Bear with me, I am going to build things up the way the Seder song "Echad Mi Yodeia / Who knows one?" does. This post is based on the Maharal's commentary on Avos 1:2 and R' SR Hirch's explanation in Collected Writings III on the symbolism of the numbers 3 & 4.
"One is Hashem". Nothing more need to be said.
"Two are the tablets". On one tablet are mitzvos bein adam laMaqom (between a person and the Omnipresent), on the other, bein adam lachareivo (between a person and their peers).
The first tablet speaks to man-the-recipient; Hashem gives and we enjoy His Good. But there is a paradox in that -- since the Ultimate Good He could share with us is his Own "Nature", to be in His Image, givers in the same way He is a Giver. And so we have the commandments of the second tablet, telling us to relate to others as givers, not takers. (There is an important distinction here between taking and receiving; receiving can be giving or taking, depending on how it's done. See R' EE Dessler's Qunterus haChessed in Michtav meiEliyahu vol I -- Discourse on Lovingkindness in Strive for Truth vol 1.)
"Three are the fathers." And so the human condition is dialectical -- we exist both to receive and to give. And out of dialectical tension grows a third entity, the "I" who has to navigate the dialectic. Every human choice grows out of a tension between two desires. One may be good and the other evil, but also between two conflicting goods, such as between choosing truth or peace (tact).
And so the Torah holds up for us three archetypes, one for each of three pillars of the world listed by R' Shimon haTzadiq in Avos 1:2: Torah, Avodah (worshipping G-d), Gemillus Chassadim (supporting acts of lovingkindness).
Abraham taught the world that we exist to be givers, and is associated with Chessed -- kindness that grows out of a feeling of love / unity with others.
Yitzchaq taught us that our ability to be kind depends on our having a relationship with G-d, so that we can draw down His Good and work with Him. (Kind atheists can only provide what seems to be good from our limited and often short-sighted human perspective. Nor can they get the same level of aid from Hashem, since they aren't trying to get any.)
And Yaaqov was the man of truth, the man of Torah, the one who taught us that unless we develop our own minds and character, all those highfalutin plans won't actually end up being lived. It is too easy to get caught up in alternate desires and invent excuses to ourselves to justify them.
And so, human action is threefold: Avraham teaches us how to improve this world and connect to those in it, Yitzchaq -- how to draw from heaven and the One Who "dwells upon high", and Yaaqov -- how to perfect that universe between our ears and perfect how we relate to ourselves and our own souls.
"Four are the mothers". In Qabbalah, like in procreation, the male is that which initiates a process, and the female is where it develops to its full form. Thus the "three fathers" is how we act on the world, and the "four mothers" is how G-d's "Actions" are received by and effects upon us.
And so, we see G-d as beyond beyond the three ways we act; if we act in three ways, His action is in "four" -- where we lump everything beyond the three in a single "beyond us" category.
"HaKel, haGadol, haGibbor, vehaNorah -- the G-d, the Great One, the Mighty One, and the Awesome One", as Moshe put it and we say at least thrice daily in the Amidah. (As translated by the Vilna Gaon ad loc.)
HaKel - G-d who is transcendent, logically prior to any attachment to Creation. Picture the yud of the tetragrammaton, floating there off the top line (the shirtut of a Torah scroll).
HaGadol -- Great, Immense, in fact, Omnipresent. This is the G-d of Creation. Everything that exists is caused by Him. Picture the first hei. G-d the Giver.
HaGibbor -- the Mighty One, in the sense of Strength of Character. Gevurah is the might of the immovable rock, not the irresistable force. The gibbor is the hero who can resist his evil inclination (Avos 1:2). It's the G-d who "steps back" from creating to give us "room" to be givers ourselves. Hashem gave us natural law saw that we can make plans and act intelligently; even if though it limits what we can expect Him to do. The constricted line of the vav, the third letter of His Name, connecting Him to us.
VehaNora -- Awe-Inspiring. The G-d of miracles, both those that defy nature and the hidden ones. Hashem's Plan is manifest even though/when He so constricts His Choice of Actions. The final hei, again spread out.
This is also:
Barukh -- the Wellspring,
Atah Hashem -- You (we can say "You"!) are the Merciful that Underlies Existence,
Elokeinu -- our Lawmaker of natural law, which is the level on which most of us generally relate to the world(s),
veElokei Avoseinu -- our ancestor's Lawmaker, creator of Moral Law, and thus the Worker of miracles when moral law superceeds physical laws.
Creation is done as "Eser Maamaros - 10 Utterances." (Avos 5:1; Rashi -- Bereishis 1:1 and the 9 times it says "vayomer -- and He was saying" in that chapter.) Each of these Utterances had four aspects, yielding the idea that Creation comes in 40. And when a person avoids creative activity on Shabbos, he rests from "40 missing one" categories of such activity. The 40 G-d performed, but one of them -- making something out of nothing -- is beyond our abilities either way. And so building the Tabernacle, a microcosm, involved 39 creative activities, none of which are performed on Shabbos. And when someone sins in a way that undermines creation, his punishment is "40 missing 1" lashes (or as many up to that number his health can tolerate).
Where, scripturally, do we (Tiqonei Zohar in three places) get this idea that all of G-d's Actions are felt in four ways?
כֹּ֚ל הַנִּקְרָ֣א בִשְׁמִ֔י וְלִכְבוֹדִ֖י בְּרָאתִ֑יו יְצַרְתִּ֖יו אַף־עֲשִׂיתִֽיו׃
Every one that is
called by My name, and
whom I have created (Barasi) for My glory,
I have formed (Yatzarti) him, even,
I have made (Asisiv) him.
And so, beyond our three world is G-d's name, the world Qabbalists call Atzilus, and our three which they call Beri'ah, Yetzirah, and Asiyah. 3+1. Four are the mothers.