Have these criticisms against Tyson been published in peer reviewed journals? I want to cite these but some venues will not allow self published blogs for citations.

It would be a more credible cite if this were published in a third party publication where disinterested editors have checked you claims for accuracy.

]]>I have linked to this article from my Fact Checking Neil deGrasse Tyson blog post.

]]>Regarding calculus, Eudoxus was achieving better approximations chopping things into smaller bits more than a thousand years before Newton or Leibniz.

I believe the truly ground breaking development was the invention of analytic geometry by Fermat and Descartes. Otherwise known as graph paper with an x and y axis. This wedded geometry and algebra. Geometrical objects like a circle could now be examined in the form of equations. For example x^2 + y^2 =1 describes a circle when plotted on graph paper.

Given this new tool it was only a matter of time before Eudoxus like methods were used to find the slope of a curve of a curve. Which is what Fermat did. Newton credits Fermat’s drawing of tangents to a curve for helping him examine rates of change.

Cavalieri’s summing slices was some beautiful geometry. Cavalieri’s quadrature formula:

Integral of x^n dx = 1/(n+1) * x^(n+1). The foundations of integral calculus also preceded Newton and Leibniz.

Isaac Barrow was one of Newton’s teachers. Barrow had done a lot of work on Infinitesmals.

The work of Fermat, Barrow, Cavalieri and others preceded Newton and Leibniz. In my opinion Newton’s discoveries were inevitable after Fermat had done the heavy lifting and opened new doors. That Newton and Leibniz made similar discoveries at the same time supports this notion.

Sure, Newton deserves credit for his contributions. But the claim that Newton invented calculus in two months is an absurd over simplification.

And Tyson uses this over simplification to support his argument. At some point he says something like someone who invented a whole branch of mathematics in two months could have easily developed perturbation theory.

]]>Even many scientists are ignorant that the origin of empirical science is rooted exactly in philosophy (in fact, science was once known as natural philosophy).

Somewhat ironic that even geniuses like Stephen Hawking mused that ‘Philosophy is dead.’ No doubt he will fool those who want to be fooled, starting with himself.

]]>But I’m disappointed you haven’t challenged Tyson’s assertion that Newton invented calculus on a dare in two months. Fermat, Cavalieri, Barrow and others had laid the foundations before Newton came along. Building this branch of mathematics was the collaborative effort of many people over many years.

Sure, Newton contributed to this effort. But to call him the inventor of calculus is silly. To say Newton invented calculus in two months is ridiculous.

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