Rambam in Yesodot Hatora (1.11) describes a transcendent G-d that knows no change:
He is not found within time, so that He would possess a beginning, an end, or age. He does not change, for there is nothing that can cause Him to change.
According to Rambam, does G-d "change His mind" to answer to our personal prayers?
Note: this question is only about how Rambam sees their influence.
Eruvin 65a
א"ר חנינא כל המתפתה ביינו יש בו מדעת קונו שנאמר (בראשית ח, כא) "וירח ה' את ריח הניחוח וגו'"
Tora and Gemara use a lot of expressions showing that G.d changes his opinion, as the above citation shows.
There are paradoxes regarding daat hashem. We are limited and created. We see such things as paradoxes. What is a paradoxe, something that is true and seems contradictory because of a lack of understanding.
Based on Rambam hilchot teshuva
ה,יב כבר ביארנו בפרק שני מהלכות יסודי התורה שהקדוש ברוך הוא אינו יודע בדעה שהיא חוץ ממנו כבני אדם שהן ודעתם שניים, אלא הוא יתברך שמו ודעתו אחד; ואין דעתו של אדם יכולה להשיג דבר זה על בורייו. וכשם שאין כוח באדם להשיג ולמצוא אמיתת הבורא, שנאמר "כי לא יראני האדם, וחי" (שמות לג,כ)--כך אין כוח באדם להשיג ולמצוא דעתו של בורא: הוא שהנביא אומר "כי לא מחשבותיי מחשבותיכם, ולא דרכיכם דרכיי" (ישעיהו נה,ח). וכיון שכן הוא, אין בנו כוח לידע היאך ידע הקדוש ברוך הוא כל הברואים ומעשיהם.
As explained in the second chapter of Hilchot Yesodei HaTorah, The Holy One, blessed be He, does not know with a knowledge that is external from Him as do men, whose knowledge and selves are two [different entities]. Rather, He, may His name be praised, and His knowledge are one.
Human knowledge cannot comprehend this concept in its entirety for just as it is beyond the potential of man to comprehend and conceive the essential nature of the Creator, as [Exodus 33:20] states: "No man will perceive, Me and live," so, too, it is beyond man's potential to comprehend and conceive the Creator's knowledge. This was the intent of the prophet's [Isaiah 55:8] statements: "For My thoughts are not your thoughts, nor your ways, My ways."
Accordingly, we do not have the potential to conceive how The Holy One, blessed be He, knows all the creations and their deeds. However, this is known without any doubt: That man's actions are in his [own] hands and The Holy One, blessed be He, does not lead him [in a particular direction] or decree that he do anything.
This matter is known, not only as a tradition of faith, but also, through clear proofs from the words of wisdom. Consequently, the prophets taught that a person is judged for his deeds, according to his deeds - whether good or bad. This is a fundamental principle on which is dependent all the words of prophecy.
if you speak from HIS point of view, he already knows about tefilla etc, about your choices etc, But the principles of Emuna are that tefilla and teshuva have influence and so we have to do a lot for ourselves. The Top-Down science of Hashem and the Bottom-Up are paradoxical because we cannot understand the Gap. This is a gap of knowledge called paradox.
According to the Rambam, G-d does not change. This means that G-d never spoke to anyone. The Rambam writes in the first chapter of his Mishneh Torah that G-d created nature, a divine creation, and Moshe copied the governing rules of nature and produced the Torah, which is certainly divine. Now that we understand that G-d is immutable, we can try to comprehend how He responds to prayer. Philosophers like the Greek pagan Aristotle felt that prayers help improve people and are a time of self-reflection. The Hebrew word for prayer is lehitpaleil. The root is p-l-l, which means “judge.” Prayer means to "judge one’s self."
Maimonides, Aristotle's philosophical successor, felt that G-d does not listen to prayer. The world functions according to the laws of nature. Nothing we do will alter or change natural law. G-d is transcendent and it is impossible for us to describe Him. Any description we put will only remove our understanding of what G-d is. At best we can say that G-d has no body and is one. Rambam says that G-d's uniqueness and oneness are so One, that we cannot compare anything else to Him. G-d is One but not in the unity of one. For instance, if I take a chair and say, "Surely this is one chair," it is not really one since it is made up of many components, that make up the chair. G-d is unlike this chair which if disassembled, will have legs, cushions, seats, etc.
Since G-d is One, it follows that G-d cannot change. If G-d cannot change, G-d cannot become angry when you sin and be happy the next when you make teshuva by making a prayer. Thus, G-d does not have emotions and He does not listen to prayer. This is, to my humble understanding, the Rambam's view on prayer (but it is by no means all of Judaism's view on prayer).
