Editor emeritus of Nature; physicist

I'm amazed that fellow beneficiaries of this site are making such heavy weather of your pre-millennial assignment. Incidentally, surely some have bent your rules in that assorted Sumarians, Assyrians and Egyptians, not to mention Chinese, Greeks and Romans, were well into the recording of history long before 2,000 years ago.

Ab-reacting a little, I was tempted to enter the central locking-systems on modern motorcars (a.k.a. "automobiles") as the greatest contribution to the convenience of modern life, but that's a trivial invention (and should have been incorporated on the model-T).

In any case, there's no doubt in my mind that the invention of the differential calculus by Newton and, independently, by Leibnitz, was the outstanding invention of the past 2,000 years. The calculus made the whole of modern science what it is. Moreover, this was not a trivial invention. Newton know that velocity is the rate of change (with time) of distance (from Galileo, for example) and that acceleration is the rate of change of velocity (with time), but it was far from self-evident that these quantities could be inferred from the geometrical shapes of Kepler's orbits of the planets. Nowadays, of course, mere schoolboys (and girls) can play Newton's game — it's just a matter of "changing the variables", as they say.

In the seventeenth century, it was far from obvious that the differential calculus would turn out to be as influential as later events have shown. Indeed, Daniel Bernoulli claimed (in 1672) that Newton had deliberately hidden his "method of fluxions" in obscure language so as to keep the secret to himself. But Leibnitz's technique was hardly transparent; it fell to Bernoulli himself to interpret the scheme, much as Freeman Dyson made Feynman's electrodynamics intelligible in the 1940s.

Both Newton and Leibnitz appreciated that the inverse of differentiation leads to a way of calculating the "area under a curve" (on which Newton had earlier spent a great deal of energy), but it was Liebnitz who invented the integral sign now scattered through the mathematical literature. That these developments transformed mathematics hardly needs assertion.

But the effect of the calculus on physics, and eventually on the rest of science, was even more profound. Where would be field theories of any kind (from Maxwell and Einstein to Schrodinger/Feynman/Schwinger/Weinberg and the like) without the calculus?

One can, of course, say much the same about the invention of arithmetic, but that long predates 2,000 years ago. The calculus was the next big leap forward.