This expository article presents a concise but up‐to‐date account of pre‐Robinson treatment of infinitesimals. It is reiterated that, though the application of infinitesimals appeared in earlier works, it was fully vindicated in the works of Newton, Leibniz, the Bernoulli brothers and Euler. It is noted that, despite Berkeley's scepticism and absence of precise logical foundation, the mathematics of infinitesimals did continue to flourish, both in applicative and foundational domains, until the final setting of the system of real numbers on axiomatic foundation in the nineteenth century when mathematicians could see ‘clearly’ that the existence of infinitesimals led to inconsistency. Subsequently a completely new foundation of calculus based on the concept of ‘limit’ and its ‘epsilon‐delta’ definition (in terms of ordinary real numbers) was led by Cauchy and Weierstrass. A host of problems which reflected the need for more ‘sensitive’ numbers than the Cauchy‐Weierstrass foundation purported is presented. Finally, it is noted that prior to Robinson's work in 1960, in which he reinvented the method of infinitesimals called ‘non‐standard’ analysis in order to exploit the powerful newly developed formal language theory, the concept of infinitesimals remained as borne out of necessity only.