In addition to professional requirements, mathematics is the crystallization of thousands of years of human wisdom, and mathematics learning can cultivate and train thinking: by learning geometry, we learn how to use deductive reasoning to verify and think; By studying probability statistics, we can learn how to avoid the dead end of thinking and how to maximize our opportunities. Therefore, we must learn math well with our heart, not half-heartedly. The most important thing is not how many math classes to attend, but to know "why" to study and gain knowledge and way of thinking from learning.
When we study a thing (such as mathematics), what we really get in the end is something at two levels.
The first level is the very specific content of this subject, such as mathematical formulas and problem-solving skills. This kind of thing can usually be written in textbooks and can be easily described in words. We can call it "explicit knowledge".
The second level is the influence on us in the process of learning this subject or some ways of thinking, habits of thinking or other subtle and obscure things learned through channels. Such things are generally difficult to express in words, and even many people will not realize that they have "learned" after mastering these knowledge and habits. This kind of knowledge can generally be called "tacit knowledge".
For example, in the history of science, Thales, an ancient Greek philosopher, said that "everything comes from water", which is considered as one of the important signs of the birth of early science. But we know that the saying that everything comes from water is actually scientifically incorrect. Then why are his words still circulating today? The reason is that although this sentence is not correct on the level of explicit knowledge, there is a kind of thinking logic behind this sentence: that is, for the first time, human beings try to find the answer to the question of world law from nature itself, instead of simply entrusting it to supernatural forces, which is one of the core ideas of science.
In fact, this tacit knowledge played a greater role than its explicit knowledge in those who recognized this sentence at that time. Although this sentence itself is wrong, those who accept this sentence will be more inclined to understand the world in a non-mystical way in future questions, and science will gradually be born in human civilization.
It can be seen that the use of explicit knowledge is often conditional and limited, while tacit knowledge is not easy to be discovered and perceived, but its function and influence can affect people's life and even the development track of the whole human civilization.
Back to your question, the explicit knowledge brought by mathematics itself may not have any direct effect on most people who are not engaged in technical work in science and engineering. As Han Han once said, the mathematics used in our life is estimated to be enough by the third grade of primary school. However, we studied mathematics for many years later, which actually shaped our rational, organized and systematic way of thinking. This way of thinking plays a very important role in solving many problems in our lives.
For example, careful thinking, classification ideas, sorting ideas and so on. In fact, many things have the influence of the process of learning mathematics, but because its mode of action is very obscure, it is not easy to trace back to the source, so we usually don't notice it easily.
Therefore, for people who don't use mathematics in their daily work, what they really learn is invisible rather than explicit knowledge, and it is this invisible knowledge that will greatly affect many key choices we make in life.