A well known paradigm in scientific thinking and development is the 

“conjecture/modeling ->experimental check-> revise model ->iterate -> established theory” cycle. Mathematics is mainly used with logical deduction to accomplish this feat that leads to scientific advance. Recently I listened to an MIT panel discussing an alternative, both philosophical and speculative, to discoveries using computers. Not being a philosopher, I cannot say that I understood every bit of the discussions. However, the seminar was sufficiently interesting that I sat through 1.5 hours of its duration. Here are my summary as I understood them and takeaways to share with ScienceNet readers:  

• Using very simple rules of manipulating bits, a computer can generate very complex diagrams far beyond what we can imagine. This they demonstrate convincingly. Thus computer can help us deducing consequences not predicted by our conjectures. 

• Computer can do massively parallel explorations using multiple manpower from everywhere in the world. The best example is Wikipedia which let everyone in the world help to develop and basically made Encyclopedias obsolete. Such knowledge gathering is impossible without computers. 

• We should hence organize our thoughts around computers vs just using mathematical models, logic, and our own thinking to advance civilizations. 

Very worth thinking about!