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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!

I recommend map-making-app for wandering around (https://map-making.app/) which is what all serious geoguessr players use.

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.

In maths, if you do well enough in the exam, you have to really mess up the interview to not get in though I would say. If you're borderline, the interview is important though - the interviews will usually be 95% maths questions so it's more like doing an oral exam where you have to explain your thinking process and answers.

Having interviewed maths applicants for Oxford, I don't think it's just corruption or biases - there are just more really bright students that you have places for and have to reject some people! We all tried really hard not be biased but I don't think there is any way to guarantee that you aren't somehow, however hard you try.

It's very hard to predict from a half hour interview precisely who will do well in future, and in fact some people might do better having gone to other universities. Oxford and Cambridge aren't the best choice for everybody - I'm sure being a bigger fish in a smaller pond suits some people better.

When my son was about 4 or 5 he used to draw pictures with pens in both hands simultaneously which I was always amazed he could do!

I am a fan of Anki for lots of things but it always puzzled me people trying to learn analysis and group theory by memorising lots and lots of parts of their lecture notes.

I would test myself on the main steps of some of the proofs before exams but that was the nearest I got to memorisation. It felt like if you needed to memorise definitions then you hadn't used them enough. Even 30 years later, not having done maths for most of that time, I could still tell you the most of the definitions and could still do an epsilon-delta proof - they feel like conceptual things rather than memory things.

Perhaps I was in a way doing spaced repetition just by trying to solve lots of problems and looking things up if I didn't know them but it didn't feel like a memorisation process, more a process of trying to really really understand the mathematics.

I don't agree with age verification, but there isn't anywhere 'set your children's ages in their device accounts' that limits their access to inappropriate content and social media.

You can set age in Google Accounts, but they can access pretty much anything when they reach age 13 (which is about the age a lot of these things start to become a real problem) and as a parent you don't have any way to limit that. They don't even need to ask to install new phone apps.

Children also use computers as well as phones and you don't want to stop them using a web browser! You also obviously can't supervise them every moment they are online even if you wanted to.

Thanks! That's interesting. It is only for pre-teens, but it's certainly a start. I do wondering if all the threats of legislation might finally encourage tech companies to actually come up with sensible solutions for parents.

Ah that makes more sense then!

Anecdotally from personal experience (gave birth to one child on back, the other in a squatting position, didn't have an epidural for either), the pain didn't depend on position - very painful both times! But pushing felt much much easier squatting than on my back.

The hospital only had two rooms suitably equipped for giving birth in a squatting position, so I was lucky to get one second time.

It's a bit weird to see the BBC reporting on this happening in Finland, when plenty of 'Libraries of Things' exist in the UK! I think they tend to be run as community efforts rather than by public libraries. though.

Children obviously access the internet in other ways too - it's not uncommon for them to share computers with adults or even access the internet via the family television. I definitely remember during covid, most children would be on their parents' computers. Although it would still definitely make sense to do something at the phone level regardless.

I think when something is an issue for 90% plus of children (which I think this is probably is in some form), then it's not something we can blame entirely on parenting.

I seem to have struck lucky with a child who didn't want a mobile phone, but he was one of only two or three children a year of 200 at school that didn't have one. I can see that it's hard to deny your child something that every other child has and phones are useful when your child starts becoming more independent. I certainly wouldn't do a long journey without my phone myself. We obviously managed without phones as children, but if your child is going to school on public transport, I totally understand wanting them to have a phone in case of problems.

The apps and websites often have good (or relatively harmless!) parts to them e.g YouTube has tons of brilliant educational videos. There is no easy way as a parent to give them access to the good parts without access to the more harmful parts. You don't want to be a total killjoy and never let them play a computer game (plus playing games with them is fun!). Schools require internet usage for homework. You end up in lots of awkward grey areas. Is watching a video about building logic gates in Minecraft ok? If so, then what about Minecraft videos generally? You can't pre-vet everything they want to watch and then supervise them closely to make sure they don't stray from that.

It feels different from smoking/alcohol because there are so many grey areas and there isn't quite as clear evidence as to what exactly is harmful. Ideally you try and prevent your children smoking and drinking alcohol with education and setting a good example rather your wrath. That's trickier with social media.

I think the current proposals are non-ideal but a bit of a desperation measure because nobody has come up with anything better.

Round here they have a locked pouch they have to put their phone in during school which seems to work reasonably well (although I'm sure not perfectly). It makes it more clearcut if they do find somebody with a phone not in their pouch anyway that they've definitely broken the rules. They get locked at registration at the start of the day and then unlocked when they leave school at special points.

Regulation does add friction. And it makes it easier for a parent to say 'no, you aren't allowed that app' (which you can obviously say anyway, but it gives you a very solid and non-negotiable reason to say no). Some children will find their ways round things, but a lot, if their friends aren't using a particular app, won't bother, or they will be the type of children who won't try and break the law.

Most apps and sites are terrible in terms of the parental controls they provide - they tend to be all or nothing. E.g. I'd like to have a group for our family on WhatsApp but I don't want my children to be able to join random WhatsApp groups and there isn't any way to have the former and not the latter.

Homework requires internet-connected devices (I guess you can semi-supervise that, but it becomes harder as they become older as you don't want to sit there watching them do all their homework).

There is also a cost socially, which is hard to navigate as a parent. If everybody is talking about minecraft every break and playing it together in the evenings, then it's hard for them if they haven't even seen the game.

It already exists in the schools near where I live in the UK, but only came into place in some of them in the last year. I was surprised that they had been so slow about it.

The vast majority of research-level pure mathematics is never going to get used in science or engineering. Obviously it is hard to predict what will be useful, but for the type of mathematics that is unlikely to be, there is a question as to why we care about it, and that almost has to come down to beauty in some sense - some mathematics gives us a new lens to look at parts of the mathematical world and others chip away at problems in more mundane ways in the hope that they inspire or contribute to new parts of mathematics that are beautiful.

Games stuff for me too - geoguessr in my case. It'd never have been worth putting in the time to build them without AI but so easy with AI.

The employers will think it requires less skill, whereas in fact it might actually require more skill to do a good job of being the human-in-the-loop.

For example, my sister is a translator and she says that checking AI translations is actually harder in many ways than doing a translation in the first place, but the agencies pay less for checking than actual translation.

As a parent of teenagers, I feel like the sites make it hard for parents.

When they were young, you had a choice between YouTube being completely locked down with no option to whitelist channels or letting them watch almost anything (although I think this has changed since but it's too late now for those of us with children that age).

Now, there is no way I can whitelist contact/groups on WhatsApp or Discord servers/friends. Once they hit 13, pretty much any option to restrict anything feels taken away from you as a parent.

Luckily, I have sensible children (I think!) but it's really hard as a parent trying to both be reasonably responsible, but not deny all technology, it's really hard to navigate a sensible course.