Inspiring Mathematicians

" In your research be both flexible and patient. "  

" Be skeptical of your own work, and don't be afraid to use the wastebasket. "  

" Learn the limitations of your tools, but also learn the power of other mathematicians' tools. In particular, you should continually aim just beyond your current range. "  

" The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise, you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marble, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance."  

" Line of reasoning by which the detective solves the mystery is more important than the identity of the murderer. "  

" I can see there's a connection between not following normal thinking and doing creative thinking. I wouldn't have had good scientific ideas if I had thought more normally."  

" 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. "  

" I don't have any particular recipe. Doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out. "