physical force to crack the case open. Once inside it was relatively easy to get the board out and find the leaking capacitors. Not exactly high-tech parts.

It was fun for me and for the volunteer, but I can't imagine anyone trying to do this for a living -- it would take a lot of time, and charging people for what the labor's worth would probably come close to the price of a new monitor.

Thanks! Do you mean MIT Scheme's C backend? I've used MIT Scheme on and off for a long time and have never touched the C backend & have no idea how it works, so this is interesting.

(MIT Scheme also has a native code compiler for Intel CPUs, which seems to be what most users of MIT Scheme (an admittedly small community) actually use.)

Wikipedia has more details on the artist and the art:

https://en.wikipedia.org/wiki/James_Hampton_(artist)#Throne_...

I was trying to figure out how large this thing was (I found it hard to tell from the picture). And wow -- a life-size throne. Must go next time I'm in DC (if the government isn't shut down :p).

Well, both Guy Steele and Danny Hillis were doctoral students advised by Gerry Sussman. Whether Hillis worked on the Scheme chip or how much overlap they had, I don't remember, but as you said they were all there around the same time.

Thanks! This sounds interesting and I looked it up.

To save everyone else a few seconds: https://www.jstor.org/stable/pdf/2318338.pdf