Mathematics plays a vital role in scientific and technological innovation. Mathematics provides accurate language and tools for scientific and technological innovation, enabling scientists and engineers to accurately describe, reason and analyze problems, so as to better understand and solve various complex problems.

First of all, mathematics provides a theoretical basis for scientific and technological innovation. Many scientific fields need to use mathematical theories and tools, such as physics, chemistry, biology, engineering and so on. In these fields, mathematical models and formulas provide scientists and engineers with a deep understanding of natural and social phenomena, thus helping them to better design and manufacture various products and services.

Secondly, mathematics has great application value in scientific and technological innovation. In many fields of science and technology, the application of mathematics can help scientists and engineers solve problems better, optimize design, improve efficiency and so on.

For example, in physics, Newton's law of universal gravitation is a mathematical formula to help people better understand the movement of celestial bodies and physical phenomena on earth; In engineering, the application of mathematics can help engineers design and optimize various structures, such as bridges, buildings and automobiles.

Mathematics also provides effective tools and methods for scientific and technological innovation.

Mathematical methods and tools can help scientists and engineers to better analyze and solve problems, such as statistical analysis, numerical calculation, machine learning and so on. The application of these methods and tools can help people better understand and predict all kinds of complex phenomena, so as to better solve all kinds of problems.

To sum up, mathematics plays an irreplaceable role in scientific and technological innovation. Mathematics provides theoretical basis, applied value and methodological tools for scientific and technological innovation, enabling scientists and engineers to better understand and solve various complex problems. Therefore, mathematics is one of the important cornerstones of scientific and technological innovation and plays an important role in promoting the development and progress of science and technology.