So maybe capitalism is very sub-optimal with respect to encouraging software progress? Microsoft's incentive is evidently not to contribute to open standards.
I guess capitalism with respect to software can only happen by software IP protection being enforced. If we could freely ripoff directX and incorporate any advances it made into openGL, then Microsoft would effectively be contributing to openGL, and the industry as a whole would benefit.
I think it would mean the end of software-only companies. Could Apple still make a profit if all of it's software free/libre? Do nvidia or AMD make money directly from software?
I agree. I'm a phd student in math, and am good at it. The main course I took where I _got_ it was a proof-based course on advanced (abstract) linear algebra. The book used was linear algebra done right, its a great place to start; you don't need to know much math ahead of time, its easy to read, and the material is extremely valuable in almost all technical areas. Our professor made us memorize many of the proofs, which may sound backwards, but it helped a huge amount. Often the pudding is in the proof...