# What cipher(s) did Isaac Newton use?

A number of sources including this one assert that Isaac Newton used encrypted messages to communicate some of his scientific discoveries, and as a way of establishing priority.

What cipher(s) did he use?

What was the ciphertext and what was the plaintext?

What discoveries did he obscure in this way?

• I've found one instance in a 1677 letter from IN to Leibniz: "Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa. / Given an equation involving any number of fluent quantities to find the fluxions, and vice versa." Anagram "6accdae13eff7i3ℓ9n4o4qrr4s8t12ux" --> a(6)c(2)dæe(13)f(2)i(7)ℓ(3)n(9)o(4)q(4)r(2)s(4)t(8)u/v(12)x – A E Dec 17 '14 at 12:19
• I've found some more here: mathoverflow.net/a/140332 from sp.rpcs.org/faculty/MillerR/towson/Readings/… – A E Dec 17 '14 at 12:34
• Absolutely excellent question, in my opinion. I would love to see an answer about this, but I have no idea how many people would be aware of a possible answer. – Danu Dec 17 '14 at 17:15
• Thanks @Danu. So far all I've found is latin anagrams, I'm hoping there's something a bit more interesting than that! ;) – A E Dec 17 '14 at 18:29
• Regarding the Comemrcium Epistolicum (dispute N-L) you can see here for an analysis, here for Newton point of view and the "classical" modern reconstruction of A.R.Hall, Philosophers at Wars (1980). – Mauro ALLEGRANZA Dec 17 '14 at 18:34

Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to decode the message until you tell what the message was.

To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in it. And the anagram consisted of the list of letters and how many times each letter occurs in the message.

An example of such anagram is given on Math Overflow:

https://mathoverflow.net/questions/140327/arnold-on-newtons-anagram

together with its decoding, according to Newton's later statements. The message was usually sent to some third party (Oldenburg, the secretary of the Royal Society in the case of Newton), who then forwarded a copy to the addressee (Leibniz).

The discoveries Newton wanted to secure this way was essentially "calculus", more precisely power series. There were two coded messages in to different letters to Leibniz via Oldenburg. You can see the exact messages in the MO (link above).

Similar methods were widely used to secure priority in 17-th and 18-th centuries. The last time that I know was in 1918 when Gaston Julia send sealed (not coded) messages to the Academie de Science, and these messages had to be publicly opened and read at some later time on his request, to prove his priority. At that time this practice was already obsolete, and Julia was criticized for using it. However he was able to prove his priority and a Grand Prix of the Academy was awarded to him (for what is known now as "Holomorphic dynamics").

http://www.springer.com/mathematics/history+of+mathematics/book/978-3-642-17853-5

• Can you give a reference on the story about Julia? I'm interested! – Danu Dec 17 '14 at 19:10
• @Conifold To link to an answer, just scroll to the bottom of the answer - you will find a "share" link in the bottom left. Click on it, and it will give you a link you can copy. Incidentally that link encodes the fact that you created it... you will see there are two parts to the link /a/answerNumber/referrerNumber. When I do it with this answer, I get http://hsm.stackexchange.com/a/681/543 but you would get a different number (I am user 543 on this site, you are number 55). – Floris Dec 19 '14 at 20:42