Can an Anarchist (someone who rejects any physical sentient being's authority) be a mathematician?
Isn't formal axioms and practical axioms ("how many digits should come after a decimal point" and alike) the very essence of authority that any anarchist would go against?
First, what you're defining isn't anarchism (the rejection of political authority): it's Greek Cynicism, which rejects all rules, customs, norms, and values of society in order to live a 'natural' life. But even Cynics respected reason, and most of mathematics is thoroughly reasoned. If there are five salad forks on a table, a Cynic might reject the idea of forks and tables, and would certainly scoff at the thought we need a special fork for salad, but it would be quite unnatural for him to dispute the idea that there were five similar things.
Well, wouldn't the same be true for using language? Language follows a grammar, uses established vocabulary based on an underlying set of characters or speech forms; why would anyone follow the rules?
Formalists in mathematics argue that mathematical structures are very much conventions, which could perhaps be otherwise*, but there are certain quite widely used conventions that have shown value in our studies of the world and/or of mathematical practice itself. Learning the Peano or Zermelo/Frankel axioms is acquiring a very useful vocabulary for the practice of a certain way of number or set theory, and we say this encapsulates a productive way of thinking about things without demanding that they are the only right way to learn to multiply or to perform abstract operations on collections of objects.
* indeed, alternative axiomatizations or even alternative axiom systems are often subjects of independent mathematical interest
Isn't formal axioms and practical axioms ("where to put the decimal point" and alike) the very essence of authority that any anarchist would go against?
I view it this way:
Science (incl. math) is a methodology for gaining knowledge without having to rely on an authority (church, philosophical leaders, politicians, ...).
There are authorities in science, but science cannot rely on mere authority.
It's a language that can be used to discuss with others. If you have better ideas about decimal points, then you may try to argue them. No-one's forcing you to abide to the rules there, but often they've been through the scientific process and thus they represent best knowledge nevertheless.
To make their way through the world as it is, all of us, including anarchists, have to be mathematicians- at least to the extent that this means we all must embrace arithmetic, and all its rules. If an anarchist rejects arithmetic, (s)he can't balance the debit card account, calculate fuel mileage, make correct change in a checkout line, etc. which makes for a very lame brand of anarchism.
Conifold is right- the anarchist rejects political and perhaps social laws but does not challenge the validity of mathematical and physical laws.
