# What is This Math Problem, And Who Solved It (John Nash?)? **URL:** \ **Category:** Factual Questions\ **Created:** [October 7, 2011, 11:14pm UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952 "2011-10-07T23:14:25Z")\ **Posts on this page:** 7\ **Page:** 2
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 9, 2011, 2:16am UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/21 "2011-10-09T02:16:30Z")
> [@pmwgreen](#): > > If I asked someone what 4 + 7 was would they be able to tell me exactly how they knew the answer was 11? Or would they just know the answer? I start with 7, and starting from there, I sing the following numbers mentally up through the fourth note of a particular melody I use just for addition, then determine which number I ended up on. Yep. Don’t get me wrong–I’m good at math. Never been quite sure how universal it is for people to be competent at math but unable to do simple arithmetic without counting. But there’s at least one in the world: me. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [October 9, 2011, 2:32am UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/22 "2011-10-09T02:32:27Z")
Please, read the link in my second post above which goes to the article in _American Scientist_ about the story. It gives there what is almost certainly the first version of the story in print, which is almost certainly the version that all later versions are derived from. Note that in the German original of the book where this story is told (which is by Wolfgang Sartorius), Sartorius refers to the problem as being about an arithmetical series in which the standard method (that the other students used) consists of counting, adding, and multiplying. Sartorius doesn’t mention the adding of the numbers 1 through 100. Sartorius doesn’t say that the teacher did this to give the students busywork so that he could do something else. Sartorius doesn’t say that Gauss used a simple method (like adding the numbers in pairs and figuring out the answer by a simple multiplication). He says that Gauss came up with the answer almost instantly. The more I look at this story, the more I think that it’s apocryphal. People who don’t know much about how mathematicians work think that they have some intuitive computer in their heads that comes up with a solution to a problem without their having to think hard at all. It doesn’t work that way. Being a mathematician is about hard work. It’s necessary to learn the proper techniques. A brilliant mathematician learns those techniques faster than other people, but he doesn’t do mathematics by pure intuition. In particular, no, a mathematician wouldn’t answer the question of the bee flight by pure intuition. He would work something out in his head. He may be able to do that very fast, but it’s not about intuition at all. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [October 9, 2011, 2:41am UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/23 "2011-10-09T02:41:09Z")
> [@Chronos](#): > > My understanding of the “sum the numbers up to 100” problem was not that the teacher already knew the answer and was honestly testing the students, but just that e was tired and needed a break, and so gave the students some meaningless work to keep them busy for a while. Of course. Once you make the teacher into a lazy good-for-nothing, all you need is a shoehorned-in reference to Gauss’ devout christian faith to hit all of the urban legend cliches. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 9, 2011, 5:26am UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/24 "2011-10-09T05:26:10Z")
Who made the teacher into a lazy good-for-nothing? ---
**Author:** ![BlinkingDuck](https://avatars.discourse-cdn.com/v4/letter/b/eada6e/32.png) [@BlinkingDuck](https://boards.straightdope.com/u/BlinkingDuck)\ **Post date:** [October 10, 2011, 2:54pm UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/25 "2011-10-10T14:54:22Z")
> [@Bytegeist](#): > > If I remember right, the story is that Gauss’ class was assigned an exercise to sum the numbers from 1 to 100 on paper — the slow way, adding in each number individually. Gauss however saw in his head that the numbers from 1 to N could be represented as a triangle of stacked rows of squares, and that this triangle would form exactly half of a rectangle measuring N by N+1. > > So the sum of 1 to 100 is just (100 x 101)/2, or 5050, which was much, much easier and quicker to calculate. And so this is what he did. > > But, as the story also goes, young Gauss then got into trouble with his teacher, who didn’t approve of his being such a smart ass. That’s not what I heard. I heard his teacher recognised the genius of what he did and refered him to a Math Prof who then took him under his wing. ---
**Author:** ![rbroome](https://avatars.discourse-cdn.com/v4/letter/r/838e76/32.png) [@rbroome](https://boards.straightdope.com/u/rbroome)\ **Post date:** [October 10, 2011, 3:58pm UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/26 "2011-10-10T15:58:30Z")
> [@BlinkingDuck](#): > > That’s not what I heard. I heard his teacher recognised the genius of what he did and refered him to a Math Prof who then took him under his wing. something of a hijack, and I suspect many will already know about Gabriel See, but here is today’s prodigy who has been reasonably well care of so far: > **[The Seattle Times | Local news, sports, business, politics, entertainment,...](https://www.seattletimes.com)** > > Local news, sports, business, politics, entertainment, travel, restaurants and opinion for Seattle and the Pacific Northwest. Reasonable people do tend to help gifted students. Sometimes the help isn’t effective, I suspect primarily because such things happen so rarely, and I certainly hope that his parents and teachers find the right support for Gabriel. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 10, 2011, 7:52pm UTC](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952/27 "2011-10-10T19:52:12Z")
> [@Chronos](#): > > I’d say more that it reflects the person thinking in a particular way, not that that way is necessarily smart. One might argue that there’s more real intelligence involved in being able to realize that there’s an easy way to solve a problem, than there is in being able to solve it the hard way. This. Any idiot can sum a series that’s handed to them, but there’s real insight in realizing that you don’t have to. [Previous page](https://boards.straightdope.com/t/what-is-this-math-problem-and-who-solved-it-john-nash/598952.md?page=1)