My answer to a question on Quora: Why is school 8 hours long?

Admittedly it was in primordial times, but, in my country, at my time at primary school (7 to 11 years old), school day was 4 lessons of 45 minutes long, with two breaks of 10 minutes and one break of 25 minutes in between, from 8:30 to 12:30 in the morning. There was some homework, but not very taxing. A plenty of time was free for whatever children wished to occupy themselves with. Parents were at work until 17:00.

A short school day is actually a physiological norm. Why in the UK, say, school day is abnormally long? Because it is an offence to leave children alone; the law is vague — The law on leaving your child on their own, but it applies with unnecessary, in my opinion, rigour. Schools are forced to act as storage rooms for children while parents are at work.

Of course, in old times there were risks involved; legs and arms could occasionally be broken while skiing (unsupervised), or playing ice hockey (also unsupervised), etc., but these were very rare events, and were seen as unavoidable and normal risks. There were no modern culture of over-protection which would, of course, cut accidents — but at expense of loss of child’s precious independence. Analysing now my and my friends’ behaviour of that time, I see that we were quite risk aware and knew how to avoid danger — it was a normal part of growing up.

My answer to a question on Quora: How many years could it take me to study and understand all the mathematics fields that exist so far?

If you mean understanding at the level of ability to do research work in every field of mathematics, then, I am afraid, there is no hope to achieve this goal. Mathematics expands, and the cutting edge of mathematical research moves further and further away from any fixed reference point, say, undergraduate mathematics. From the point of view of an aspiring PhD student, mathematics looks like New York in the Capek Brothers’ book  A Long Cat Tale:

And New York – well, houses there are so tall that they can’t even finish building them. Before the bricklayers and tilers climb up them on their ladders, it is noon, so they eat their lunches and start climbing down again to be in their beds by bedtime. And so it goes on day after day.

It was written in the first half of the 20th century, but Joseph and Karel Capek understood thing or two about futurology (although the term “futurology”, most likely, did not exist in their time): they were the people who coined the word “robot”. We live in the world where, in almost every field of human endeavour, no-one can understand everything. The human civilization that we transform and build is immensely complex, and mathematics is perhaps its most complex part.

[For this post, I cannibalized some bits of my paper Mathematics for makers and mathematics for users; it discusses some relevant themes.]

The famous geneticist James Watson, of the double helix fame, about his relations with mathematics:

All through my undergraduate days I worried that my limited mathematical talents might keep me from being more than a naturalist.  In deciding to go for the gene, whose essence was surely in its molecular properties, there seemed no choice but to tackle my weakness head-on.  Not only was math at the heart of virtually all physics, but the forces at work in three-dimensional ;molecular structures could not be described except with math. Only by taking  higher math courses would I develop sufficient comfort to work at the leading edge of my field, even if I never got near the leading edge of math.  And so my Bs in two genuinely tough math courses were worth far more in confidence capital than any   I would likely have received in a biology course, no matter ;how demanding.  Though I would never use the full extent of the analytical methods I had learned, the Poisson distribution analyses needed to do most phage experiments soon became satisfying instead of a source of crippling anxiety. [From J. D. Watson, Avoid Boring People , Vintage Books, New York, 2010, p. 51]