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By my extreme size, I escape your eye
The nature of every thing, is but many of I
Since my unveiling, the inexact came by
And there came a new discipline to unify
What am I?


The explanation

So there are answers for the atom and radiation. Both are very close, but arguably jhabbott got closest with their guess of elementary particles.

So, my own answer:

Particles that are, elementary
Finer than a germ, so small you can't see
Apples ants and me, all comprise many
For the inexact, that's uncertainty
What to unify? Quantum gravity

Explanation:

By "escape your eye" I did mean that one can't see it with naked eyes.
The second sentence of course means that it is a building block of matter (everyday or not).
While two answers are right that the third sentence refers to Heisenberg's Uncertainty Principle or the probabilistic nature of quantum-scale stuff (one is the consequence of the other, right?) the answer that guessed the atom made a mistake here: that didn't exactly come by with the concept of the atom, rather this appeared with the rise of quantum mechanics.
Regarding the new discipline to unify, it refers to the discrepancies between quantum mechanics and general relativity that lead to many different theories trying to resolve the problem. It can mean to unify quantum mechanics with relativity, or to unify those new theories and come to a single, widely agreed physical model again.

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    $\begingroup$ Something that rhymes with this is $\pi$ $\endgroup$ – manshu Jan 30 '16 at 14:47
  • $\begingroup$ @manshu Nice suggestion, but I couldn't fit it in. $\endgroup$ – busukxuan Feb 1 '16 at 16:14
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    $\begingroup$ Don't worry, not putting $\pi$ somewhere is not a sin. (Note that this comment rhymes with your last comment.) $\endgroup$ – manshu Feb 1 '16 at 16:27
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While there is another answer that states

the atom

is the answer, which I agree fits very well. I think there is something else the also fits, perhaps better.

Sub-atomic particles (Quarks, Leptons, Bosons).

By my extreme size, I escape your eye

They are too small to see.

The nature of every thing, is but many of I

Atoms are made of these, as larger structures are made of atoms.

Since my unveiling, the inexact came by

This refers to the probabilistic "nature of nature" at this quantum scale.

And there came a new discipline to unify

The new discipline was quantum mechanics / quantum theory. It was thought at the time that it would be a unifying theory, where Einstein's efforts for a unifying theory so far had failed. However, although this new discipline came to unify, it has not yet delivered.

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My guess is:

an atom

Argument:

By my extreme size, I escape your eye

Atoms are extremely small, and cannot be seen with bare eyes

The nature of every thing, is but many of I

Everything is made of many atoms

Since my unveiling, the inexact came by

Heisenberg's uncertainty principle

And there came a new discipline to unify

Nuclear sciences

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    $\begingroup$ I don't know why, but making your answer rhyme is something I would like to see you try $\endgroup$ – Desmond Hung Jan 30 '16 at 14:59
  • $\begingroup$ @DesmondHung then I'll give an official answer that rhymes :-) $\endgroup$ – busukxuan Feb 1 '16 at 16:15
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I think it is

Radiation

By my extreme size, I escape your eye

Here I think that escape doesn't mean "Fail to experience" but rather it means "Run away from confinement". And of course we can see each other's eye. I am not saying here that we can see the shape of the photon but I am saying that we can see the eye because of it. (For the fun fact I once saw a question in which the OP thought that he could see photon)

The nature of every thing, is but many of I

Every object emits radiation

Since my unveiling, the inexact came by

Here we can see that the first calculated value of light was $220000$ $km/s$

And there came a new discipline to unify

And finally in 1983 the speed of light was finally concluded to be $299792.458$ $km/s$ by the definition of metre.

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