(Re-post from the FUHFUHora and SI.)
Newtonian thought (modern mechanics, optics, differential eqs, etc.):
and all was light! (If we actually had to ask, this ability of Newton's to maintain an incredibly complicated and ingenious construction (of the sort in geometry, number theory, analysis) is exceedingly rare, in the entire history of thought. In terms of the sheer power of a single construction, there were only several others at his level - Gauss, C. L. Siegel and the Soviet mathematician Kolmogorov . In a narrower domain, it was also achieved by Apollonius of Perga, Steiner (the greatest plane geometer), and Besicovitch.)
Michael Faraday who was greater in the wealth of discovery than anyone else, whose "geometrical language" of discovery maintains its relevance today no less (and rather somewhat more) than Clerk Maxwell's analytic one:
Faraday, the greatest discoverer of nature's ways
A new language of discovery , in general. There's a significant difference between a method and an entire language of discovery; for more of the latter, see Heaviside's purely heuristic "operational calculus" by which he found certain (very difficult) exact expressions - far before the Laplace transform was studied by Norbert Wiener, and Bocher/Sobolev/Schwartz formulated distributions theory. Now Dirac's heuristic procedure was similar to that of Heaviside, except he used Baker's book on projective geometry, and (in the early stages) certain involuted analogues between classical and quantum physics. (Dirac was half English, half Swiss.) This book makes it all clear. Later in the century, Feynman did something far less significant; his method of "diagrams" is purely notational. It seems, that the greatest masters of pure discovery were English.
The industrial revolution:
George Boole, symbolical methods, Boolean algebra:
"To be or not to be is true." Boole's treatise on differential equations (republished by AMS Chelsea) is still one of the best, in which he introduces "super high tech" methods not seen before or since.