The following quote is attributed to Richard Feynman: “We are trying to prove ourselves wrong as quickly as possible, because only in that way can we find progress.”
To paraphrase this, if you want to prove something first you should try to disprove it. When you have tried everything, then perhaps, perhaps you have a new idea. It is possible that don’t have enough information, to prove yourself wrong.
When I heard this on a podcast today, I had listened to a few other podcasts about mathematics. It was either on SGU November, or Science(ish) the episode about Pi.
When I consider knowledge I tend to visualise it like wet paint on a canvas flowing but not covering all the space. Different colours representing different depths of the material. We start off with a smattering of something and then we continue to cover the canvas or move to another one and leave this idea partially known, or learning a little.
This year to date, I have painted very slowly and very sporadically for reasons not entirely within my control.
pomdi - Paul's Thoughts 