On the (Un-)Reality of Mathematics

I stumbled upon a paper by Barry Mazur titled "Mathematical Platonism and its Opposites" which points out a few things to keep in mind when thinking about the question: Is mathematics discovered or invented?

philosophy of science - popper vs howson

The current german edition of the "scientific american" magazine contains an essay about philosophy of science. It's questioning the Karl Popper view of theories in science and the idea of falsification of theories. The rivaling idea is one of "degrees of belief" by Colin Howson. I haven't accessed his book (scientific reasoning: the bayesian approach) yet and can only link a review for now (http://www.glennshafer.com/assets/downloads/review15.pdf ).
I don't really like the idea (even though it scores some imporant points and Popper might fail at some) because of its randomness. For me it seems more like a guideline to establishing theories which ultimately adhere Popper's requirements. I'll write more on it once I've read the book and got a better grip on the whole picture of howson's theory.