# Historical developement of analysis and partial differential equations (especially in the 20th century)

Q: Is there a set of some comprehensive surveys or monographs describing (in technical detail) the historical development of the various subareas of analysis and partial differential equations?

I'm especially (but not only) interested in expositions of the most recent ($20^{\text{th}}$ century onwards) developments.

For instance, I already know the following works:

• History of Functional Analysis, by J. Dieudonné;
• Partial Differential Equations in the 20th Century, by H. Brezis and F. Browder;
• A History of Analysis, edited by H. N. Jahnke.

A slight variation on the theme of this question is:

Q': Which "texbooks"/monographs (dealing with subareas of analysis and PDE) strongly embrace an historical point of view?

For example, I've some good memories of the following book (which deals with topics in basic calculus):

• Analysis by Its History by E. Hairer and G. Wanner.

A quite related question is Motivation for and history of pseudo-differential operators.

• This is way too broad, there are many areas covered by heavy monographs... You should specify what you are interested in. – András Bátkai Oct 6 '15 at 17:56
• @AndrásBátkai, thank you for your remark. Actually, the question is intended to be quite broad (it is marked as [big-list] indeed) because I'm very curious to learn more about the general historical development of these field. However, if it can be useful, now I'm personally most interested in functional analysis and PDE; especially variational methods and nonlinear elliptic problems. – user81051 Oct 6 '15 at 18:06
• It is unlikely that a reasonable comprehensive history of such a broad subject as "analysis and pde" in 20-s century will be written any time soon. You can only hope for surveys in more narrow subjects. – Alexandre Eremenko Oct 6 '15 at 21:14
• @AlexandreEremenko: Indeed, that's what I hope to find: several different surveys/monographs each dealing (in a 'comprehensive', that is to say, broad and detailed) with the historical development of a certain specific sub-area. – user81051 Oct 6 '15 at 23:26
• You might be interested in asking questions like these at History of Science and Mathematics Stack Exchange. – Joel Reyes Noche Oct 12 '15 at 1:49

If you are interested in the history of Banach space geometry, then the monograph

is a good reference, even if it reflects at places the personal taste of the author.

About Sobolev spaces and this direction of PDE's, besides your references the book

Tartar: An Introduction to Sobolev Spaces and Interpolation Spaces

contains plenty of historical remarks and references.

• Thank you very much for your advice. I'll surely have a look at these works. – user81051 Oct 6 '15 at 18:21

Another interesting reference could be

Functional analysis in historical perspective, by A. F Monna. Halsted (Wiley), New York, 1973. viii, 168 pp.

J. Lutzen, The prehistory of the theory of distributions, a companion book of which can be considered the autobiography of Laurent Schwartz, which contains quite nontrivial remarks on the math side.