I may be misremembering, but I think we had simple topology, linear programming (mainly just 2D, but I remember a 5D problem at the end of the section), matrices with eigenvalues and eigenvectors, set theory, and a bit of group theory. No programming, though there was some in the text book. It was pretty good fun. I don't remember anyone finding it conceptually difficult.

It would also be worth mentioning Nuffield Physics. I thought that was a really great course for learning how to do physics. Very oriented towards finding solutions, devising experiments.

I don't think we're talking about the same thing. New Math was targeted at elementary school students.

If you're having a hard time squaring that with "cardinality" and "set theory"... yeah, that would be the problem.

Also if they did have identical sizes and there was a need to measure those sizes, we would expect a lot of much simpler devices to measure them - say a flat piece of metal with differently sized holes. Fancy versions like the dodecahedron might exist, but they would be outnumbered by the utilitarian devices.

And on the number of the pegs. And five pegs would be far too few for practical purposes.

Coming up with a possible use is a very long way from being able to declare this "solved". There are many such claims. For the idea you discuss, a problem is that the projections were balls - not the easiest of things to dislodge loops from, which you would have to do at every step.

You don't need 12 holes of varying sizes to hold a candle, and these would have been disproportionately expensive to make for that role.

The problem is that one can poke similar holes in other proposals. Personally I favour the "proof of skill" explanation but there are also arguments against that.

RPL (Reverse Polish Lisp, a high level language for HP calculators) possibly drew on it a bit, though the main antecedents are RPN and Lisp, and possibly Poplog (a Poplog guru was at HP at the time, but I don't know if he contributed).

Chief Dexitroboper.

The other thing I would hope for is wildcard certificates. I stopped using S/MIME because I usually create a new email (based on the same domain) for each vendor that I deal with. I would find it useful to be able to get a single certificate covering all email with that domain. Obviously that does mean that anyone else using an email from that domain would have to share the certificate, but for private use that can be acceptable - I don't worry about my wife reading my currently unencrypted email!

OTP via SMS: depends on the country. These days it's not very common in the UK. They often ask for an email address, but my experience is that most of the time they don't check it for validity.

Not for Mac. MacOS is an open garden: there is an app store; or you can install signed apps (requires Apple cooperation); or you can install unsigned applications. MacOS gives you a nudge to the app store (which has genuine advantages) and a much stronger nudge away from unsigned non-app-store apps, but it is still an open garden. iOS is closed garden, which makes some sense for the security guarantees it can give for financial applications.