dmch-1

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.

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.

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.

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?

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.

It's a joke man, why downvoting? :)

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)?

Incidentally we still have "Silk Road" today. In its modern usage it refers particularly to some oil and gas pipelines running from the east to the west.

In the latest news on the Silk Road, Azerbaijan, after its victorious war over Armenia, secured a direct land transport corridor through Armenian territory to its enclave of Nakhchivan and further to Turkey. https://menafn.com/1101103191/Another-important-issue-is-tha...

Did some googling, and came across this article about this Basque Pidgin https://core.ac.uk/reader/230764570. It contains many interesting facts. Including the passage:

"Certain surprising similarities among pidgins and creoles spoken in places distant from each other and with different linguistic components in their formation have led some linguistic to formulate a monogenetic theory that would trace many pidgins and creoles to a common ancestor: A Portuguese based pidgin or even to the Lingua Franca or Sabir spoken in the Mediterranean Basin from the Middle Ages (Whinnom, 1977)."

Even after the middle ages Portuguese seems to be an especially common source of pidgins, found in South east Asia, Africa and the Caribbean (curiously, in now Dutch territories) among other places.

Yes, yet we humans do it all right.

Some time ago I needed ball video tracking for a demo at work. I failed to find any out of the box solution which worked satisfactorily. It was way easier to find solutions for seemingly more complex tasks of people tracking or human pose estimation, for which you have numerous publically available algorithms/models.

I saw a couple of comments complaining about making people into data points, and that this is dehumanising. But I do not see this.

Growth of data based technologies and information surely create risks to privacy, which is another story. However, treating people data as just data is neither new nor dehumanising. Science does that with everything and that is called abstraction. Just make sure that personal data protection measures are there.

This is perhaps more about economic competition than data safety. China has been doing this for a long time. USA is also taking the same approach recently.

This article reminded me of when I was in academia some people used to take notes of talks with Latex, including typesetting diagrams. It was quite impressive. I tried it myself I think, but I can't remember to what results.

There has been a strong movement to more unity in Europe. But, this has not been accompanied by democratisation.

To stay competitive Europe needs unity in the political process, defense and border security for example, and not in regulations in economy, finance, immigration etc, which are excessive already.

You are asking for an advice, but it is not clear what is bothering you. You think that you are a terrible developer. What is the problem you have with this?

Do you think this impedes you in your career?

Do you feel bad about not being good enough at work?

Are you unable to follow pursuits which interest you?

Or do you just want to be better and smarter?

This types of predictions disregard human factors. Many occupations are inherently human. Digital audio is no worse than human voice, however people still go to live concerts. Computers play chess better than humans, but there are still human chess players. Besides entertainment and sports machines can never function as politicians or business people. It is also unlikely that many service jobs involving human to human interaction could be replaced by machines. 95% is just too off.

This is pretty much Murphy's Law in action. Murky business dealings, poor governance and mismanagement is a norm in big parts of the world. Then from time to time things go wrong, and that is just statistics.

It may be harder to combine two skills such as sales and engineering, than knowledge in bio and AI, e.g., which are both technical.

When I read the title I thought the point was that companies can't afford to create life-saving drugs, as it is in their interest people to stay ill and keep buying less effective drugs.

These types of notations have been around for a long time. In fact they fist started to study geometric objects (such as knots and braids) with algebraic tools. The graphical notation does the opposite - represents algebraic objects by geometric ones. These may have some benefit for human eyes, but for machines they are quite useless indeed.

Incidentally, I partially agree with you on category theory, especially on computer science. In abstract maths, however, category theory has more significance than pure language. It can serve more or less like an algebraic tool. There are abstract mathematicians who see deeper meaning in it too.

I agree that numbers don't exist in the real world. However, we humans have an ability to perceive the world through numbers. The question then is about our perception of the world if you wish.

I find the existence of number theoretic problems quite puzzling. I wonder what are the implications about the world we can make from them.

Russian empire had the same policy. They justified it by the fact that unversities were financed by public money, and it would be unfair if most of the student, who this money would go to, turned out jews due to "this group's propensity" to education.

Covid-19 might be a major challenge for the society, but individual risks for younger people wothout health issues are still small, at least based on the knowledge we currently have. I am afraid the attitudes described in the article are more due to uninformedness and normal parental anxiousness than anything rational.