Answer

This comes from the Oral Torah (a lesson I gave in the kollel). My claim is that the course of the world proceeds according to the laws of nature, and the Holy One, blessed be He, does not run it. At most, He intervenes on rare occasions, if at all. True, in the past He apparently was involved, but just as miracles and prophecy came to an end, so too His involvement came to an end. Therefore, for example, the Holocaust was not a punishment for anything, but rather the Nazis' decision to murder Jews.
See a bit here:
https://mikyab.net/%D7%9B%D7%AA%D7%91%D7%99%D7%9D/%D7%9E%D7%90%D7%9E%D7%A8%D7%99%D7%9D/%D7%97%D7%99%D7%A4%D7%95%D7%A9-%D7%90%D7%97%D7%A8-%D7%90%D7%9C%D7%95%D7%94%D7%99%D7%9D-%D7%91%D7%A2%D7%95%D7%9C%D7%9D/
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Questioner:

A response to the main points of your argument
I think the root of the “problem” lies in the huge gap between what you wrote to me privately in the email and the way the same ideas came out in the summary you gave to Odiya. On the very same issue, one time you come across as “shocking,” and the second time as “measured and reasonable.”
A. Your explanatory remarks attached to the email
"This comes from the Oral Torah (a lesson I gave in the kollel). My claim is that the course of the world proceeds according to the laws of nature, and the Holy One, blessed be He, does not run it. At most, He intervenes on rare occasions, if at all. True, in the past He apparently was involved, but just as miracles and prophecy came to an end, so too His involvement came to an end. Therefore, for example, the Holocaust was not a punishment for anything, but rather the Nazis' decision to murder Jews."
B. Your summary to Odiya
"My answer to Odiya, then, is that God is present in everything we look at. He has no need or desire to reveal Himself, because He is revealed before us all the time. In an age of mature humanity, that revelation does not take place through miracles and transcendent events, but rather through the laws and natural order, and through the norms and values He gave us in His Torah. Those who do not see this simply need to grow up. And those who do see it certainly do not need to indulge in a childish romanticism of a miraculous relationship with the transcendent."
Regarding part A, which seems very problematic to me:

1. "that the course of the world proceeds according to the laws of nature, and the Holy One, blessed be He, does not run it" – This is the explicit Aristotelian philosophical approach that Judah Halevi attacked vehemently (almost Spinozist). Rabbi Aviner calls the role you assign to God “the chairman of the universe association, invited only to sign the report at the end of the year.” The Holy One, blessed be He, does not manage nature, but He is outside the natural world and is its Creator. If you agree with that—that is, if you deny holding a Spinozist position—why call it “does not run it”? Why not call it “runs it in a way that makes it look as if there is no one running it”? Exactly as you wrote in part B. If you agree to that formulation, that is the root of the difference between what you think and what you write or say.

To paraphrase, God's greatness in the Greek approach is expressed through the intensity of His distance (He doesn't know, isn't familiar, etc.), whereas the Jewish approach says, “With God's help, the cholent will turn out well”—that is, bringing Him into the cholent pot expresses His greatness. There are countless sayings of the Sages that explain His hiddenness as humility, or, in your language (version B), as an educational God.

1. "At most, He intervenes on rare occasions, if at all"—what does “intervenes” mean? Is His hiddenness not itself His intervention? In the analogy of the teacher and the students, there are three situations: a teacher in the classroom, a teacher who left a written text as a lesson but is absent, and a classroom with no teacher and no text from the teacher. Even in situation 3, where the students ask, so what are we supposed to do today in the teacher's absence—that is super-active intervention. Because they are in a classroom in a school, and they are obligated to something. Why add “if at all”? It sounds awful!!

1. "But just as miracles and prophecy came to an end, so too His involvement came to an end," How do you know that miracles have ended? Why tie this to the end of the age of prophecy? And even if it is true, to call it “His involvement came to an end”? You are actually idealizing the state of “hiding of the face,” whereas the Torah treats that as a punishment!!

4."Therefore, for example, the Holocaust was not a punishment for anything, but rather the Nazis' decision to murder Jews." Where did your two levels of explanation disappear to? And how do you know what goes on in the divine system of considerations? Doesn't this contradict, for example, the whole section of Bechukotai?
By contrast, your summary remarks to Odiya sit well with the heart, do not arouse antagonism, and it seems to me that they also reflect your true opinion when you momentarily abandon the desire to shock or to be crystal clear, as befits your rationalist approach. Do not underestimate the aspiration for things to sit well with the heart—of course, not at the expense of speaking the truth.
Also on the deep philosophical level, there really are no miracles and no nature; it is all just a matter of terminology. Everything is from the blessed God. The aspiration to rebuild the Temple and restore the institution of prophecy after the world has reached maturity, in your language, seems unnecessary according to your approach. However, despite Maimonides' words, in my opinion closing the circle is intended to answer that part of humanity and Judaism that lives its whole life under the impression that everything is nature. Will fire descend from heaven on the day the altar is dedicated? Will the crimson thread function on Yom Kippur? Yes and yes, and that would not be a regression to the realm of childish faith. Quite the contrary, it would be the answer to those who have not matured enough. Even Maimonides, with his principle that the world follows its natural course, speaks about building the Temple, and I would add: and about all the miracles that occurred there at every step.
There is no obligation, of course, to accept my “prophecy,” but it does not contradict the vision of the prophets, and in any case it offers an interpretation of reality. 

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Rabbi:
It is hard for me to conduct the discussion here because it is long and requires definitions and detailed logical analysis. I think you are very mistaken already on the conceptual level (if He runs everything through the laws, that is what it means that He does not intervene. Everything else is semantics). I spell all this out in my books and answer all these claims, and it is hard to elaborate here.
I am not particularly impressed by quotations from the Kuzari, and certainly not by Rabbi Aviner, and not even by the Sages (in the book I explain why they have authority only in Jewish law and no more than that, and even there not because they are always right but because we accepted their authority upon ourselves). Even if they hold that view (and in my opinion the Sages did not hold that view, certainly not all of them), I disagree with them on this matter. And if I am Greek, then I am Greek. Titles and labels are not arguments.
But all the quotations here do indeed describe my position accurately.
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Questioner:
If He runs everything through laws that He legislated, and He also intervenes in them from time to time, then by definition that is called not being involved? I am astonished! But fine, let us say that is a matter of definition—what definition would you give, according to your view, to His relation to the world? “He abandoned the earth”? How could that be? 
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Rabbi:

My claim is that contrary to the accepted view, God does not heal the sick and does not free the imprisoned (except perhaps in very rare cases—and even that seems highly doubtful to me). Therefore there is no point in praying to Him for this or that need, except in extreme cases when there is no other way out; nor is there reason to thank Him for healing or any other “miracle” (see the latest column on my site about the law of small numbers). My claim is that the laws of nature determine what will happen, and even if the Holy One, blessed be He, set them up (which is of course entirely acceptable to me), and perhaps even still operates them to this day (which I doubt says anything meaningful, in my opinion), there are still no deviations from them. Therefore the philosophical question whether He is constantly operating them or whether they operate on their own is not really important. It is semantics. The substantive claim is that there is no deviation from them (except for rare cases, if even that), and in that sense today we are on autopilot and not under the hands of the Holy One, blessed be He.
"God has abandoned the earth" sounds to me like not a bad description of that picture. But I do not see much point in arguing about terminology and expressions.

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Questioner:
Thank you for the clarification. As a loving friend, I am telling you that terminology matters. See how we clarified the issue itself and it is not actually in dispute. I know you; others may know you less. That terrible sentence has a negative connotation and an awful meaning regarding the Holocaust. You draw fire even בלי the terminology. I know you do not care and that truth is what matters. I am certainly not trying to educate or preach.   
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Rabbi:

On the contrary, my remarks are mainly in connection with the Holocaust. Indeed, God has abandoned the earth. He has no connection whatsoever to the Holocaust. The Nazis did it by their own decision.