human calculators

[tali1]

How good as mathematicians are human calculators? are they accepted in the maths community or are they considered one trick freaks?
Where do they fit in the scale of mathematicians at lower end or top end?

[Loosehead]

They have talent for mental arithmetic so I'd imagine that they would not generally be consiidered mathematicians in the normal sense. They can do complex calculations sure but ask them to actually do some maths I'd imagine they'd struggle. There may well be examples that are also good mathemeticians though.

[kwicky]

One of the best examples of mental arithmetic I witnessed was done by a person regarded as backward but was actually a dyslexic. He was able to calculate in his head the day you were born just by giving the birth date. There is no algorithm for this I believe.

[Loosehead]

there is an algorithm for the day thing kwicky but it requires a computer generally! We use it all the time in IT it's not a formula more a list of instructions.

[WaldoMcFroog]

How to calculate a day of the week from a given date (Zeller's Law):

F = k + [(13 x m-1)/5] + D + [D/4] + [C/4] - 2 x C

k is the day of the month.
m is the month number. Months have to be counted specially: March is 1, April is 2, and so on to February, which is 12 (this makes the formula simpler, because on leap years February 29 is counted as the last day of the year). Because of this rule, January and February are always counted as the 11th and 12th months of the previous year.
D is the last two digits of the year - bear in mind that Jan and Feb have to be counted as the previous year.
C stands for century: it's the first two digits of the year.

Now, I'm not saying I could do it, but it's not that difficult either. Just need to remember your 13 times table.

Going back to the question, there are people who can do extraordinarily complex mathmatics in their head, but they're often autistic, and may not possess highly developed social skills in other areas.

This chap is someone who is not only a savant, but also high functioning to boot:

http://60minutes.yahoo.com/segment/44/brain_ma n?comment_offset=541

[jake-the-peg]

I don't think any savants like this have made significant contributions to mathematics but many major mathematicians have had significant mental arithmetic and other skills at an early age.

One famous story involves Gauss - As a child his teacher said "I have to go out, while I'm gone add up the numbers from 1 to 100"

Before his hand hit the door handle Gaus said "5050".

He realised that if you add 1 to 100 you get 101, 2 to 99 =101 etc. So pairing up the numbers ( there are 50 pairs of course) you get 50 x 101 = 5050.

Another famous story involves the great Indian Mathematician Ramanujan.

He was very ill in hospital and his friend G.H Hardy was visiting him he says:

"I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways"

This number is now named after him and you'll find it crops up in Futurama a lot

[squarebear]

That day of the week thing is actually pretty easy to do once you practise it. I do it as a party trick but I'm certainly no savant.

[chakka35]

Yes, the day of your birth is (or was) a routine party piece of mine. I'd need about ten minutes brushing-up before doing it again. It's very easy and involves "casting out sevens" .

[kwicky]

It seems obvious to me after seeing that savant clip above no calculation was taking place when finding the day in a calender. His memory feat of memorising a string of numbers even in a backward direction points to some sort of sumpreme photographic memory,
If the dates are arranged in some sort of array it would be simple to pinpoint the day given the parameters using memory.

[squarebear]

Once you practise it, you hardly need to calculate anything.
Here is a website explaining how to do it.
http://www.terra.es/personal2/grimmer/
While it looks impressive, it's really very simple once you have done a few.