Man's duty in the world:
Torah and Mitzvot.
The world exists only for the sake of Torah (Pesachim 68b)
Torah and Mitzva are practically synonymous:
And I will give you the tablets of stone, the Torah, and the Mitzvah
The Torah and Mitzvot are Hashem's Wisdom and Will absolutely (Tanya Ch. 34). By performing them, we are fulling our reason for being created; our mission and purpose. This is to serve Hashem, and this is considered a service because we are performing His Will, i.e. giving Him what He wants.
Should one keep the Torah and Mitzvot altruistically or should one do so for the reward?
Ideally yes, they should be done altruistically, without thought of reward.
Antigonus a man of Socho... used to say: do not be like servants who
serve the master in the expectation of receiving a reward, but be like
servants who serve the master without the expectation of receiving a
This takes explanation and as Micha Berger rightly pointed out, it takes a book (at least). However, as a summary and introduction to encourage the reader to take on further study:
It says in Derech Hashem that Hashem created the world in order to give goodness from His goodness to another (1:2:1). He then proceeds to explain that our duty is to emulate Him, and this is how we receive that good.
So what we know so far is that the best good is Hashem, and what's good about Him is that His desire is to give to another. Therefore conclude that the best good of all is giving to others (serving others).
He gave us a good mashal in Shir Hashirim:
I am for my beloved, my beloved is for me (6:3)
There are quite a few ways a relationship can work. Both parties can be selfish but complement each other and therefore exist in a functional relationship with some goodness. This is not Godly though, and therefore not the best good.
The best good is when both parties are into each other more than they are into themselves. The only way to make sense of this, is following the line of the Rambam on the Mishna in Avot:
And this pious one said that you should not serve God, may He be
blessed, in order that He will do good to you and benefit you with
kindness and that you should hope for the benefit and serve Him for
its sake. Indeed, serve Him like servants that are not hoping for
endowment or the giving of kindness. He meant with this that they
should serve Him from love, as we said in Chapter Ten of Sanhedrin.
and what Ramchal states clearly in Mesilat Yisharim Chapter 18:
"Fortunate is the man whose toil is in the Torah and gives
gratification to his Maker"... he who truly loves the Creator, blessed
be He, will not strive and intend to discharge himself with the known
obligations binding on every Jew. Rather, what will happen to him is
the same as that of a son who loves his father. Even if his father
reveals a slight indication of something he desires, already the son
will strive greatly, to the best of his ability, to fulfill this thing
Conclude from all this that the greatest good is serving others, one's beloveds.
Taste, and see that Hashem is good (Tehillim 34:8)
By default, our entire orientation in life is to gain pleasure by fulfilling our own desires and wants. During that time, the idea of serving others being pleasurable sounds far fetched, and at best a nice little idea that is probably true to some extent. The truth is, it takes wisdom (via Torah learning) and experience (i.e. taste it, via performing Mitzvot, especially the Mitzva to get married) for one to see the truth of it.
A truly holy and devoted husband will tell you, hands down, no pleasure or wonder of the universe could possibly compare to the delight he takes in bringing his wife a coffee in the morning. Not because he will get a reward out of it, but actually serving her, fulfilling her needs great and small, is its own reward. He is for his beloved, not himself, his own needs and desires pale in comparison to hers - he feels the tug of her need as a true delightful privilege for him to be able to serve - and he has been blessed to experience a taste of true goodness and Godly delight.
So now we can understand our Mishna. Is there reward in serving Hashem and each other? Yes, the best reward imaginable. Should we be doing it for that reward? No, this ruins it. It is no longer a true service, it is simply a self service, and adds a bitter taste to what should be only sweet - fulfilling the needs and desires of someone else, because one is completely and utterly devoted, one, with them.
שְׁמַע יִשְׂרָאֵל ה' אֱלֹקֵינוּ ה' אֶחָֽד
As we stated above, the Torah and Mitzvot are Hashem's absolute Will. Therefore by performing them, we are truly serving Him. In-so-doing, we are emulating Him and becoming One with Him, and we will receive Him in Olam Haba (as our "reward", see Derech Hashem 1:2 onwards). Another way to see it, don't read Hashem gave us the purpose of receiving the best good. Hashem's purpose is to give the best good. It's His purpose, not ours. Ours, as stated above, is Torah and Mitzvot and in-so-doing emulate Hashem by giving from our goodness to others.
The Lubavitcher Rebbe clarifies for us a couple of points:
- This aspect of relationship with Hashem comes from being His servants, and this is the husband-wife relationship mentioned throughout Chazal (i.e. a husband and wife view each-other as their master, and they are the servant of the master).
- At Har Sinai when Hashem became ours and we accepted, we accepted b'mesiras nefesh, which means we gave up our entire life to Him, which included our pleasure. Therefore the reward in Olam Haba cannot be us having our own pleasure. He clarifies that in Olam Haba, Hashem will reveal to us how much our performance of the Mitzvot meant to Him, and that knowledge is going to be "delighting in Hashem" as mentioned in the introduction to Mesilat Yisharim - a reward and delight far greater and more holy than personal gratification.
The astute reader will read between the lines and see what the greatest goodness of all is - having each other, not the things about each other. "I don't want Your Olam Haba, all I want is You" - Alter Rebbe. It's enough to, so to speak, satisfy God, and if we follow His guidance (Torah), we will taste it for ourselves, and by keeping the Mitzvot, we will bring about this great Oneness He is after, for His sake, and for the sake of everyone. We might also enjoy it too, but let's not focus on that :)
והיה ה' למלך על־כל־הארץ ביום ההוא יהיה ה' אחד ושמו אחד (Zacharia 14:9)
May this great day arrive without delay.