A proof has been understood when one can forget the details and still be able to reconstruct it if needed. Only some ‘supporting points’ remain to be remembered (the German word ‘Stützpunkt’ fits very well here).

Another aspect of forgetting is linked to habits and experience. After a year of continuous training a swimmer cannot remember how she approached breast stroke one year ago. Even if she watches a video of herself, this will be another person swimming. She will be able to remember a few things but she will not be able to remember her approach to breast stroke from that time. The same holds for playing a musical instrument. And the same holds for doing mathematics. A person seems to have only one attitude only one approach to a certain domain at a certain time (even if this approach consists of a variety of strategies). The point is that through dedicated training the approach changes and the old one disappears – I cannot think like one year ago. Of course by ‘one year’ I mean a reasonable time-interval during which new habits are acquired – this depends strongly on the person.

Testimonials

W.T. Gowers (source: http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/):

A small remark about the previous comment: there are numerous examples of singly authored papers where the author (after a suitable time lag) doesn’t really understand the paper. There’s even a famous example (the details of which I’m afraid I’ve forgotten) of a result that was independently proved by three people of whom two were different time slices of the same person.

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