The Math Genius Who Gave Us Sudoku [Euler]

Newhouse News ^ | 4/15/2007 | Amy Ellis Nutt

[Allan]

The more sophisticated sudoku solvers use algorithms that I certainly would describe as mathematical.

[CarolinaGOP]

“Now I have books on each floor of the house, in my purse, on my pocket PC...”

Those books come in very handy if you have a long ride in the car, or an extended wait at the Dentist’s office!;)

[djf]

I think his name was actually John Carl Frederick Gauss.

You know them old dudes.

Didn’t have alot of good clothes, so they took a bunch of names.

[patton]

Actually, the Bavarian Prince of Math was quite wealthy, by the time he died.

[discostu]

Allow me to quote from that link: There’s no math involved.

[Allan]

Have a look at this page
where the solver uses techniques from abstract algebra
(group theory)
and graph theory.

Are you saying this is not mathematics?
I don't think my students in algebra and group theory would agree.

[discostu]

Just because somebody found a way to apply math to it doesn’t make it math. Accept reality, the very site that YOU pointed to said thagt it is not math. Live with the reality that even YOU managed to find. Can you use math for it? Sure. But that doesn’t make it math. There’s a lot of stuff that if you want to be a math nerd and over think thing into abstract algebra land can be delt with mathetically but that doesn’t make the thing itself innately math. Sudoku is not innately math, your own site says so. Bye bye now, we’re all done, sorry if any of this has injured your delicate math nerd sensibility.

[MarkL]

Man, sometimes I can’t help but get angry that there were guys two hundred years ago that know calculus and analytic geometry better than I ever will. These were guys who were crapping into jars, but they’re way smarter than me. That galls me to no end.

I know the feeling... I once heard Radia Perlman say that she spent more time working on a poem that described the spanning tree algorithm ( "The Algorhyme) than actually inventing the algorithm itself! Everybody in the audience had their jaw on the floor.

I think that I shall never see
A graph as lovely as a tree.
A tree which must be sure to span.
So packets can reach every LAN.
First the root must be selected.
By ID, it is elected.
Least cost paths from Root are traced.
In the tree these paths are placed.
A mesh is made by folks like me.
Then bridges find a spanning tree.

Mark

[MarkL]

But a great read.

Except for the "infinite numbers" e and pi. Mark

[MarkL]

While I was taking a CS class in college, I started bouncing checks, because I had been working so much in octal, I actually began balancing my checkbook in octal. It was nearly a month before I realized there it had been a long time since there was an 8 or 9 in my ledger!

Mark

[snarks_when_bored]

...I know e and pi are irrational, but are they infinitely so? Like at the quadrillionth place, do they start repeating numbers from the beginning, etc.

The real numbers (all of the numbers on the number line) are of two types: rational and irrational. The rational numbers are (roughly speaking) the fractions, which include the integers, that is, zero and the positive and negative whole numbers. Any rational number has a decimal representation that either terminates (for example, 1.75) or eventually repeats (for example, 8.7432143214321...). The irrational numbers are precisely those numbers whose decimal representations neither terminate (so they "go on forever") nor repeat (so no pattern of digits starts, after a certain stage, to replicate itself "forever"). An easy example of an irrational number is 0.12345678910111213... As far as we know, the first number ever proved to be irrational was the square root of 2.

Note that there are infinitely many rational numbers and infinitely many irrational numbers, but, interestingly, it can be shown that there are 'more' irrational numbers than rational numbers (so there are 'orders of infinity'...in fact, it turns out that there infinitely many orders of infinity, but that's another story). The infinite set of rational numbers is said to be 'countable', that is, each rational number can be associated with a positive whole number and, after that's done, no rational number has been left over that hasn't been counted. On the other hand, the set of irrational numbers is said to be 'uncountable', that is, there is no way to count all of the irrational numbers, since no matter how cleverly you associate positive whole numbers with irrational numbers, it can be shown that you missed one when the counting's done.

[Ole Okie]

Except for the "infinite numbers" e and pi.

Yeah, the writer didn't know much about math.

But I found the biography of Euler to be interesting.

[MarkL]

OOOOWWWWWW!!!!! Stop it! My brain hurts!

Actually, the first morning of honors calculus 1 at SUNY @ Stony Brook, the professor (a REAL professor, not a grad student! And she was a visiting professor from Hungary) asked us to take out a piece of paper and prove that between every two rational numbers, there's an irrational number. And between every two irrational numbers, there's a rational number. More than half of us just sort of stared at her with dumb looks on our faces... A few (I wasn't among them) proceeded to prove it...

Mark