Mathematics relies on the assumption that objective facts exist, or at least the function of objective facts exists approximately at the scale level of our work. Without it, there is no concept of repeated observation, and different observers will find the same result. Without it, the concept of evidence is meaningless.
Based on this assumption, the goal of mathematics is to discover the truth constantly, and the truth is inferred from the observation of the world, including the planned experimental results. But no one expects us to reach the final truth, but every stage of development will be closer to the truth than our previous best state. This applies to every small problem being investigated, as well as to major and important issues.
Axiomatic system and the right and wrong of mathematics;
For the application of mathematics, you just think that a formula can be used to solve a phenomenon in real life. If you find something wrong, it's your tools, not your math. It can be said that the right or wrong of mathematics has nothing to do with truth. Mathematics is full of things that do not exist in reality. Perhaps, mathematics is not as perfect as people think.
With the increasing intelligence of computers, these trends show that computers will replace human thinking in the future. Due to the emergence of computers and the rise of life science, modern economics and complexity science, new discrete mathematics will soon replace continuous mathematics and take the lead.