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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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up vote -1 down vote accepted

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: 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 '14 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. – apnorton Apr 4 '14 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 '14 at 13:10

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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