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my favorite apocryphal story of all time

April 17, 2009

Johann Carl Friedrich Gauss (1777–1855), painted by Christian Albrecht JensenLegend has it that the great mathematician Carl Friedrich Gauss discovered a much faster way to do summations while still a young boy in primary school.

His teacher assigned the busy work of adding the numbers 1 to 100, thinking his pupils would do the long-hand method of going 1+2+3+4+5 and so on.

But Gauss noticed quickly that :

  • 1 + 100 = 101
  • 2 + 99 = 101
  • 3 + 98 =101

In other words, pairing the terms from opposite ends of the list of consecutive integers produced an identical intermediate sum.

From this observation, he was able to determine that the math could be done this way:

1/2(100) (100+1) = 50 x 101 = 5050

and proceeded to turn in his work in record time, to the amazement of his teacher.

This works for the summation of any number:

1/2(12) (12+1) = 6 x 13 = 78

would work more expeditiously than

1+2+3+4+5+6+7+8+9+10+11+12

and produce the same correct result.

Voila! You can now do summations faster than anyone, even if they used a calculator.

Gauss, of course, went on to write the Disquisitiones Arithmeticae (which developed number theory and the algebra of congruences), father non-Euclidian Geometry, and become known as the “Prince of Mathematicians” for his outstanding work in various branches of mathematics.

Gauss was a phenomenally brilliant dude.

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