I will start with the second example as it's bit clearer to me.
'Few' and 'Few of the'
When we say 'few books', it means that there were few of them to begin with. For instance, if I have only 3 books at home, and they are stolen, I would say "Few books were stolen from my house". But if I have 300, and of them 3 were stolen, I would say "Few of the books were stolen from my house".
Now the nuance of 'more x' and 'more of an x'
He is more of a mathematician -is okay.
He is more mathematician -is not grammatical because more here should serve as a comparative word.
It could be...
He's more a mathematician than a [something]
The same logic of the second example applies here but in an abstract sense.
Say, you are a teacher by profession but you are also a cook. So, you can say
I am more of a cook
In such context, we use the preposition of to be a part of something.
Another example - are you a cyclist or a swimmer? Mind it, none of these is your profession. So, in this case, you could be 'more of a cyclist than a swimmer' 'Of' implies to the part OF whole.
You could be more of a cook than a gardener. You are neither professionally, but a part of both as a hobbyist.
[Wish you a very happy new year].