Saturday, March 12, 2011

The Integers

Leopold Kronecker (December 7, 1823 – December 29, 1891) was a German mathematician who famously said, "God made the integers; all else is the work of man."

There are, I suppose, many ways in which to interpret this statement. I do not presume to know what Kronecker's intent was, though I rather hope he intended to confine man's "creation" in this instance to the world of mathematics. In such case, he may have been right. If the intent was to state that except for the integers, all creation was accomplished by man, Image: Wikipedia then that is ludicrous.


It is a matter of record that on this statement hinged the alienation of Kronecker from his more famous student, Georg Cantor, who was not buying the statement in any of its possible permutations. Or at least, so say some math historians. It is certainly the case that the two gentlemen represented opposing philosophies of mathematics.

Arithmetic reminder: Take your clock and Spring Forward one hour before you fall asleep!

9 comments:

jimgrey said...

God created all of mathematics. Man's work is to discover it all.

Anonymous said...

Don't you wish this would be done automatically. I have way too many clocks.

Bob

vanilla said...

Jim, I think your assessment is exactly correct. I was hoping someone would point that out!

...all of mathematics and all of everything else.

FishHawk said...

"String Too Short to Tie" has been included in this weeks A Sunday Drive. I hope this helps to attract even more new visitors here.

http://asthecrackerheadcrumbles.blogspot.com/2011/03/sunday-drive_13.html

vanilla said...

FishHawk, thanks for including STSTT in your tour.

Blessings.

Sharkbytes said...

Huh? Things like pi and e are inexplicable mathematical relationships that just work and humans have nothing to do with them. And they aren't anything like integers. If anything, I would say that integers are creations of humans to try to cram God into discrete constructs.

vanilla said...

Shark, I think I'm with Jim on this one: it is all created by God, it is man's job to discover it.

Sharkbytes said...

Yes, I'm pretty much agreeing with you. I'm only trying to be cute and saying that there are infinitely more numbers that aren't integers than those that are, and a lot of them are pretty interesting.

vanilla said...

Shark, certainly there are infinitely many numbers, both rational and irrational. Isn't math fun?