I'm 35 years old and my boyfriend is only 23, a full 12 years between us. After knowing each other for less than a month, we've already had countless fights, and to be honest I'm the one losing my temper most of the time. The main problem is that he's too fun-loving, stays up until 3 or 4 am almost every day, and has a completely different rhythm of life. A while ago after a big fight, he suddenly said he was going to a distant place, the return date is not yet determined, and asked me if I was willing to wait for him. But not two days later, he changed his attitude, directly drive me away, said he did not want to continue. I was cold and did not contact, but two days later I called to ask him to leave, the results of his crazy call back, we somehow and good. He also asked me to move to live with him, I was hesitant, a friend of his out-of-town back, he went to pick up early in the morning, and now five days did not meet. He said he went home to sweep the grave, but I do not take the initiative to find him, he will never contact me. When I post my daily life on my friend circle, he will ask me where I am and who I am with. Last night, I half jokingly sent a message saying, "Why don't I change my boyfriend", he actually replied, "As you wish", and said that there are things at home, so there is no time to understand me. I seriously said my feelings, and then directly closed the circle of friends.
In fact, I am clear that the age gap is too large, he is playful, and I also clearly feel that he is becoming more and more cold to me. This relationship, should I continue or not?
A truly healthy love and intimate relationship actually has little to do with the age gap, but more importantly whether two people can support each other and grow together.

As you can see from your description, there are quite a few differences between you and your boyfriend's understanding of life and love, as well as each other's needs and expectations.
But as the old saying goes, "It takes two to tango", and there must be something about you that attracts you to each other and fulfills each other's expectations.
So when you ask "should we continue", you may want to ask yourself first: in this relationship, I can not let go of what is? What makes me feel bad? What do I really need?
When these questions are figured out, you will naturally be able to find a way to get along with your boyfriend or make a decision whether or not to continue.
I hope these ideas are helpful to you. I wish you all the best.