jvvw

I've had a couple of second opinions for far less serious stuff in recent years. In both cases the original doctors suggested major surgery pre-emptively, even though they were very different types of thing.

In the first case, I decided to talk to an expert in the particular area who then ordered different tests. These indicated the issue had actually gone away completely, and I avoided surgery as a result of those.

In the other, a grade 2 ACL tear, it was less clear-cut, but I felt like the explanations given by the second doctor as to why he'd recommend against surgery were clearer and made more sense to me.

I'm glad I got both second opinions and the first case in particular, made me much more likely to get second opinions in future as well as more confident about doing so.

We're about to get a heatpump (in the UK) and our pipework is fine but we need to replace pretty much all the radiators, both the old ones, about 45 years old, and the newer ones, about 15 years old, in order to be able to heat the house to a sensible temperature.

Based on the research mathematicians I have known, I'd disagree with 'they'd probably be doing something else if they had absolute freedom over their time' for at least a large number of them, although it probably varies from individual to individual.

In the UK, you could always choose to go 'ex-directory'. More and more people did over time I think and the personal part of the phone directory got slimmer and slimmer, basically just leaving the business part.

I believe that compactness has a different meaning in topology than in logic btw (though my degree was so long ago now that I'm rusty on it all!).

I do find it implausible that you'd need the type of background that I had in logic back then, which included the type of stuff mentioned, for doing stuff in Lean though.

Having got a tutor for one subject for one of my children, I'd say that tutors are about motivation/structure/instilling confidence not just subject matter. Our tutor has been great as a general mentor during the period leading up to exams, not just as a subject expert.

I have experimented a bit with AI and have found that AI isn't always great at catering precisely to the syllabus/marking criteria of a specific exam boards even when you give them all the docs publicly available (although I haven't tried frontier models). Somebody who has worked as an examiner for the exam board knows the tricks for how to structure longer answers to both get the marks and to not waste time in the exam. Of course, it may be that I haven't prompted well enough, but if I can't manage to do that, then I probably can't expect my children to!

As somebody who has spent a bit of time accessing archives both in real-life and online for history research, my natural reading of 'private collection' is privately-owned not private as in not-accessible to the public.

PhD in maths here, no longer a mathematician, partly because I wanted to do stuff more connected with real life.

I actually want to see interesting theories and mathematical ideas come out of proofs more than I want solutions/proofs. After all most maths doesn't have direct practical applications. So although unsolved problems are a good barometer of 'there's still stuff left to understand here', the interesting part about solving them is less knowing what is true and more 'how does this help us understand this field better than we did before?'.

I would still like to know if the Riemann Hypothesis is true though!

I think intuition is hard to test in a way that feels 'fair'.

You can do it - I doubt you could have got a first when I was at Oxford just by learning and understanding the material, but you should probably have been able to get an upper second. The final part of every question virtually always involved insight, but you'd obviously then have to prove what that insight helped you understand.

If you give people questions like those, there is the risk of complaints about the university not having been taught the material for the exams I guess, or you might find that nobody can answer those harder intuition parts. Certainly most students at Oxford couldn't answer that many of them - you needed to answer about three 'final' parts out of about ten questions say in each three hour exam to get a first and perhaps about 20 percent of students got firsts?

It might still be a bit too early to tell I would have thought - Scratch 2.0 was released in 2013 so a child who was 7 when that was released would only be 20 now. It might also be hard to disentangle from the effect of AI on early careers in programming these days.

I have mixed feelings about Scratch but it does engage children more than most other tools out there and I suspect its value isn't so much for the children who would have become programmers come what may, but in terms of increasing a baseline understanding of some programming concepts in the more general population and helping some children discover they enjoy programming who never would have done otherwise.

It's very hard to not give them internet access at all though even if you don't give them a phone, because they need it for homework and you can't and don't want to supervise them every moment they are doing homework.

A lot of parental control systems stop working when they turn 13 so you have a system that works fine and then suddenly it stops working. I know a lot of parents who have complained about this.

Likewise at Oxford - only the final exams counted (though you had to pass first year exams to continue to the second year).

But you had tutorials each week, and if your tutors thought you weren't doing enough work they could set you exams mid-course called 'penal collections' and if you failed them you could be thrown out. They were rare but definitely not unknown.

I do feel that if there were actually decent parental controls on the most used systems out there then we might not have got to this point in the first place! It is either a nightmare or impossible to set any sort of sensible controls on internet and social media access for children and teenagers.