Thank-you I’ll look into it.

Practical users of math have already switched by virtue of the fact that programming applications or spreadsheets requires entering formulas in a textual format.

And how can you imply that enjoying the benefits of a computer do not qualify as a massive advancement? Infact it’s such a massive improvement that practical users of mathematics have already switched.

Likely what drags US education down is the underlying notion that things must be ‘fun’ for children to do them. Most of the highest-achieving education systems are significantly less technology- and fun-orientated than the US system. And you can hardly argue that the young adults who emerge from these systems are psychologically scarred by the lack of ‘entertainment’.

Oh, and regarding note-taking: I’d argue that there’s a strong distinction between the need to record notes and the ability to use those notations in an ‘active’ or ‘computable’ form. Until very recently there was no ‘self-computing’ notation at all simply because everything had to be processed by a human. The idea that a notation should be machine-readable is obviously a fairly recent one (whether by ‘recent’ you imply either Turing or Leibnitz is fairly irrelevant in the grand scale of things). Arguing that notation must be machine-readable and ‘standard’ is somewhat inconsistent.

Standard mathematical notation is wildly inconsistent already (witness the confusion that arises when students first encounter subscripts and ‘powers’ in tensor notation); I don’t see any reason why this inconsistent ad-hoc hodgepodge should be protected to the extent of impeding further advancement.

I disagree.

Usually (though not necessarily) it makes students dependent on mysterious ‘black boxes’ and engenders them to become dependent on one implementation and it’s quirks. Technology should only be introduced gradually to provide ‘shortcuts’ for that which is already understood but tedious to perform.

And never, ever, should we promote reliance on technology. If we provide students with tablets and on-screen keyboards and spellcheckers, are we going to exempt them from having illegible handwriting and awful orthography when we examine them? Or are we going to examine them on tablets, allowing millennia of calligraphy and writing skills to be lost?

People, we’re technologists. It’s fine for us to love gadgets. It’s harmful for us to try to use technology to solve every single problem - particularly problems that either don’t exist or have arisen precisely because of technology.

Most of the most proficient education systems are significantly lower-technology than the current US system. I think that is no coincidence.

I hadn’t realised (and don’t quite accept) that I am unusually ‘flexible’ in using text-mode mathematical entry. Indeed I think you’ll find that if you consider the sum total of programmers and spreadsheet users most non-academic users of mathematics are already using non-traditional notations for mathematics (though, I do readily admit, spreadsheet formulas and program statements are not terribly convenient for deriving symbolic statements).

Notations do change, have changed, and will change again - consider for example the switch from Roman to Arabic numerals. That brought a huge boost in convenience, sufficient to promote the adoption of the unfamiliar new notation.

Anyway, it is education that we are talking about here. Quite distinct from the fact that I do not believe adding more technology to the mix is the solution to a (non-existent) problem, I think you’ll agree that since education teaches ex nihilo, we can easily teach new learners whatever new notation we please, and it will be accepted by them as the norm. Provided they are sufficiently acquainted with the old notation to translate from it (and into it) if and when the need arises, there is no disconnect in their experience.

I absolutely agree.

Let’s remember that all those figures in history (both recent and remote) whom we admire were educated the old way: by one-on-one contact between educators and children. Tech industry’s drive to replace that quintessentially human bond with mechanistic devices strikes me as fundamentally misguided.

Wanting better technology is fine. However the best technology for dealing with people (particularly kids) is still other people.

It seems like we’re on the verge of institutionalising autism.

I don’t really agree with that I’ve been using the full gamut of Computer Algebra Systems (CAS) ranging from Macysma to Mathematica to HP Prime for years, and I find text-only entry to be very comfortable. Mathematica even has photoshop-style palettes if you wish to choose familiar notations.

Don’t confuse mathematics with mathematics notation. The latter is totally arbitrary and can easily be replaced, most obviously by the various prefix notations common in CASes ( Integrate[x^2,x,a,b] , for example).

The future of education is human teachers teaching human kids.

Please stop using prospective educational uses to justify technolust. There’s no harm in wanting better gadgets, but there is harm in fixing things that aren’t broken.

The best thinkers in history were educated by people. I see absolutely no reason to replace competent, compassionate humans with impersonal and inflexible machines.

This reminds me of a time when an online translation tool mistranslated ‘condone’ as ‘condemn’.

Based on my limited understanding, proving P = NP would not necessarily and automatically provide a manner of constructing reductions. It might. But there are proofs in computation theory that demonstrate limit complexities but do not provide the algorithms that might implement them, nor do they (currently, visibly) provide any indication of how that algorithm may be arrived at.

Besides, proving P = NP would have a vast number of consequences that would echo across mathematics and the more fundamental sciences. To harp upon the security implications is as short-sighted as fretting that all-out thermonuclear war would negatively affect the postal delivery service.

I wish I could mod you up.

Not only that... as I understand it, the underlying technology was a breakthrough for the time. It was one of the first cluster-based web systems. Those things are a dime a dozen nowadays but much of the foundation work derived from those early experiences.

Because in the late nineties it was rather impressive, and the layout appealed to my WIRED-intoxicated, angsty-cypherpunk teen self.

In at least an infinite subset of the infinite number of universes it straddles, yes - but most likely not this one.