Having mentioned Euler and twentieth century physicists in the question, Pierre Cartier's '[Mathemagics? (A Tribute to L. Euler and R. Feynman)][1]' should provide good cases for you. > My thesis is: there is another way of doing mathematics, equally > successful, and the two methods should supplement each other and not > fight. > > This other way bears various names: symbolic method, operational > calculus, operator theory . . . Euler was the first to use such > methods in his extensive study of infinite series, convergent as well > as divergent. The calculus of differences was developed by G. Boole > around 1860 in a symbolic way, then Heaviside created his own symbolic > calculus to deal with systems of differential equations in electric > circuitry. But the modern master was R. Feynman who used his diagrams, > his disentangling of operators, his path integrals . . . The method > consists in stretching the formulas to their extreme consequences, > resorting to some internal feeling of coherence and harmony. [1]: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/SLC/wpapers/s44cartier1.pdf