To ultimately sum up the above work, it says: The universe is Infinite.
Math is an approximation by its very nature. For example, if we attempt to determine the movement of a planet around the sun, if we don't account for other planets we will be inaccurate. If we account for other planets, we will increase accuracy but we will still not be accounting for other systems. As the universe is infinite, it is impossible to account for all infinite systems. So, yes, I would agree that it is impossible to write an equation or set of equations that encompasses all that is. However, that does not preclude us from recognizing the universe to be the manifestation of infinity.
Regarding the Vedas, they are a portion of all that is. Like any portion of all that is, they contain a portion of the truth. But no single portion of all that is contains the whole truth; that is reserved for all things as a whole. While there are truths in the Vedas, many are not even able to be extracted without careful consideration of a large enough spectrum of sources so as to understand the universe's Infinite nature.
Quantum theory is an invalid model that violates exactly what you mention of the incompleteness theorems. They attempt to contain within a single set of equations the entire fundamental workings of the universe, and in so doing they are inherently built as an approximation that falls apart with ease the further from the source of approximation an observation is. They do not recognize the infinite structure of the universe and as such cannot in any way describe the universe, as it is the manifestation of infinity.
The Vedas are certainly of value and I agree that they contain vast wisdom. However, they alone do not contain all the knowledge of the universe because they, just like an equation, are a limited part of all that is and create only an approximate picture of the infinite universe. When only one source is looked to for information, it produces a skewed reality that is limited. As such, individual sources of information are effectively incapable of capturing the full extent of truth. This even includes individuals such as myself. I do not claim to know everything, but this theory is instead the cornerstone of understanding upon which an infinite progression in knowledge can be obtained without approximation. It is the beginning of understanding rather than the ending.
The Vedas are not speculative, and Sanskrit grammar is arguably superior to mathematics. The Vedas are pure ecstatic knowledge as Kṛṣṇa said in Śrīmad-Bhāgavatam:
SB 11.21.38-40: Just as a spider brings forth from its heart its web and emits it through its mouth, the Supreme Personality of Godhead manifests Himself as the reverberating primeval vital air, comprising all sacred Vedic meters and full of transcendental pleasure. Thus the Lord, from the ethereal sky of His heart, creates the great and limitless Vedic sound by the agency of His mind, which conceives of variegated sounds such as the sparśas. The Vedic sound branches out in thousands of directions, adorned with the different letters expanded from the syllable oṁ: the consonants, vowels, sibilants and semivowels. The Veda is then elaborated by many verbal varieties, expressed in different meters, each having four more syllables than the previous one. Ultimately the Lord again withdraws His manifestation of Vedic sound within Himself.
I didn't call the Vedas speculative. I called them a part of all that is. Because they are. They aren't everything that exists, and thus they do not contain all that exists. Regarding speculation, interpretation of reality using a single source--whatever that source may be--is indeed speculative in nature. Thus it is the speculation of a human being regarding the nature of reality to draw upon the Vedas and the Vedas alone as a basis for the total description of how reality functions. It is impossible to understand one thing without first understanding all things.
Veda means knowledge, and one of the categories of knowledge in the Vedas is Vedānta, which means the conclusion of knowledge. Such a conclusion must be complete and consistent.
The thousands of books of the Vedas are summarized in extremely terse form in the Vedānta-sūtras, and the Vedānta-sūtras are explained in the Śrīmad-Bhāgavatam. Śrīmad-Bhāgavatam describes itself as the literary incarnation of God, not as a part of the universe. The words and texts texts have definite forms represented in the world, but the knowledge they represent is full and absolute.
Multiple books of the Vedas say Brahmā heard the seed verses of the Vedas after he awoke in a world of nothingness, and these sounds taught him how to create the objects of the universe.
The Vedas are traditionally known as apauruṣeya, which means having no human author. Here is an example of a verse from Śrīmad-Bhāgavatam claiming to be of Divine origin, albeit with a somewhat awkward translation from Sanskrit:
SB 11.21.38-40: Just as a spider brings forth from its heart its web and emits it through its mouth, the Supreme Personality of Godhead manifests Himself as the reverberating primeval vital air, comprising all sacred Vedic meters and full of transcendental pleasure. Thus the Lord, from the ethereal sky of His heart, creates the great and limitless Vedic sound by the agency of His mind, which conceives of variegated sounds such as the sparśas. The Vedic sound branches out in thousands of directions, adorned with the different letters expanded from the syllable oṁ: the consonants, vowels, sibilants and semivowels. The Veda is then elaborated by many verbal varieties, expressed in different meters, each having four more syllables than the previous one. Ultimately the Lord again withdraws His manifestation of Vedic sound within Himself.
What do the Vedas have to say about the existence of Christianity? Of Islam? Of science? Do they explain how gravity works? Do they disclose the nature of human beings with relationship to the nature of the cosmos?
I am not questioning their truth. What I am saying, however, is that they cannot be comprehended by purely reading their texts alone. It is impossible.
Let us take the sanskrit you reference. It is not straight-forward nor is it simple to follow. It is not in its original language and is littered with interpretations of those who read it in its more original form and attempted to rewrite it into different languages. Is it to be taken literally or figuratively?
There is One Truth. And if every single person were to study the full texts of the Vedas, they would not arrive at the same perception of what that One Truth is. Because the texts are only part of the Infinite All.
I appreciate your passion for the Vedas and I can admit that I have not studied them as thoroughly as I have many other sources. Indeed, I will be more driven to look into them much more thoroughly now that this conversation has happened. But I don't need to look at them to know that they cannot be understood in a vacuum, because nothing can.
The above post is a compilation of many links. You were driven to respond to my post within minutes. I posted my article at 4:47pm (EST) and you responded at 4:52pm (EST), indicating to me that you did not actually look at the post itself whatsoever but wanted to simply put forth your opinion on something that you felt was stepping on what you hold at highest esteem. What do the Vedas say about disregarding completely what others have to say?