Answer the second question first. The so-called problem solving is the basic method and thinking of learning mathematics.

Know some martial arts. The seemingly invincible masters actually use the most basic tricks, but they are perfect and almost omnipotent. This is what I want to say, whether it is mathematics or other subjects, we should attach importance to basic training. Its significance lies in that you can deepen your knowledge and understanding of this subject repeatedly, and even in the end you can skillfully use the knowledge of this subject to solve complex problems. In the words of our teacher, if you master the foundation, you will master everything!

Learning mathematics well is a long-term thing, and its function is even more long-term, because mathematics exists in every corner of life. For example, have you noticed the shape of piano and harp? Everyone has a similar curve, which is actually a piano curve. Through mathematical deduction, we can know that only by designing them to conform to the "piano curve" can we satisfy the law of twelve averages and make them produce wonderful music.

You can consider your hobbies. There must be many things closely related to mathematics in your hobby. If you can master math well, you can do what you like better and better. Similarly, the greater the significance of mathematics here.

In a word, what's good about mathematics and what's the significance. It depends on how well you use mathematics.