From my reading there is no doubt they were independent, but since Leibniz published first, Leibniz and his friends suspected Newton of poaching. The Dictionary of Scientific Biography articles on Newton and Leibniz give the details. Today we use Leibniz’ notation for the derivative and integral, which, aside from the method and proof of calculus, is itself a significant innovation. Interestingly, we use Newton’s notation for and interpretation of fractional and negative exponents (great primary source article in James R. Newman, The World of Mathematics The World of Mathematics

).

And that leads me back to Wolfram, whose abbreviated operators in the Mathematica programming language are a great modern innovation in mathematical notation. For those interested, my talk on a new Mathematica programming syntax is here: A New Mathematica Programming Style

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