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Did famous physicists/mathematicians do basic arithmetic (add/sub/div/mult) in their heads, or would they work them out on paper?

Is there a scale of difficulty for this? I.e. "Erdos could do 5 digit multiplication in his head, but Feynman could at most do 3 digit reliably".

Or do they all do it on pencil/paper?

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2 Answers

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Does anyone do all basic arithmetic in their head? No, so the answer to your first question is that they certainly did some basic arithmetic on paper.

As far as a scale of skill in mental math... I would sincerely doubt this exists. This would have to be similar to a World Records maintaining group, and maintain a record for all "famous" researchers. Of course, then they'd have to define famous.

I would be willing to bet that you will only find individual stories of the mental math capabilities of mathematicians or physicists, but with no organization maintaining a ranking system or scale.

Related: Euler carried a math problem to 50 decimal places in his head: http://library.thinkquest.org/22494/stories/Euler.htm Then again, he was Euler. :)

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There are a number of competitions in mental arithmetic where people compete at a very high level, using special techniques. A specific mathematician may not know about these techniques but they certainly exist. –  Jørgen Fogh Apr 2 at 15:43
    
@JørgenFogh Nowhere in my answer do I claim that the special techniques do not exist, nor do I claim that there are competitions in this field. The asker requested to know if there was a "ranking system" for mathematicians in this area; competitions do rank participants, but too many mathematicians do not participate in those competitions to warrant calling such events a "ranking system." To use analogy: the OP is looking for something akin to a "black belt, green belt" system for mental math, rather than a "1st place karate competition" award. –  anorton Apr 4 at 23:57
    
My comment was on the first part of your answer. Yes, some people do in deed perform all basic arithmetic in their heads. –  Jørgen Fogh Apr 5 at 13:10
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It to a large extent depends on how much logically one thinks. One can do the same by breaking a big problem into smaller simpler ones. In Feynman's 'Surely you are joking Mr. Feynman', Feynman mentions how he defeats a Japanese abacus expert.. simply by breaking a problem logically into known steps.

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