In your letter of December 14, you ask me whether mathematics is a worthwhile endeavor. Mathematics absolutely is not a worthwhile endeavor! I can imagine only three possible reasons for studying mathematics:
(1) Entertainment.
(2) To promote technological progress.
(3) To promote one’s own career.
Reason (1) is harmless; but one doesn’t refer to entertainment as a “worthwhile endeavor”; it’s just a pastime.
As for reason (2), modern technology is the worst thing that ever happened to the world, and to promote its progress is nothing short of criminal. Read Our Final Century, by Martin Rees; or read “Why the Future Doesn’t Need Us,” an article by Bill Joy that appeared in Wired magazine, April, 2000.
As for reason (3), to choose mathematics as one’s career would be very risky. Not long ago I received a letter from a gravestone sculptor whose craft had been rendered obsolete by a laser-guided machine that carved gravestones automatically. He was in his forties, unable to find work, and depressed. Maybe you think that can’t happen to you if you become a mathematician. But you’re wrong. Martin Rees, Bill Joy, and many other distinguished experts believe that within a few decades machines will be developed that will be more intelligent than even the smartest human beings. When that happens, people will be obsolete; they will be phased out and will be replaced by computers and robots. This will happen to everyone eventually, but mathematicians probably will become obsolete before anyone else does, because mathematics is more amenable to computerization than any other field. Hence, computers probably will surpass humans in mathematics before they do so in other areas.
He skips over understanding our world which is probably the reason most pure maths is done.
I'm not sure I agree with this. I suppose it could be that we have different defintions of what "our world" means.
You might like the quote below. I suspect you're arguing that most pure math is performed for option #2 below (utilitarian purposes). Like I said, I'm not so sure.
In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither. Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were [someone to] drive all the people belonging to these two categories out of the temple, the assemblage would be seriously depleted, but there would still be some men, of both present and past times, left inside. Our Planck is one of them, and that is why we love him.
I guess I was including maths and imagine mathematicians investigate stuff of the general type like the riemann hypothesis, whether all non-trivial zeros of the Riemann zeta function lie on the critical line where the real part equals 1/2, which are interesting but of little practical value.
Comments
Transcribed letter (from chatgpt):
Dear Mr.,
In your letter of December 14, you ask me whether mathematics is a worthwhile endeavor. Mathematics absolutely is not a worthwhile endeavor! I can imagine only three possible reasons for studying mathematics:
(1) Entertainment. (2) To promote technological progress. (3) To promote one’s own career.
Reason (1) is harmless; but one doesn’t refer to entertainment as a “worthwhile endeavor”; it’s just a pastime.
As for reason (2), modern technology is the worst thing that ever happened to the world, and to promote its progress is nothing short of criminal. Read Our Final Century, by Martin Rees; or read “Why the Future Doesn’t Need Us,” an article by Bill Joy that appeared in Wired magazine, April, 2000.
As for reason (3), to choose mathematics as one’s career would be very risky. Not long ago I received a letter from a gravestone sculptor whose craft had been rendered obsolete by a laser-guided machine that carved gravestones automatically. He was in his forties, unable to find work, and depressed. Maybe you think that can’t happen to you if you become a mathematician. But you’re wrong. Martin Rees, Bill Joy, and many other distinguished experts believe that within a few decades machines will be developed that will be more intelligent than even the smartest human beings. When that happens, people will be obsolete; they will be phased out and will be replaced by computers and robots. This will happen to everyone eventually, but mathematicians probably will become obsolete before anyone else does, because mathematics is more amenable to computerization than any other field. Hence, computers probably will surpass humans in mathematics before they do so in other areas.
Sincerely yours, Ted Kaczynski
He skips over understanding our world which is probably the reason most pure maths is done.
The Joy article mentions is here https://www.wired.com/2000/04/joy-2/ by the way, and includes discussion of Kaczynski.
I'm not sure I agree with this. I suppose it could be that we have different defintions of what "our world" means.
You might like the quote below. I suspect you're arguing that most pure math is performed for option #2 below (utilitarian purposes). Like I said, I'm not so sure.
In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither. Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were [someone to] drive all the people belonging to these two categories out of the temple, the assemblage would be seriously depleted, but there would still be some men, of both present and past times, left inside. Our Planck is one of them, and that is why we love him.
I guess I was including maths and imagine mathematicians investigate stuff of the general type like the riemann hypothesis, whether all non-trivial zeros of the Riemann zeta function lie on the critical line where the real part equals 1/2, which are interesting but of little practical value.
The full text is here. It's a speech by Einstein on Max Plank's 60th birthday. https://www.site.uottawa.ca/~yymao/misc/Einstein_PlanckBirth...