Mathematics is not merely an idle art form, it is an essential part of our society.
If the prior distribution, at which I am frankly guessing, has little or no effect on the result, then why bother; and if it has a large effect, then since I do not know what I am doing how would I dare act on the conclusions drawn?
He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.
Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way.
True greatness is when your name is like ampere, watt, and fourier-when it’s spelled with a lower case letter.
It may be said “In research, if you know what you are doing, then you shouldn’t be doing it.” In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.
One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can’t, almost surely you are not going to.
Science is composed of laws which were originally based on a small, carefully selected set of observations, often not very accurately measured originally; but the laws have later been found to apply over much wider ranges of observations and much more accurately than the original data justified.
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
Good teachers deserve apples; great teachers deserve chocolate. A favorite quotation, written in calligraphy on his office door.
Computer scientists stand on each other’s feet.
Vicarious learning from the experiences of others saves making errors yourself, but I regard the study of successes as being basically more important than the study of failures. There are so many ways of being wrong and so few of being right, studying successes is more efficient.
Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.
The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish.
It is not easy to become an educated person.
Moral: to the extent you can choose, work on problems you think will be important.
While the problem of ai can be viewed as, “Which of all the things humans do can machines also do?,” I would prefer to ask the question in another form: “Of all of life’s burdens, which are those machines can relieve, or significantly ease, for us?
In closing I want to remind you yet again of Pasteur’s remark, “Luck favors the prepared mind.” Yes, it is a matter of luck just what you do; it is much less luck you will do something if you prepare yourself to succeed. “Creativity” is just another name for the great successes which make a difference in history.
A second reason the systems engineer’s design is never completed is the solution offered to the original problem usually produces both deeper insight and dissatisfactions in the engineers themselves. Furthermore, while the design phase continually goes from proposed solution to evaluation and back again and again, there comes a time when this process of redefinement must stop and the real problem be coped with – thus giving what they realize is, in the long run, a suboptimal solution.
Assuming you rise to the top, please remember: what made you great may not be appropriate for the next generation.