l__l

how does this differ from alternatives like Hardcover, Fable, etc.?

This oughtn't be super surprising, even the DE comment at the end - people do just have bits of maths they gel with more than others!

Even so, CT is not easy to motivate without a lot of experience in a few specific areas of maths - it's definitely a very "meta" subject (even though a lot of these blogs pretend it's super applicable to everyday engineering) and is a very different lens from the maths taught up to that point.

I'm surprised to see no mention of topos theory in this page? The sense in which category theory is a generalisation of set theory is pretty weak imo until you bring in concepts like subobject classifiers. This isn't the only thing topoi generalise, but is a pretty significant one

I know it varies by topic, but my experience asking ChatGPT about things I already know about (eg a smattering of topics in algebra) was bad. Like, bad bad. It got the intuition completely wrong, and asking for more explanation just got you complete garbage that ignored everything except the most trivial cases. Just be careful for anything outside of a 101 class!

Not commenting on whether it's good/bad, but I think it's completely different to your examples. Both of those say "here is context of my past achievements; this is an indication that what follows may be of high absolute quality"

As opposed to the "I am N years old", which is saying "here is context, which doesn't by itself indicate achievement, which may be an indication that what follows is of high relative quality"

Last I checked this was opt-in on Android; it's been default on iOS since I think 2017ish?

I remember using this site for checking my work in a number fields course years ago; I never realised it had so much more

Very weird seeing this on the front page

That's not the best way to view it. You can prove it by showing that for an n-dimensional disc, there is no contraction to its boundary; which I think is a bit more illustrative of what this FPT is doing

Cool! I love collections like this :) A 10-min format and sort (alphabetical or chronological) would make this so much more scanable though

I honestly don't know. This might be a skill issue on my part (very much not an educator), but I think of it as a language for thinking about structural abstraction, so to me the question is akin to "is there a real-life problem that German relates to?"; I can certainly think of lots of problems that would be made much much easier by understanding the language (e.g., getting around Germany, i.e. noticing abstractions), but it's tough to point to anything for this explicit question other than "conversing with someone in German".

I guess to try and mirror your calculus example, I'd try and motivate why someone should care about abstraction itself, perhaps with examples like 'calculating my taxes each year is exactly the same problem, except the raw numbers have changed'.

Alternatively it might go over better to say something like: "Imagine you have a map with a bunch of points, and paths which you can walk between them. CT is the study of the paths themselves, the impact of walking down them in various routes: for mathematicians, this means looking at things like turning sentences such as 'think of a number, add 4 to it then divide by 2 then add 6 then subtract 1' into 'think of a number and add 7'. Once you've spotted this shortcut on this silly toy map, you'll recognise the same paths and the same shortcut when you see on your tax form 'take your income, add £400 to it, divide by 2, add £600 and subtract £100"

This is my field :)

Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from this perspective, is pretty clear.

As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work.

There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.

This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems.

(Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)

Not a solution but FWIW, in my time working at Apple, they encouraged you to log in to work devices with your personal ID (with the expectation you don't allow files to sync). There were some people who kept them apart, but the overwhelming majority just used their personal with no issues. Personally I made a new one, but at the time it was my first Apple device so wasn't really a decision.