Mathematical quickness and research in theoretical physics

Do outstanding minds differ from ordinary minds in any special way? I don’t believe that there is anything basically different in a genius, except for having an unusual combination of abilities, none very special by itself.

– From “Why people think computers can’t’”, an essay by Marvin Minsky

Certain kinds of talent are extremely evident in mathematically-oriented pursuits, such as theoretical physics. Solving simple mathematical problems (“Prove that any set of 51 numbers in the range 1 to 100 must contain two numbers with no common factor” [*]) is an important part of doing research in the mathematical sciences.

Some people will solve the problem just posed effortlessly and instantaneously. A smaller group of people can do the same even with much more complex problems. Other people will struggle with the problem, requiring several minutes or more of laborious thought to convince themselves of the truth of the statement.

It can be rather depressing to meet someone who is clearly much faster than you at this type of problem-solving. Some promising students give up and change fields for something less mathematically demanding, or leave science altogether.

In my opinion, this is a pity. Such mathematical quickness is, unfortunately, both easy to spot, and idolized within the culture of the mathematical sciences. People frequently comment on how “bright” another person is, and mathematical quickness seems to play a major role in forming such assessments.

Yet, such quickness does not seem especially important to make a creative contribution. As Minsky’s comment indicates, a whole plethora of skills and attributes are involved in making such creative contributions. It is more important to be reasonably competent across that entire range of skills and attributes than it is to be extremely talented in just one or a few ways.

[*] I believe I first heard this problem in a biography of the mathematician Paul Erdos.

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