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Maths has much older roots: it existed for millennia before Isaac Newton invented infinitesimal calculus as a way to lay the foundations of physics.

If the axioms were mutually incompatible, it would seem that the entire edifice of maths — which encompasses a broad range of subfields such as infinitesimal calculus or game theory — was on shaky foundations.

They afford yet another great advantage in that the derivation of the results requires only the analytic operations of the infinitesimal calculus.

In his work he gave the first sketch of an infinitesimal calculus and in his own way performed an integration.

Along with Sir John Herschel and George Peacock he laboured to raise the standard of mathematical instruction in England, and especially endeavoured to supersede the Newtonian by the Leibnitzian notation in the infinitesimal calculus.