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I bow to that unmanifest avyakta algebra/unmanifest part of mathematics, the one seed of the entire manifest vyakta arithmetic/manifest world, which the Sāṅkhyas proclaim to be the generator of the intellect, established by the Supreme Being satpuruṣa True Person/Supreme Being. (1)
Subodhinī: The word "generator," etc. This verse is reconciled in the context of Gaṇeśa, in the context of Nature prakṛti, in the context of the Lord, in the context of mathematics, and in the context of the father. There, first—
In the context of Gaṇeśa: I bow to the Lord of the Intellect, the leader of the Gaṇas. Although Gaṇapati is the Lord of Success and Intellect, here, because this algebra is achieved solely by the intellect, the salutation to him as the Lord of the Intellect is appropriate. Because of the necessity of requesting intellect from Gaṇeśa, the teacher himself has said, "Algebra is the intellect, aided by various signs." What kind of Lord is he? He is the creator of all manifest vyakta known objects; that is, he is the producer of the entire manifest physical world, such as the earth and mountains.
Now, according to the dictionary which states "A pandit is one who possesses numbers, a poet," the Sāṅkhyas, the poets, proclaim that the unmanifest avyakta unknown, as a principle, is established by the Supreme Being, because the unmanifest, such as the ether, is permeated by Him. This is the meaning: the arising effect establishes the creator; this is the logic. Just as the earth, etc., has a creator because it is an effect, like a pot, the creator is the Supreme Lord himself. Therefore, it is said to be the Lord. What kind of mathematics is it? It is that which is combined with calculation or is the principal calculation. Again, what kind of one-seed is it? It is that which has no other seed; it is the unique seed. This is said with the intention of the single-syllable mantra of Ganapati.
In the context of the unmanifest: The unmanifest pradhāna nature is famous in the Sāṅkhya philosophy as the cause of the world. The Sāṅkhyas proclaim it to be the generator of the intellect, because the emergence of the principle of the intellect, called the "Great" mahat, is the manifestation here, for they are proponents of the satkāryavāda doctrine of the pre-existence of the effect. If it is asked how the insentient nature produces an effect, it is said "established by the Supreme Being." Just as the clay, established by the sentient potter, produces the pot, so it is here. They proclaim that Nature, independent of the Puruṣa, is the producer. It is said, "Just as the flow of milk is for the growth of the calf, so is the activity of Nature for the liberation of the ignorant soul."
In the context of the Lord: The Lord is the one who is Existence, Consciousness, and Bliss, known through Vedānta. The Sāṅkhyas are those for whom the soul ātmā is the known quantity, and the internal organ antaḥkaraṇa is the form of that soul. Established by the Supreme Being, through the four-fold path of discrimination, He is whom the soul-knowers proclaim to be the generator of the knowledge of the intellect. It is the one unique seed, the material cause of all manifest effects. "From whom these beings are born, having created them, they enter into Him; from this soul, the ether was born," such Vedic texts are the proof of His being the material cause.
In the context of mathematics: Mathematics here is the unmanifest, because it is the specific focus. By saluting it, the presiding deity is also saluted, as seen in the case of the Śālagrāma stone. The Sāṅkhyas, the knowers of numbers, the calculators, proclaim that which is established by the Supreme Being—meaning it is practiced by a person of capability—to be the generator of the knowledge of questions and answers.