It is often said that the genius of Carl Friedrich Gauss was first discovered when his teacher told the students to calculate the sum of all integers from 1 to 100 to keep them occupied and young Gauss did that in seconds.

How much truth is in that story?

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    I suggest a more descriptive title – Richard Stelling Mar 31 '11 at 10:45
  • I hope the new title is OK – matt_black Feb 23 '12 at 16:42

Brian Hayes (writer for American Scientist) has done some research into this and collected 109 versions, in eight languages, of this story:

After reading all those variations on the story, I still can't answer the fundamental factual question, "Did it really happen that way?


The story of Gauss and his conquest of the arithmetic series has a natural appeal to young people. After all, the hero is a child—a child who outwits a "virile brute."

  • The story is pedagogically useful in any case; the lesson is "Some seemingly difficult problems can be solved with a easy 'trick'." – dmckee --- ex-moderator kitten Mar 30 '11 at 21:45
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    I suspect many children with an affinity for numbers have worked out the the formula n(n+1)/2 for triangular numbers by the age of 9, especially if they were brought up with the counting sticks of various colours and lengths. Gauss was incredible, but this is one of his less impressive achievements. – Henry Mar 30 '11 at 22:35
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    @Henry-- I like to think I have an affinity for numbers, and I know that many of my peers do. Learning that formula by the age of nine requires a great deal of insight, especially if you have no one older to guide you to that thought. If you discovered this formula on your own by the age of nine, I would love to read whatever math you've come up with since. – mmr Feb 23 '12 at 16:48
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    @dmckee "Math teachers hate Gauss for using this one weird trick!" – Ben Hocking Nov 20 '15 at 22:31
  • It doesn't take that much insight. You just have to figure out that instead of adding 1 + 2 + 3 + ... + 100, you add (1 + 100) + (2 + 99) + (3 + 98) ... + (50 + 51), and then you see that each pair or numbers adds up to 101, and there are 50 pairs. – gnasher729 Jul 20 '19 at 17:49

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