I guess my impression is that determining which mathematical problems are worth solving is more abstract and difficult than determining which problems need to be solved in, for example, biology. That is, it is obvious to me that “develop new antidepressants” is a better decision than “kill all humans,” whereas “develop new factorization algorithm” may or may not be a better decision than “use group theory to study certain differential equations.”
Obviously there is a problem here of specificity; more technical decisions in biology may be equally hard, but it is in general hard to reduce problems in mathematics to external applications.
Also, I got the impression that killing all humans was pretty much a solved problem. Fortunately, the solution has not yet been implemented.
Also, I got the impression that killing all humans was pretty much a solved problem. Fortunately, the solution has not yet been implemented.
The real question is how easy it is. Requiring a significant coordinated effort by a major lab is one thing (though I don’t even think we are there yet)---requiring one particularly careless guy with $100,000 is another.
I guess my impression is that determining which mathematical problems are worth solving is more abstract and difficult than determining which problems need to be solved in, for example, biology. That is, it is obvious to me that “develop new antidepressants” is a better decision than “kill all humans,” whereas “develop new factorization algorithm” may or may not be a better decision than “use group theory to study certain differential equations.”
Obviously there is a problem here of specificity; more technical decisions in biology may be equally hard, but it is in general hard to reduce problems in mathematics to external applications.
Also, I got the impression that killing all humans was pretty much a solved problem. Fortunately, the solution has not yet been implemented.
The real question is how easy it is. Requiring a significant coordinated effort by a major lab is one thing (though I don’t even think we are there yet)---requiring one particularly careless guy with $100,000 is another.
Sure. “Killing all humans” is solved in the sense that “factoring large integers” is solved.
We can do it in O(3+log(x)/log(phi)) time, but can we do it faster?