[FredZarguna]

Newton was a genius, but was himself rather backwards in mathematical language. We use Leibniz’s symbolism — and not Newton’s — for a reason.

[dr_lew]

But even if we do think Leibniz was forging ahead of him on this account, surely Newton, who invented calculus out of his own head, was very sophisticated in his mathematical thinking. But how could this be possible if mathematics is a language in which he was not conversant?

I’m saying that the identification of mathematics with a certain style of language is an oversimplification, and a ham-handed one at that.

[dr_lew]

... and let me add. I recall reading somewhere some while ago, that Leibniz labored for a week or a month under the error of thinking that the differential of xy was dxdy.

What an absurd error! I recall this because at the time it gave me tremendous encouragement that Leibniz himself could have been so wrong. Now we regard it as a matter of "language" that d(xy) = xdy + ydx, and we kid ourselves that this understanding is somehow automatic.

Well, now I'm thinking, I sure hope this is true!