When teaching discrete math a while back I told the following story which some had already heard in High School:
When Gauss was in 1st grade the class was being bad. So the teacher made them sit down and add up the numbers from 1 to 100. Gauss did it in 2 minutes by noting that if S was the answer then
2S = (100+1) +(99+2) + ... + (1 + 100) = 100*101
So S = 50*101. Then he went to Google and typed in 50*101 for the answer.
The class laughed because of course the last part about Google was false. But I then told them that the entire story was false and showed them the following slides: here Take a look at them (there are only 4 of them) before reading on.
(ADDED LATER: here is an article by Brian Hayes that documents the history of the story.
)
So I told them the Gauss Story was false (I am right about this) and then told them a lie- that the story's progression over time was orderly. I then told them that that was false (hmmm- actually I might not of, oh well).
One of my students emailed me this semester
Dr Gasarch- one of my Math professors is telling the Gauss story as if its true! You should make a public service announcement and tell people its false!
So I told them the Gauss Story was false (I am right about this) and then told them a lie- that the story's progression over time was orderly. I then told them that that was false (hmmm- actually I might not of, oh well).
One of my students emailed me this semester
Dr Gasarch- one of my Math professors is telling the Gauss story as if its true! You should make a public service announcement and tell people its false!
I do not think this is needed. I also don't know how one goes about making a public service announcement I also suspect the teacher knew it was false but told it anyway.
OKAY- what do you do if you have a nice story that has some good MATH in it but its not true?
Options:
OKAY- what do you do if you have a nice story that has some good MATH in it but its not true?
Options:
Tell it and let the students think its true.
Tell it and debunk it.
Tell it and debunk it and tell another myth
Tell it and debunk it and tell another myth and then debunk that
Ask your readers what they would do. Which I do now: What do you do?
The story's included in Waltershausen's 1856 biography of Gauss: https://archive.org/details/gauss00waltgoog/page/n15/mode/2up, page 4.
ReplyDeleteso what's the 'true' story behind this?
ReplyDeleteWas it actually Gauss that came up with
this 'trick' or is the provenance of this
incorrect?
one might want to jump to slippery slope conclusions that
von neumann's stories are false/fabricated?
I have added a link to a paper by Brian Hayes that documents the history of the story.
ReplyDeleteThere are much better things to do with your precious time and energy. This is not one of them.
ReplyDeleteI did exactly this in fifth grade. I'm no "Gauss", so I don't doubt he did it earlier in life than me.
ReplyDelete1 to 100 was easy to pair, and realizing 50 was the number of 101's took 3 seconds or so, and multiplying 50 x 101 to get 5050 was easy. All this after learning multiplication sufficiently.
DeleteI have no doubt Gauss could do this once he could multiply 50 x 101.
DeleteLeafing through the Hayes article, the story seems essentially correct, as told by Gauss himself to others. Maybe not 1 to 100, maybe some more general arithmetic sequence. As a child he noticed he could add in pairs, which allows him to see the formula more easily.
ReplyDeleteThe rest seems nitpicking. What is exactly debunked here?
It's better than true, it's epic.
ReplyDelete