A Quote by Israel Gelfand
The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.
Related Quotes
America has a lot of problems, believe me. I know what the problems are even better than you do. They're deep problems. They're serious problems. We don't need more.
If you go deep into a problem, you'll find most all of the time that there are yet more problems to be solved from the ground up.
At some point, I thought that, as I got older, I'd come to terms with a lot of things. I'd solve some big problems, and eventually I'd become content. It's almost more depressing to think that the older you get, the more your problems multiply.
The problem is if you really believe in a society where those who merit to get to the top, get to the top, you’ll also, by implication … believe in a society where those who deserve to get to the bottom also get to the bottom and stay there.
In terms of putting the cast together, no problems. You know, the only problem always is just price-point. Our ambitions as we get older, all of us, is to try and do more.
I used to look at composing music as problem solving. But as I get older, it's not about problem solving anymore. There are no solutions, because there are no problems. You just turn the tap and it flows out.
When you have different kinds of scientific and mathematical minds approaching problems, you will get more solutions. This leads to more innovation and more creative design.
President Obama and Hillary Clinton have, and Kerry have allowed tens of thousands of people into America. The FBI is now investigating more people than ever before having to do with terror. And it's from the group of people that came in. So look, look, our country has a lot of problems. Believe me. I know what the problems are even better than you do. They're deep problems, they're serious problems. We don't need more.
The classes of problems which are respectively known and not
known to have good algorithms are of great theoretical interest. [...]
I conjecture that there is no good algorithm for the traveling
salesman problem. My reasons are the same as for any mathematical
conjecture: (1) It is a legitimate mathematical possibility, and
(2) I do not know.
We are more than our problems. Even if our problem is our own behavior, the problem is not who we are-it's what we did. It's okay to have problems. It's okay to talk about problems-at appropriate times, and with safe people. It's okay to solve problems. And we're okay, even when we have, or someone we love has a problem. We don't have to forfeit our personal power or our self-esteem. We have solved exactly the problems we've needed to solve to become who we are.
An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.
I think very often problems are so big, people approach problems from the bottom up: 'If only I do this little bit, then hopefully there will be some sort of snowball effect that will be bigger and bigger.' I'm much more in favor of the top-down approach to problem-solving.
The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.
It is one of our most exciting discoveries that local discovery leads to a complex of further discoveries. Corollary to this we find that we no sooner get a problem solved than we are overwhelmed with a multiplicity of additional problems in a most beautiful payoff of heretofore unknown, previously unrecognized, & as-yet unsolved problems.
For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.
Every small problem most likely stems from the same root as large problems, and so there is no need to always go deep. One can use anything for the therapeutic process and/if this link is made.
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