Fundamental Anagram of Calculus

The controversy around the invention of calculus and the priority dispute between Newton and Leibniz is widely known and often presented as they were isolated thinkers, working independently, not exchanging any thoughts. This, however, isn’t so, because they were actively communicating, through common acquaintances, such as Henry Oldenburg, to whom Newton wrote the following in a letter [1] dated 24 October 1676: The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus:


On this foundation I have also tried to simplify the theories which concern the squaring of curves, and I have arrived at certain general Theorems. The anagram displays the number of occurring letters in a sentence, which Newton wanted to keep in secret. It’s a simple way of making sure that the information is secure and its keeper, in this case Newton, can easily prove his priority to others by revealing the encrypted message. So let’s turn to the content of the above anagram. It expresses the fundamental theorem of calculus by stating that

“Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa”

which means “Given an equation involving any number of fluent quantities to find the fluxions, and vice versa”, which is the fundamental theorem of calculus using Newton’s terminology. Nevertheless, the priority debate is not settled, since at the time of writing the cited letter neither Newton nor Leibniz had published anything specific. Only half-baked ideas, manuscripts and vague statements were circulated. In short, the whole story is much more subtle, than it’s usually told to be. For more on this topic, see [2]. Finally, here the page containing the anagram:



  1. Letter from Newton to Henry Oldenburg, dated 24 October 1676, Cambridge University Library, Department of Manuscripts and University Archives.
  2. Leibniz-Newton calculus controversy, in Wikipedia.

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