Hinduism is a vast religion, and it has great philosophies of theism. Probably there might be some atheistic philosophies too. It would be a great amusement to see if this thought of Atheism was also in Hinduism.
So are there any verses, teachings, ideas, arguments e.t.c, conveying Atheism? Here 'atheism' is being pointed to, not 'Astika-Nastika'.
There are two kinds of schools of Indian philosophy, Astika and Nastika. The Astika schools are part of Hinduism, whereas the Nastika schools like Buddhism, Jainism, Charvaka, and Ajivika fall under the broader category of Dharmic faiths. Now what the six Astika schools have in common is that they accept the authority of the Vedas. But they differ on other issues, like the existence of God. Four Astika schools unequivocally accept the existence of God - Yoga, Nyaya, Vaisheshika, and Vedanta. Here's what the other two Astika schools believe:
Samkhya: The Samkhya school rejects the existence of God outright. Here are the arguments against the existence of God that Kapila gives in Adhyaya 5 of Samkhya Sutras:
Not because (the cause is) directed by Ishvara, (that there is) the resulting of fruits, because the production thereof takes place by means of Karma.
Because of his own benefit, (Ishvara's) superintendency (will be) like that of man.
Otherwise, (Ishvara will be) like the human lord.
(Otherwise, Ishvara will be like the human lord), or nominal.
Without Raga or passion, superintendence is not established, because Raga is the invariable and unconditional cause of all activity.
On (the admission), again, (of) connection with Raga, (he will) not (be) eternally free.
If (you say that the condition of being Ishvara arises) through connection with the powers of Prakriti, (then there will be) the implication of (his) attachment.
If (it be said that the condition of Ishvara may arise) through the mere existence (of Prakriti by the side of Purusha), (then) the condition of being Ishvara (will belong) to all (Purushas).
On account of the non-existence of evidence (there is) no proof of an eternal Ishvara.
Owing to the non-existence of the Vyapti or pervasion (there is) no inference (of Ishvara).
The Shruti also (speaks of the web of creation) being the product of Prakriti.
For more details, see this PDF which gives the relevant portions of Aniruddha's Samkhya Sutra Vritti and Vijnanabhikshu's Samkhya Sutra Bhashya. By the way, as I discuss in my answer here, Vijnanabhikshu argued that Kapila just pretended to reject the existence of God, in order to deceive people for their own benefit. The idea is that if people believe in Ishwara, they will seek to have the Aishwarya or lordliness, i.e. the same powers that Ishwara has, and the pursuit of such powers will distract them from attaining Jnana. But Vijnanabhikshu had unusual views.
By the way, the Samkhya school at least believed in the Devas; here's what Ishwara Krishna says in verse 53 of the Samkhya Karika:
aṣṭavikalpo daivas tairyagyonaśca pañcadhā bhavati |
mānuṣyaścaikavidhaḥ samāsato bhautikaḥ sargaḥ ||The divine class has eight varieties, the sub-human has five and the human has one (only). Such, in brief is this creation.
Purva Mimamsa: The Purva Mimamsa school was divided on the existence of God. But one thing they all agreed on was that God (if God even existed) was neither the creator of the Universe, nor the author of the Vedas, nor even omniscient. In fact, they didn't even believe the Universe is ever created or destroyed! Here is what Kumarila Bhatta says in this excerpt from his Shloka Vartika:
And as for the fixing [of the meaning of words] at the beginning of Creation, - we do not admit of any such time (the world being eternal and as such having no beginning in time. [Objection:] "But, if there be such a Person as would create the world, and then set going the processes of Dharma and Adharma, and the uses and relations of words, for the sake of the world,—then, such a fact Would not in any way vitiate the Veda." Reply: Yet this theory is as difficult to prove, as an omniscient person; hence we have not admitted it. At a time when all this did not exist, what could have been the condition of the universe? As for Prajapati himself, what could be his position? And what his form? And at that time who would know Him and explain His character to the later created persons? Without perception, how can we determine this? Then again, in what manner do you believe the world to have had a beginning in time? Since Prajapati is without a material body, etc., how could He have any desire towards creation? And if He has a body, assuredly this body could not have been created by Himself; thus then we would have to postulate another creator. If Prajapati's body be held to be eternal, then - so long as earth [has] not been produced, of what material would that body be composed? Then again, in the first place, how is it that He should have a desire to create a world which is to be fraught with all sorts of troubles to living beings? For at that time he has not got any guiding agencies, in the shape of the virtue, etc., of the living beings themselves. Nor can any creator create any thing, in the absence of means and instruments. Even the production of the spider's net is not held to be without some sort of a basis; as the saliva, which is produced out of the body of the animals eaten (by the spider). In the absence of objects of compassion, no Pity could be possible for Him. And if He were urged to creations by pure compassion, then He would create only happy being. If it be urged that " without some pain, neither the creation nor the continuation of the world would be possible," - then when everything depends upon the mere will of the Creator Himself, what could be impossible for Him? And if He were to depend upon Laws and Agencies, then this fact would deprive Him of His independence. What is that end which He desires, and which could not be gained without creating the world? For without some end in view, even a fool does not act. Then if He were to act so, then what would be the good of his intelligence? If the activity of the Creator were due to a desire for mere amusement, then that would go against his ever-contentedness. And the great amount of work would be a source of infinite trouble to Him. And His desire to destroy the world too would be hardly explicable. And such a Creator could never be known by anybody. Even if He were known in form, the fact of His being the Creator could never be known. Because, at that time what could the living beings, appearing at the beginning of creation, understand? They could not understand where from they have been born; nor could they know the state of the world prior to creation, or the fact of Prajapati being the Creator. Nor could the idea that they would derive from His own assertion (with regard to His being the Creator), be altogether trustworthy; because even though He may not have created the world, He might speak of having done so, in order to show off His great power. In the same manner the Veda that would proceed from him would only be doubtful, and hence could not be admitted as a sure proof of His existence. And as for that which is eternal, how could it make a mention? For, if the Veda existed before the objects (created), then there can be no connection between this (Veda) and the objects created. Therefore the passages must be interpreted as praising up something else.
But some Mimamsakas like Kumarila Bhatta, Laugakshi Bhaskara, and Apadeva did believe in some notion of God; see my question here.
By the way, note that while it might be fair to call all followers of Samkhya and some followers of Purva Mimamsa "atheists", they weren't materialistic atheists of the kind found in modern society. They still believed in the Vedas, the Atma, reincarnation, and Yagnas, they just didn't believe in God. Modern materialistic atheism corresponds to Charvaka, which was a Nastika school of Indian philosophy.
It's also worth noting that the Astika schools which do believe in God have produced detailed refutations of the arguments quoted above. Udayana's Nyaya Kusumanjali, which you can read here, is a Nyaya-Vaisheshika work which seeks to refute not just the Purva Mimamsa and Samkhya arguments given above but also the arguments against the existence of God given by Charvakas and others. And the Vedanta school, the dominant school of Hindu philosophy today, has produced lots of refutations of such arguments. See my answer here for how Vyasa refutes rival schools to Vedanta in the Brahma Sutras.
