A Master of Us All

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.Albert Einstein

This garden universe vibrates complete,
Some, we get a sound so sweet.
Vibrations, reach on up to become light,
And then through gamma, out of sight.
Between the eyes and ears there lie,
The sounds of color and the light of a sigh.
And to hear the sun, what a thing to believe,
But it’s all around if we could but perceive.
To know ultra-violet, infra-red, and x-rays,
Beauty to find in so many ways.

Two notes of the chord, that’s our poor scope,
And to reach the chord is our life’s hope.
And to name the chord is important to some,
So they give it a word, and the word is OM.
Graeme Edge, Moody Blues

euler_mosaic

There have been many times I have heard an individual say something to the effect: I hate (don’t like, don’t do) “math.”  Shame on our ignorant “math” educational system, but now with the Khan Academy there is no excuse for such a lament from our kids.

I always enjoyed “math” — hey, I am a nerd from the sixties.  But I “hit a wall” in mathematics in the second-year of college. And even modern “mathematicians” have to “specialize” because the “difficulties” of “mathematics”. Practically all believe that mathematics, even for the “mathematicians,” is too vast and large to now to “see” the whole elephant (so to speak).

In mathematics you don’t understand things. You just get used to them.
— John Von Neumann

Someday information science [in some form of Formatics] will encompass all of math and science, but until then:

The religion of Mathematics is a Master of Us All.

Except when in the 1700’s,
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The Exceptional Twins

They varied in creed and circumstance.

They were the same in Temperament and interest.

They were exceptionally invariant in their passion.

They were the exceptional invariant twins.

invariant_twins

You don’t chose your passion, your passion choses you — Jeff Bezos

Passion breeds talent — Stanislas Dehaene

Passion requires Temperament — David M. Keirsey

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One Ring that Binds Them All

rings_that_bind

They were her boys.

And she revolutionized the way to they thought about things.

And she proved it.

No, not a physical proof, for there is no such thing.  But a Mathematical proof.  Ironclad, never changing — Well almost.

To imitate, but not too much, if our discipline is not to become a marsh, a large one to be sure, but stagnant, with neither life nor movement. First imitate to learn, and then renew ourselves. … I love, at least when I am able, to regard science from a personal point of view, and always, again when possible, go beyond current opinions and look at the problem from a new perspective. I have the impression that some ways must be left behind, some mental habits must be abandoned, if we are not to clip the wings of progress. Even to science we must sometimes repeat Charon’s cry: By another way, by other ports, not here, you will find passage across the shore. In my role as teacher I hope to be able to show you other ways, if not other ports. — Giuseppe Vitali

Emmy was a teacher too.  And she fabricated some mathematics that binds them all, as they sought their own passages and ports of call. The Rings that Bind.

For she had had obstacles and a vast ocean to cross in her own passage in life — she was able to reach another shore and dwell for only a short while.  But her perspective and rings will live on forever.

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The Gift

He said softly, “I don’t see the point of us meeting.”

The conversation had essentially ended at that point.  It was a complex point. An awkward social moment in time.

Very likely he wouldn’t accept a gift of million dollars.

The Riemann Zeta Function.

It was a clopen topic to him; you see, it hadn’t anything to do with Mathematics proper.

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