I share with you the idea you handle as to the analogy between the work of the mathematician and the work of the philosophers. You handle interesting ideas as to the work of the mathematician, which in this particular case you point out. You talk about the work of the mathematician as something that may not be finished in this way and as a middle mathematical construction, but you do not mention the contributions that in the growth of mathematics has had the application of this real issues, which for me , I consider is part of the work of the mathematician.
I was speaking mainly from a pure mathematicians perspective but you are right there are many things I did not mention in the brief post.