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Thanks to this I know that there is exactly 1 way of positioning 0 queens on 0x0 chessboard without any two of them attacking each other.


There is Artin's approach, and then there is a more abstract approach by Grothendieck relating to the fundamental group of algebraic topology.

In the movie Beautiful mind there is a scene, where a student tells John Nash that he can proof that 'Galois extensions are the same as covering spaces'. This follows from the Grothendieck's approach. However the analogy between Galois extessions and the fundamental group was known even before Grothendieck.

Then there are even more general approaches in the category theory setting.

Today these generalisations are taught indeed without much regard to the computational spirit of 19th century mathematics. They have their merit as you say, but I agree understanding the computational aspects are instructive in fully appreciating the generalisations and analogies.


Very true. When I was doing PhD in pure maths I had random people explain to me that a PhD would not necessarily give me an advantage in the job market. Like I would come to do a PhD without figuring that out.


I have found that having a PhD in pure math has been enormously helpful in making me look more attractive to the job market.


Not specifically in pure maths, but agree I also found that a math PhD is good to have for jobs in AI, finance etc. But an equivalent industry experience might be worth the same at least.


For what sort of jobs?


For me, data science, quantitative finance, software engineering jobs. A large part of software development is about identifying and building abstractions to solve problems, which is also what mathematicians do. A common sentiment I've seen expressed by hiring managers is that someone with a strong math background can become very competent in a wide variety of technical fields.


I know several PhDs who actually thought a doctorate in music theory or similar fields was a ticket to a good job.


Samuel Eilenberg, one of the founders of category theory, used to tell to his students "You should have you own category". Meaning, that when you work on category theory you should have in mind applications to something. One of his students used to say "my category is Cat". Cat means the category of categories.


To what extent can you get into category theory or homotopy type theory without learning some algebra or algebraic geometry/topology?


"Algebra" by itself doesn't appear on this map. Clicking through and reading some of the descriptions, my impression is that this was not created by mathematicians.


Perhaps being recorded was a big deal back then. So they made more effort. Today it is common to have ones speech recorded, even for mass media.


One of the highlighted characteristic of this recording, is it is a live conversation, not something rehearsed.

So, while what you said may be true for radio broadcasts, I am not sure it is at play here even if the interviewee knows he is being recorded.


In 1912, the recording equipment would have been quite conspicuous.


To be honest, the most disadvantaged are the native English speakers. Nobody understands them.


The idea that people with darker personalities will succeed may also be a perception bias.

According to this article we are talking about 20% of people with some degree of "dark traits".

Of course a group this large will intersect with the most successful portion of the population.

And, successful people with bad traits are likely to stand out in peoples perceptions.


It is not true that traits that are not advantageous are unlikely to be maintained over many generations. For example, many genetic diseases have survived for many generations. This may happen because, for example, they correlate with some other more positive traits. Or, because of other indirect, external factors.


How do psychologists measure personality traits to classify people in these kinds of categories (dark/light)?


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