# History of PDE's in the 19th Century (part 2)

This is a follow up to this question: History of PDE's in the 19th Century The question I have been given to answer is:

The history of partial differential equations in the 19th Century belongs to applied mathematics, not pure mathematics. To what extent do you agree, and why?

I plan to argue that the question is misconceived as there is far too much overlap between the definitions of pure and applied to definitively categorise mathematicians work as solely pure or applied and to some extent why does it matter?

The mathematicians whose work I have been asked to look at are Cauchy, Kovalerskaya, Fourier, Thomson, Dirichlet, Schwarz, Poincare, Riemann, Hamilton-Jacobi, Hilbert and Hadamard. Clearly there are mathematicians who lie on either side of the pure/applied spectrum with Cauchy clearly focused on pure and Thomson focused on applied for example.

I am really struggling on sources for the whole pure vs applied question, I can find more than enough sources giving detailed reviews of their work so it comes down to my classification which I do not entirely trust. I also need to consider obvious counter arguments so I would be interested to see other points of view on the question so I can deal with any refutations to my answer. So what I am asking for is any sources you may think relevant and your opinions on the question, thanks for any reply in advance.

• In the previous question you were given two excellent sources. It is not clear what you are asking now. The distinction between pure and applied mathematics is not sharp, at any time, and it hardly existed in 19th century (except number theory and combinatorics which were pure then). The question seems meaningless. 90% of important work on PDE in 19th century is BOTH pure and applied mathematics. Dec 12, 2017 at 0:56
• Hamilton and Jacobi are two (very) different persons, why do you use a dash between them?? Dec 12, 2017 at 1:01
• Because of the Hamilton-Jacobi partial differential equation so their work goes in tandem Dec 12, 2017 at 10:47