I suspect that there are. However, I doubt my ability to accurately find such problems and solve them.
I am in particular interested in finding non-math things that I am interested in and could reasonably pursue, and narrowing down such “non-apples” to something like this or this (the part about biotech); and then especially I’m interested in turning that into a set of tasks.
What I would like to leave with is a to do list that reads like: “Take chemistry classes next year and earn a degree in biology while remaining a graduate student, then apply for biotech internships.”
Obviously this is somewhat personal and I’ve digressed into something that is more of an addendum to the OP rather than a reply to your comment.
However, I doubt my ability to accurately find such problems and solve them.
I am not convinced that this gets too much easier in other fields. For example, in biology, a natural and apparently rather straightforward problem (compared to some of the long term goals of the field) is killing all humans. Its not clear how the field should proceed to accomplish something useful without introducing a serious existential risk. If you feel unable to evaluate the long-term impacts of your work, it seems possible to do a great deal of harm, nevermind doing no good.
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 suspect that there are. However, I doubt my ability to accurately find such problems and solve them.
I am in particular interested in finding non-math things that I am interested in and could reasonably pursue, and narrowing down such “non-apples” to something like this or this (the part about biotech); and then especially I’m interested in turning that into a set of tasks.
What I would like to leave with is a to do list that reads like: “Take chemistry classes next year and earn a degree in biology while remaining a graduate student, then apply for biotech internships.”
Obviously this is somewhat personal and I’ve digressed into something that is more of an addendum to the OP rather than a reply to your comment.
I am not convinced that this gets too much easier in other fields. For example, in biology, a natural and apparently rather straightforward problem (compared to some of the long term goals of the field) is killing all humans. Its not clear how the field should proceed to accomplish something useful without introducing a serious existential risk. If you feel unable to evaluate the long-term impacts of your work, it seems possible to do a great deal of harm, nevermind doing no good.
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?