One problem with putting too much time into learning math deeply is that math is much more precise than most things in life. When you’re good at math, with work you can usually become completely clear about what a question is asking and when you’ve got the right answer. In the rest of life this isn’t true.
So, I’ve found that many mathematicians avoid thinking hard about ordinary life: the questions are imprecise and the answers may not be right. To them, mathematics serves as a refuge from real life.
I became very aware of this when I tried getting mathematicians interested in the Azimuth Project. They are often sympathetic but feel unable to handle the problems involved.
So, I’d say math should be done in conjunction with other ‘vaguer’ activities.
So, I’ve found that many mathematicians avoid thinking hard about ordinary life: the questions are imprecise and the answers may not be right. To them, mathematics serves as a refuge from real life.
Have you noticed any difference between pure mathematicians and theoretical physicists in this regard?
I used to follow your “this week” blog for a while, but I must have lost track of it a few years ago. Must have been before this showed up on the radar.
Yes, but it is genuinely the case that imprecision and low quality of answers indicate lower utility of an activity, or lower gains due to mathematical skill. Furthermore, what you are saying contradicts existence of mathematicians who did contribute to philosophy (e.g. Godel). edit: I mostly meant, the stories of such—it seems to me that mathematicians who come up with important insights not so rarely try to apply them.
Well, not existence per se, that was a very poor wording on my part, but specific circumstances of their contribution. I think that whenever a mathematician has relevant novel insights, they not so rarely apply it to various relevant problems including ‘fuzzy’ ones. Or, when they don’t, applied mathematicians do.
It’s just that novel mathematical concepts are very difficult to generate in general and even more difficult to generate starting from some broad problem statement.
I agree that math can teach all these lessons. It’s best if math is taught in a way that encourages effort and persistence.
One problem with putting too much time into learning math deeply is that math is much more precise than most things in life. When you’re good at math, with work you can usually become completely clear about what a question is asking and when you’ve got the right answer. In the rest of life this isn’t true.
So, I’ve found that many mathematicians avoid thinking hard about ordinary life: the questions are imprecise and the answers may not be right. To them, mathematics serves as a refuge from real life.
I became very aware of this when I tried getting mathematicians interested in the Azimuth Project. They are often sympathetic but feel unable to handle the problems involved.
So, I’d say math should be done in conjunction with other ‘vaguer’ activities.
Have you noticed any difference between pure mathematicians and theoretical physicists in this regard?
Thanks for pointing me toward the Azimuth Project.
I used to follow your “this week” blog for a while, but I must have lost track of it a few years ago. Must have been before this showed up on the radar.
Yes, but it is genuinely the case that imprecision and low quality of answers indicate lower utility of an activity, or lower gains due to mathematical skill. Furthermore, what you are saying contradicts existence of mathematicians who did contribute to philosophy (e.g. Godel). edit: I mostly meant, the stories of such—it seems to me that mathematicians who come up with important insights not so rarely try to apply them.
It doesn’t; “many mathematicians avoid...” doesn’t imply that all do.
Well, not existence per se, that was a very poor wording on my part, but specific circumstances of their contribution. I think that whenever a mathematician has relevant novel insights, they not so rarely apply it to various relevant problems including ‘fuzzy’ ones. Or, when they don’t, applied mathematicians do.
It’s just that novel mathematical concepts are very difficult to generate in general and even more difficult to generate starting from some broad problem statement.