Love the bit about the misconception that Mathematics is mainly about utility. I remember reading something about G.H. Hardy (which I can no longer find) in which he said he would get a little bit disappointed if he found that one of his results ended up finding a practical use.
He actually argues quite the opposite in [1] (see footnote, pg 33) - a good read in itself. The quote you're probably referring to is this:
"a science is said to be
_useful_ if its development tends to accentuate the existing inequalities in the distribution of
wealth, or more directly promotes the destruction of human life" (emphasis mine).
And Hardy's response (excerpt):
> It is sometimes
suggested that pure mathematicians glory in the uselessness of
their work, and make it a boast that it has no practical applications.
> I am sure that Gauss’s
saying (if indeed it be his) has been rather crudely misinterpreted.
If the theory of numbers could be employed for any practical and
obviously honourable purpose, if it could be turned directly to the
furtherance of human happiness or the relief of human suffering,
as physiology and even chemistry can, then surely neither Gauss
nor any other mathematician would have been so foolish as to
decry or regret such applications.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
