Given that all the answers here are rational leaning answers from the Rambam (he's, I'm glad to say, very popular here), I thought I'd just add, for completeness, that Chassidus tends to explain that we can know Hashem completely. That's the whole point of Torah and Mitzvot, to give us a true understand of Hashem, who reveals Himself in them completely (see for example much of Tanya, e.g. ch 35). This is the hidden meaning of Ana Nafshi Ketovit Yehovit, (Shabbat 105a), which literally means "I put My Soul in writing and gave it".
When the Rebbe Rashab was asked "how can you know Hashem, for didn't it say if 'I knew Him, I would be Him' (Yedayah Ben Abraham Hapenini cited in Ikkarim 2:30), implying we can only know Hashem if we are Him?" he responded "so be Him".
So to understand how this works and how we can taich this with the Rambam, we'd need a huge amount of study, however, I'll give a quick mashal that I've often heard Rav Manis Friedman give that helps:
A father has a young child and sits down to play with him. They play a
game of horsey. The father is a sophisticated banker, head of his
firm. He's 40 and has a rich inner life, a set of interests,
complicated memories, feelings and relationships, ideas and
responsibilities way way beyond the childs level of comprehension. Of
course, the father can't bring any of that to the child, he just sits
down, simplifies and plays.
An onlooker, such as one of his employees, might look over and feel
like the father is unable to connect to the child. The employee knows
the father well, and what he sees in front of him - the father
giggling, saying silly sentences, playing imaginative games, and
flushing with his delight in his child - will feel like this is not
the father. The father is just acting, in an effort to give some joy
to his child.
But let's really think about this. When the father sat down and got
into "connect with my child mode", what happened? Did he really depart
from "himself", become "someone else" for a while? The father would
strongly object! Of course not, I am still me, being me, 100%. It's
not an actor, it's not a demon, it's not a puppet. It's me. In fact,
pay close attention, because you are seeing more of me than you
normally see... My love for my child, our bond, IS me...
So what we are saying is, while it's impossible to know the details of Hashem, for they are infinite, and beyond comprehension (Essence cannot be shared as the Rambam explains), Hashem in his incredible omnipotence, is able to create an external expression of Himself that contains everything that He is, and gives us a way to know that. It's all there, and the Nimshal and the mashal are one.
Once you are done with Tanya, may I finally recommend a reading of Ma'amar Veyadata (english translation here), for a very exquisite treatise on this concept, with lots of detail and examples from the Rebbe Rashab. The conclusion is that by performing mitzvot, especially the mitzva of learning Torah, we are getting to know Hashem completely.
Therefore I disagree with the premise. Or rather, I agree that knowing half way is not knowing, but I disagree that that is our mission. Our mission is to get to know full-way. Full-way doesn't mean every detail, it just means get to the Essence (the Essence is simple, not detailed).
Here is a long message I wrote a friend recently to help them understand the above mashal based on all my thousand hours of listening to the Rav who originally gave it, and I believe it helped him, so fwiw:
(note, there are two separate ideas in the mashal, the last
sentence was the second).
What I am trying to hone in on is: what is a person? I would
argue many of the statements the objectors to our perspective have
declared about Hashem apply to anyone. You cannot know me. In fact, I
hate to say it, but even my wife cannot know me, in and of myself. I
can't even know myself in that way! There's too much to me, not only
is my finite set of attributes, experiences and actions far larger
than is possible to enumerate (and most of it is too esoteric for
words anyway), but there's also an infinite amount of potential in me
too, all of it utterly unique to me and me alone. How I relate to
every aspect of the universe is purely a me thing (essence can't be
shared), and you have zero access to it. You can't know me in and of
myself - if I could share that with you I wouldn't be me. So is the
situation hopeless? Far from it.
Whenever we act, we are able to put ourselves into that action to
whatever degree, from zero to infinity. If I am forced to do something
I hate doing, chances are the action will contain zero of me. If I am
doing my favourite thing, chances are I am fully putting myself into
that action. This is why the child knows the father better than the
employee. The employee knows more about the details of the father, but
certainly he hardly knows the father. The child, who knows nothing
about the details of the father knows the father best of all.
Why? What's the difference? What's powering all this? The answer
is desire. Desire is just one word, and it's not good enough by
itself. This concept goes beyond desire, beyond words altogether. The
father's real life, real desire, real place, real delight is his
child. If the father had to give up all his business, his
sophistication, his memories, his abilities, his other relationships
in order to be with his child, he wouldn't even think twice. "All that
stuff isn't really me, but this is really me, and I can't not be
So, many commentors on the Torah, and in fact I'd argue the Torah
itself, tells us this is also true of Hashem. It's 100% right when we
say we can't know Him in and of Himself. So, some people say that
there is a disconnect between Himself, and the way He manifests in the
creation, but we have to be very careful about what we say next. Is
this disconnect a severance, or simply a "tzimtzum"? I would say that
we must not say it is the former. It is the latter (fact), and what
that means is this. Whenever Hashem "acts", He pours Himself 100% into
that action - it is really Him, not an avatar, not an act, not a lie
or a fakeness or an "as if". Unless "as if" only means this: It may
not be the totality of His eternal infinity, i.e. the father's
sophisticated adult life and sumtotal experiences/feelings/thoughts in
a very literal way. But nay, it gets to the core of Who He IS,
So does Hashem get angry? You bet He does. When the Nazis
sadistically humiliated and then murdered whole families including
little innocent children, to say that Hashem "didn't really get angry"
is just about the most blasphemous thing a person can utter (sorry, I
don't think anyone who says this is really being blasphemous or a
heretic etc, but I have to say what I just said). Certainly, you'll
never find anything in gemara or midrash that would ever say that, and
there's a reason for that.
So, hold on. Am I saying that Hashem is just like us? Am I
removing the "Ultimate Mystery"? The words of the Rambam, Rabbeinu
Bachaye, and all the other great men who exhorted us to not personify
Hashem, or attribute parts to Him (chas veshalom) etc simply mistaken?
Definitely not. This is the Ultimate Mystery:
Firstly, I would argue far harder to understand about Hashem is
not His infinity (by the way, I would say that He is beyond infinity,
not 'infinite'), but the fact that He was never created. This means
that He must be utterly simple, One. This is the bit that's impossible
to get our heads around. We can't comprehend how it's possible for Him
to get angry, because we can't picture non-created, non-timebound
anger, non-disconnected/part-like anger. On top of that, we can't
understand what it is like for a (beyond) infinite being to get angry -
surely that anger is infinite and that is something I can't understand. If I felt it, raw, I'd be blotted out of all existence on
every level! Thank GOD, He is able to "mtzamtzem" Himself in some
miraculous paradoxical way that allows us to have a relationship with
Him and not die an infinite death. And good for Him too (this is why
the Rebbe says "chas veshalom" in Tanya Shaar HaYichud VeHaemuna
So how can I relate to His anger? Why does the Torah even bother
to tell me that He gets angry if I can't actually understand it? Three
steps: I can't even understand your anger, friend. Your anger is very
you-flavoured, very you-themed, and certainly unless I am you, I can't
possibly know what that is like. But also, I can know your anger,
because we both get angry, it's the same raw material, but built into
a different structure (l'havdil). So does that argument work with
Hashem? No, and yes. The gulf between my anger and yours, vs my anger
and His, is infinite. But what specifically is the difference? His
anger isn't created, His is infinite, His is ultimately simple and not
a separate part of Him, His is perfect, and He always, only
pours/identifies/"personalizes" (Zohar) His complete Self into His
anger in a way I can only envy (and I think this roughly explains what
it means that He is Simple/One; His anger IS Him). Mine is none of
those, and the bridge between any one of them is infinite. But also,
it's the same "raw material". Meaning: He gets angry in response to
injustice, and I also get angry in response to injustice - that's what
anger is. If He got angry in response to chesed and I got it in
response to gevura, that would be a step too far. The qualia of anger
I have, which is indescribable, is from Him (where else?), so in that
sense it's the same.
So, can I know Him in and of Himself? No. Can I know Him?
Completely. Who is He? The God of Israel. That's all I need to know.
What is His delight? Where is His home? When can I see the "real Him"
as oppose to "the totality of his being"? He tells us: "Ha'ben yakir
li, Ephrayim". This "desire", "need", "delight", "home" of His is who
He really is - and He can't not be Him! It doesn't tell me everything,
and I can't know it "in and of itself", but I know it's true, it's
Him, He pours His complete Self into it, and tell's me all I need to
know. In fact, Kabballah teaches that "need" is the closest possible
"attribute" to perfect simple Oneness that you can get. Every other
one adds an extra layer of "tzimtzum" and distance from the
Aye, I can only understand it in finite terms, there's still an
infinite bridge to walk across to get to Him. Baruch Hashem. If I
could figure Him all out by the time I am 5 (or 120), that would be
disappointing! Thankfully, He gave me the mitzvot, and the Torah, and
a finite guf to perform and learn them, and insodoing, I can walk
across that bridge towards my Father, Who I know, step by step, closer