If you think that people working in synthetic biology and bioengineering are doing worthwhile work (and I entirely agree that they are), then go help them. Why the ennui? Set yourself to spend a month investigating these fields and find if you are able to suss out interesting ideas that might (how can you know?) be of use. If your imagination is sparked, then you should find a job in a lab on a trial basis and take your investigations further. I would encourage anyone with a good mind to go into this area of research, as it will doubtless benefit me (I cannot speak to society).
I think your arguments against the utility of mathematics can be applied generally to any science, which is why I reject them. However, the weakness of my objection (it relies on unstable induction) is also the weakness of your argument. Look, sure, you cannot KNOW that what you are doing is going to result in something useful. But I see no evidence at all that anyone who has made worthwhile discoveries knew otherwise. It just is not true, we have no evidence for it, that Newton set out to lay down the mathematical foundations of physics for the benefit of anyone. He seems to have done it for reasons of curiosity and perhaps ambition. I imagine he had a bit of fun with it. Like it or not, this is why people do things, especially when said things require years of work.
I would posit (but do not know), that if you do want to make a useful contribution, the state of ignorance is exactly the right position to be. The x-ray, the laser, the computer, antibiotics, physics, Greek geometry, etc. etc. down the line are the result of accident, aimless research motivated only by curiosity, or people having fun with ideas. Some of these might even have been the result of chaps trying to get the girl. That is how it goes. I see almost no evidence at all (with exceptions of specific technologies, the airplane, for example) that the best way to go about making discoveries is to trying to make specific discoveries. You get interested in something and, if you find something useful, good for you, but most people do not. Given this, that we would find that the most successful scientists are motivated by curiosity, playfulness, and perhaps a little ambition. A survey of the history of science reveals, I think unquestionably, that yes, this is exactly the case!
It is certainly possible, even likely, that if you do spend your time doing theoretical math, that you will do nothing of importance or use to society. The chances, I think, are, at best, only very slightly better if you switch fields to do something else. You should do what gets you excited and interested, because only then, no matter what your pursuit, can you really increase your chances of doing something useful for yourself and society. At the very least, you will be happy, and that is not nothing.
If you think that people working in synthetic biology and bioengineering are doing worthwhile work (and I entirely agree that they are), then go help them. Why the ennui? Set yourself to spend a month investigating these fields and find if you are able to suss out interesting ideas that might (how can you know?) be of use. If your imagination is sparked, then you should find a job in a lab on a trial basis and take your investigations further. I would encourage anyone with a good mind to go into this area of research, as it will doubtless benefit me (I cannot speak to society).
I think your arguments against the utility of mathematics can be applied generally to any science, which is why I reject them. However, the weakness of my objection (it relies on unstable induction) is also the weakness of your argument. Look, sure, you cannot KNOW that what you are doing is going to result in something useful. But I see no evidence at all that anyone who has made worthwhile discoveries knew otherwise. It just is not true, we have no evidence for it, that Newton set out to lay down the mathematical foundations of physics for the benefit of anyone. He seems to have done it for reasons of curiosity and perhaps ambition. I imagine he had a bit of fun with it. Like it or not, this is why people do things, especially when said things require years of work.
I would posit (but do not know), that if you do want to make a useful contribution, the state of ignorance is exactly the right position to be. The x-ray, the laser, the computer, antibiotics, physics, Greek geometry, etc. etc. down the line are the result of accident, aimless research motivated only by curiosity, or people having fun with ideas. Some of these might even have been the result of chaps trying to get the girl. That is how it goes. I see almost no evidence at all (with exceptions of specific technologies, the airplane, for example) that the best way to go about making discoveries is to trying to make specific discoveries. You get interested in something and, if you find something useful, good for you, but most people do not. Given this, that we would find that the most successful scientists are motivated by curiosity, playfulness, and perhaps a little ambition. A survey of the history of science reveals, I think unquestionably, that yes, this is exactly the case!
It is certainly possible, even likely, that if you do spend your time doing theoretical math, that you will do nothing of importance or use to society. The chances, I think, are, at best, only very slightly better if you switch fields to do something else. You should do what gets you excited and interested, because only then, no matter what your pursuit, can you really increase your chances of doing something useful for yourself and society. At the very least, you will be happy, and that is not nothing.