If one has understood something in mathematics, one is ‘in command of the situation’. This has important personal/psychological aspects. This ‘command’ is often the reason why somebody decides to do mathematics or logic or computer science. But this is very different from being ‘in command of the situation’ in ordinary life.
Interestingly the above argument can be expanded to technology, where the basic idea is again, that the ‘situation’ is under command (and ‘under control’, but this is another issue).
Is this some kind of human (and mostly male) demand, which can be satisfied by mathematics? Is this something like an absolute presupposition??
In mathematics one speaks of ‘sound’ arguments, of proof in form of a demonstration and obviously demonstrations are the carriers of authority. There is no opposition to a ‘valid’ demonstration.
But… what are the presuppositions (relative or even absolute) that bring out the authority of a demonstration? Or is it a question of habit? What about Luria’s examples of central-asian peasants who do not accept the authority of logical demonstrations (check here)?
Prizes, medals, chairs, professorships, editorial boards, etc.
‘Leading’ mathematicians… What is meant by ‘leading’? What about the non-leading ones?
What are the processes concerning decision making in mathematics? Who decides about grants?
Self-similarity vs. originality? Does authority lead to the breeding of similar mathematicians, of expected ones (even if they are better than their teachers)? There are some problematic cases like Grassmann and Heaviside, who were not accepted by the authorities of their time.
The German expression for doctoral advisor is ‘Doktorvater’ which means ‘doctoral father’ and transports a hereditary connotation.
Alain Connes (source: http://seedmagazine.com/slideshow/mathematicians , slide 2):
[W]hen you get started, to really become a mathematician, the key step is to realize that at some point you have to stop reading books. You have to think on your own. You have to become your own authority.