Avoda zarah is one of the things prohibited by the Seven Noachide Laws. But what about atheism? I know that the 7 Laws are often taken to include a larger number of halachot from the Torah, so would the prohibition against avoda zarah expand to include kefira as well?
Rav Moshe Feinstein, in a t'shuva about allowing children to say a generic prayer in public school (Orach Chayim II #24), refers to the Ramba"m's statement in Mishne Torah that Adam Harishon was given 6 commandments, including belief in God. No'ach and his descendants later got one more, adding up to 7. They both conclude that not only the negative aspect of believing in God is necessary - i.e. not serving other deities - but also the positive affirmation of His creation and provenance over the world, when circumstances call for it. Rav Moshe also uses the inference from the words of Ramba"m explained in @Yishai's answer.
Given the Rambam's statement:
It would seem that the answer is no, it is not permitted.
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