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September 24, 2008 / Toby Dayton

The Best Math Story You’ll Hear Today

In Prime Obsession: Bernard Riemann and the Greatest Unsolved Problem in Mathematics, author John Derbyshire tells a fabulous story about arguably the greatest mathematician that ever lived, Carl Friedrich Gauss. Gauss was one of, if not the first mathematician to shine light on the Prime Number Theorem which led to the now infamous Riemann Hypothesis. In any event, when Gauss (1777-1855) was 10 years old (as the story goes), his schoolmaster decided that he needed an hour or so break from the classroom so he assigned the following problem to the kids: add up every numeral between 1 and 100. Almost instantly, before the master had even sat back down at his desk, Gauss threw his slate onto the master’s desk, exclaiming “ligget se!” or ‘there it is!’

Gauss had mentally listed the numbers 1-100 horizontally across, did the same in reverse order, and summed the two rows vertically so that each column totaled 101. So Gauss knew that there were 100 occurrences of 101, but since each number was listed twice, Gauss had to halve the sum to get the final answer: 50 x 101 or 5,050. It’s so simple, elegant, and brilliant it’s dumbfounding.

3 Comments

  1. Eric Caron / Sep 25 2008 4:23 am

    I just love stories involving students making discoveries like this. My favorite though is the Mpemba effect (taken from http://en.wikipedia.org/wiki/Mpemba_effect):

    The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in 1963 in Magamba Secondary School, Tanzania when freezing hot ice cream mix in cookery classes and noticing that they froze before cold mixes. The headmaster had invited Dr. Denis G. Osborne from the University College in Dar Es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question “If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a freezer, the one that started at 100°C freezes first. Why?” only to be ridiculed by his classmates and teacher. After initial consternation, Dr. Osborne confirmed Erasto’s finding and they published the results together in 1969.

    Note to self: Cut back on mocking seemingly absurd ideas.

  2. Eric Caron / Sep 24 2008 11:23 pm

    I just love stories involving students making discoveries like this. My favorite though is the Mpemba effect (taken from http://en.wikipedia.org/wiki/Mpemba_effect):

    The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in 1963 in Magamba Secondary School, Tanzania when freezing hot ice cream mix in cookery classes and noticing that they froze before cold mixes. The headmaster had invited Dr. Denis G. Osborne from the University College in Dar Es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question “If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a freezer, the one that started at 100°C freezes first. Why?” only to be ridiculed by his classmates and teacher. After initial consternation, Dr. Osborne confirmed Erasto's finding and they published the results together in 1969.

    Note to self: Cut back on mocking seemingly absurd ideas.

  3. Eric Caron / Sep 25 2008 4:23 am

    I just love stories involving students making discoveries like this. My favorite though is the Mpemba effect (taken from http://en.wikipedia.org/wiki/Mpemba_effect):

    The effect is named for the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in 1963 in Magamba Secondary School, Tanzania when freezing hot ice cream mix in cookery classes and noticing that they froze before cold mixes. The headmaster had invited Dr. Denis G. Osborne from the University College in Dar Es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question “If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a freezer, the one that started at 100°C freezes first. Why?” only to be ridiculed by his classmates and teacher. After initial consternation, Dr. Osborne confirmed Erasto's finding and they published the results together in 1969.

    Note to self: Cut back on mocking seemingly absurd ideas.

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