That Answers That Question -- Gauss and Series Summation

For years, I have mildly wondered what was the name of "a mathematical genius" (the teacher's words, not mine) to whom my 8th grade math teacher had accidentally or inadvertantly compared me.

Almost off-handedly, in a recent post by David Friedman, I learn that it was Gauss (as a child).

Here is Mr Friedman's comment:

... I am now imagining that instructor as the schoolteacher who tried to keep a class of children-among them the young Gauss-quiet by having them add up the numbers from one to a hundred.

And here is why I had been wondering at the name for so many years:

Early in the school-year of my 8th grade (it was private/religious school into which my siblings and I had just been enrolled), the math teacher instructed the class to sum the numbers 1 through 100 (inclusive). I turned in my answer within just a couple of minutes (most of which I'd spent verifying that I really had hit upon such a simple and time-saving way to get the correct answer). This prompted him to ask whether I'd already been taught about this before transfering to that school (I hadn't). Embarassingly to me, he referred to Gauss, whose name I didn't catch, as "a mathematical genius" ... you know, embarrassing because of that whole social structure of children-in-groups thingie: one is allowed to be smart, but not too smart; being "too smart" is almost worse than being "dumb."

I'd calculated the correct answer by modifying a method I'd invented years before to more quickly sum a column of numbers -- when presented with a column of numbers to sum, I mentally rearrange them so that I can count/add by 10s and 5s. At least one of my sisters also does this, but we don't know whether I taught it her (I'm 3.5 years older) or she independently hit upon it.


So, googling Gauss' name, I found this page, which says:

The formula, if you will, is to add 1 +100, 2+99, 3+98, ...48+53, 49+52, 50+51. So, we have the number 101 fifty times or 5050.

In my case, because it was my habit to mentally rearrange a series to be summed into multiples of 10s, the "formula" I came up with was (0+100) + (1+99) + (2+98) + (3+97) ... + (49+51) + 50 = 50 * 100 + 50 = 5050


===============
In another recent post, Mr Friedman links to this excellent essay: 'Why nerds are unpopular,' which offerers a thoughtful analysis related to my comment about "that whole social structure of children-in-groups."

And, incidentally, a *huge* part of the problem of children-in-groups has to do with the fact that the educationists (that's a curse word, in case Gentle Reader isn't yet aware) have a fixation on consolidation, of herding their defenseless charges into larger and larger schools in larger and larger school districts -- so as to justify larger and larger bureaucracies of educationists.

In that religious school my siblings and I attended for three years (and it wasn't even my family's denomination), the problem of cliques just wasn't a problem ... for a clique with but two or three members simply isn't.

The school was grades 1 through 10 (with two grades in each classroom, both taught by the same teacher). With the four of us, the student population came to about 130, in a school originally intended for 100 pupils. My particular grade/class had 10 pupils, with two of us being "smart" enough to be "nerds" in a public school (the other guy would have been toast in a big public school) and one being "dumb" (he'd have been pushed by social pressure into being a real trouble-maker and ultimately a drop-out).

In that scool, including the principal (who was also a teacher, and the paddler-in-chief), the cook, and the (part-time) custodian, there were 8 adults supervising the 130 children.