Find the 3 Famous Numbers

Question

There are 3 clues hidden in the poem below.

Each clue reveals a famous number.

Find the 3 famous numbers and explain your answer in detail.

By. This. I. reveal three clues displaying
The relentless nature of numbers.
I value relationships very much,
And most, being most beautiful of all,
The big three first to define relationship like none ever thought of.

Transcend all the preconceived notions and understand.
Circle back to others.
Observe what nature makes.
Border walls are around me, but totally without power to trap.
Mathematics is very justified in its special veneration of these climbers, indeed, awe- what height!

---

Edit: It's May 7th, so a hint will be given today. I've decided to combine hints 1 and 2 and move directly to the 250 bounty stage. I hope it is the only hint necessary.

Hint #1 is really 9 hints:

1. When you find one hidden clue, you will very quickly find the other two.

2. Each hidden clue is one sentence.

3. There is no riddle tag because the hidden clues are too direct to be good riddle clues.

4. No letter manipulation (turning, twisting, reversing, breaking apart, etc.) or assigning of numerical values to letters is necessary.

5. No cryptography or ciphering skills are necessary.

6. No thesaurus or dictionary will be of help (beyond defining the words in the poem).

7. Unlike many riddles, this puzzle involves no (or very little) subjectivity in interpreting the answer.

8. You need only the words in the poem. In other words, none of the words need to morph into other words.

9. Other than the three periods after the first three words, there is nothing significant about the punctuation in the poem.

Answer 1

The three famous numbers are

the golden ratio, e and π

How to find them:

As JLee said, it won't be a guess, you have to count the words.
The first one is the golden ratio, which is 1.6180339887...:
You take the first word ('By'), then there is the point and then you count to the sixth word ('displaying'), then one word further ('the') and so on, to get:
'By displaying the very, very most beautiful relationship, the others are totally in awe.'

The third one is π, which is 3.141592653589793...: here you take the third word ('I'), then there is the point and then you count one ('reveal'), four ('the') and so on to get:
'I reveal the relentless value of the relationship of the circle border to its height.'

Thanks to @Rand al'Thor I tried e again. I'm so sorry, I must have counted wrong - but nevermind, it's 2.718281828459045... and so we get:
'This relentless nature, and being first to transcend the others, makes me very, very special indeed.'

Answer 2

The "big three" would be

Euler's constant, pi, and the imaginary unit

whose "relationship like none ever thought of" is, of course,

$e^{i\pi}=-1$

The hints:

Transcend all the preconceived notions and understand. [e and pi are both transcendental numbers]
Circle back to others. [pi is sometimes called the circle constant.]
Observe what nature makes. [You use an i to observe. Also, nature likes to make exponential spirals, and $e^{it}$ is a function that generates one.]
Border walls are around me, but totally without power to trap. [Another reference to spirals, which encircle a point but enclose no area.]
Mathematics is very justified in is veneration of these climbers... [i and pi have climbed on top of e]

Answer 3

Perhaps AxiomaticSystem is right about the three numbers being

$e,\pi,i$$,

but the three clues could be more direct inside the poem:

I value relationships very much,
And most, being most beautiful of all,
The big three first to define relationship like none ever thought of.

I feel like this should be something to do with equationd (relationships), defined by an equals sign ($=$), invented by Robert Recorde. If Recorde was the "first to define relationship like none ever thought of" (by introducing the equals sign), then this line might clue $e$ since his name has an extra e compared to the modern English word it resembles.

Transcend all the preconceived notions and understand.
Circle back to others.

This surely indicates $\pi$, a transcendental number which is given by circling.

Border walls are around me, but totally without power to trap.
Mathematics is very justified in its special veneration of these climbers, indeed, awe- what height!*

This could be $i$, an imaginary number which is unfettered by inequalities (border walls). The axis of imaginary numbers is drawn vertically, which would make them "climbers", and it goes up to infinity, hence "awe - what height".

It's a bit tenuous, but somehow fits together. Other things I thought of from the poem were

infinity, from the "relentless nature", and natural numbers, from "what nature makes".

Thinking of different ways of hiding clues, I also tried checking

letter counts in words, and word counts in phrases/sentences, to see if they spelled out any interesting numbers,

and

Morse code in full stops and commas, to see if it spelled out anything interesting, but all I got was SETME EEEN(?) which doesn't seem to make sense.