Recently I read about Intuitionism and I can tell you unreservedly that I do not believe in it. I believe that objective things can exist independent of human minds and the most salient example I could give is in your computers. In your computer you can calculate 1 + 1 = 2 and you can do so quite independently of a human mind. 1 + 1 = 2 is an objective truth which can easily be modelled in a machine. Certainly mathematics can *also* be the result of constructive mental activity in human minds, but it is not limited to that. Also it might be interesting to note that machines will be able to find objective mathematical truths which are beyond the capacity of a human mind alone, in fact I’m quite sure that will have been done already (if you can think of an example feel free to let me know!).
Some light reading. /s
I forget how it happened but I ended up over here: Works by Gary Aylesworth.