E.
_1867, Nov. 8_.
MY DEAR SIR,
I think it best to put in writing the purport of what I have said, or
have intended to say, in reference to the Mathematical Studies in the
University.
First, I will remark on the study of Partial Differential Equations.
I do not know that one branch of Pure Mathematics can be considered
higher than another, except in the utility of the power which it
gives. Measured thus, the Partial Differential Equations are very
useful and therefore stand very high, as far as the Second Order.
They apply, to that point, in the most important way, to the great
problems of nature concerning _time_, and _infinite division of
matter_, and _space_: and are worthy of the most careful study. Beyond
that Order they apply to nothing. It was for the purpose of limiting
the study to the Second Order, and at the same time working it
carefully, philosophically, and practically, up to that point, that I
drew up my little work.
On the general question of Mathematical Studies, I will first give my
leading ideas on what I may call the moral part. I think that a heavy
responsibility rests on the persons who influence most strongly the
course of education in the University, to direct that course in the
way in which it will be most useful to the students--in the two ways,
of disciplining their powers and habits, and of giving them scientific
knowledge of the highest and most accurate order (applying to the
phenomena of nature) such as will be useful to them through life.
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