About James Harris Simons: James Harris is an American mathematician, hedge fund manager, and philanthropist. He is a code breaker and studies pattern recognition.
The best way to conduct research on a larger scale is to make sure everyone knows what everyone else is doing... The sooner the better - start talking to other people about what you're doing. Because that's what will stimulate things the fastest.
Why don't we have enough teachers of math and science in the public schools? One answer is well, if they knew the subject well, they'd also know enough to work for Google or Goldman Sachs or God knows where.