G. H. Hardy’s scientific contributions

... Putting these pragmatic tools on a rigourous footing, (as Berkeley asked: " What, pray tell, are these differentials, these ghosts of departed quantities? " [7]), took well over a century, and led Dedekind, Cauchy, Weirstrauss, and numerous others to develop and codify the real number system — with its associated theory of real analysis and mathematically rigourous theories of differentiation and integration [8, 9, 10]. No-one can reasonably doubt the pragmatic effectiveness (the possibly " unreasonable effectiveness " ) of real analysis [1] — just consider the theory of ordinary and partial differential equations, the associated existence and uniqueness results, and the vast body of mathematical physics that has grown up over the last few centuries — almost all of which is based on straightforward application of real analysis (or its offspring, complex analysis). ...

Reference:

Which Number System Is “Best” for Describing Empirical Reality?