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Newton was known to keep manuscripts of his thoughts and workings on math/physics (and even more related to religion) which are kept in Cambridge I believe.

My question is, are there examples of the contrary; mathematicians who are thought not to have made extensive use of physical media (parchment/paper/computers) to do their work? Instead, they may have had strong mental "note-keeping" skills so to speak, as well as strong mental imagery.

They could still publish their results of course.


I originally posted this question on math.stackexchange, but closed it to post it on HSM. Some of the comments I received were broadly:

  • Euler continued to work after becoming blind. In fact, half of his work was published after becoming blind.
  • Ramanujan mostly wrote only his final results in his notebooks.

One other mathematician who was blind that I've come across since originally asking this question is Lev Pontryagin.

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    $\begingroup$ Until 18th century paper was expensive. I suppose for this reason Fermat wrote on margins of Diophantus book, and Newton used a single notebook for all his records during his 5 years of studies in Cambridge. Most mathematicians had to keep most of their results in their memory. $\endgroup$ – Alexandre Eremenko Nov 4 '20 at 23:25
  • $\begingroup$ Ramanujan famously did all his calculations and derivations on slate with chalk and only stored final results on paper. He couldn't not afford too much paper because of poverty and that's why resorted to chalk and slate. $\endgroup$ – Paramanand Singh Feb 18 at 3:24
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Lagrange is one example. For instance, W. W. Rouse Ball wrote in his book "A Short Account of the History of Mathematics" that Lagrange:

... always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction.

Another example is Shiing-Shen Chern. From the tribute article for Chern in the October 2011 AMS Notices, Robert Greene recalled that Chern

... would come in every day and fill the blackboards with the long calculations that are needed in treating the subject in terms of differential forms. He never brought any notes, never paused to pursue any elusive recollection, and never made mistakes. The whole subject unfolded as smoothly and gracefully as if he were reading from a perfectly written book.

Finally, one of the more courageous students asked him after class how this was possible. He replied quietly that in fact he had developed the whole subject to begin with without writing anything down. He said it was as if he had a blackboard in his mind on which things could be written and stayed forever.

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  • $\begingroup$ Thanks Mark, I really liked the 2nd extract from the Chern article $\endgroup$ – Colin McDonagh Nov 9 '20 at 9:47

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