TITLE: Unrigorous British mathematics prior to G.H. Hardy
QUESTION [25 upvotes]: I was looking at a bio-movie of Ramanujan last night. Very poignant.
Also impressed by Jeremy Irons' portrayal of G.H. Hardy.
In G.H. Hardy's wiki page, we read:
. . . "Hardy cited as his most important influence his independent study of Cours d'analyse de l'École Polytechnique by the French mathematician Camille Jordan, through which he became acquainted with the more precise mathematics tradition in continental Europe."
and
. . . "Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics."
Are we to understand from this that up to the late 1800s, British mathematics used only partial or inductive proofs or what ?
On the face of it, this would have been quite a state of affairs.
What exactly - in general or by a specific example - did Hardy bring to mathematics by way of rigour that had previously been absent ?
If someone introduced a new and sketchily proven theorem in the days of Hardy's childhood - and we are talking about Victorian times here (...) - then surely all the mean old men of the profession would have been disapproving of it and would obstruct its publication ?

REPLY [8 votes]: The quote in question contrasts Hardy’s rigor with “the hydrodynamics that was an important part of Cambridge mathematics.”
So to understand Hardy’s role, it makes sense to look at that hydrodynamics, e.g. Alfred Basset’s “Treatise on Hydrodynamics, with Numerous Examples”, conveniently available online at the Internet Archive. (Since Basset studied math at Cambridge, did his math afterwards without any professorship, and published multiple editions of this book with Cambridge University Press, I think it’s fair to call this “Cambridge math”; one could probably find this or similar books listed in Cambridge math syllabi too.)
Browsing through the book, I do not see a lot of proofs; I see calculations from mathematical hypotheses deemed appropriate for various physical problems.
So Hardy brought his rigor to pure mathematics; what came before him in England was less about pure mathematics done unrigorously, and more about applied mathematics done under different constraints.