Artificial intelligence is very closely related to mathematics, and mathematics is the foundation and core of artificial intelligence. Artificial intelligence relies on mathematical algorithms and models, including machine learning, neural networks, optimization algorithms, and more. In machine learning, mathematical knowledge of probability theory, linear algebra, statistics, etc. all play an important role, and they are used to build and optimize models to achieve data analysis and prediction. In neural networks, knowledge of mathematical calculus, matrix theory, topology, etc. are essential, and they are used to simulate interactions and information transfer between neurons. In optimization algorithms, knowledge such as mathematical optimization theory and nonlinear optimization theory is used to build and optimize models to achieve problem solving. In addition, the development of artificial intelligence has also promoted the development of mathematics. For example, the development of deep learning has promoted the further development of matrix theory and optimization theory in mathematics, and also provided mathematicians with new research directions. Therefore, the relationship between mathematics and artificial intelligence is mutually reinforcing and interdependent.
Mathematics is not logic, but a logical system based on axioms, without which mathematics does not exist, such as without the five axioms, Euclidean geometry does not exist. Similarly, any intelligent algorithm has boundaries, constraints and conditions, without these prerequisites, intelligent algorithms will be completely different, and the design and application of intelligent algorithms must be carried out under certain boundaries, constraints and conditions. These premises can be technical, such as the scope of application of algorithms, the quality and reliability of data, or ethical and legal, such as protecting privacy and personal rights and interests, and complying with laws and regulations. Without these premises, the results of intelligent algorithms are likely to be problematic or even have adverse effects. Therefore, when developing and applying intelligent algorithms, these prerequisites must be carefully considered to ensure the normal operation of the algorithm and safety and reliability.
Theoretically, the development of artificial intelligence needs to rely on mathematical algorithms and models, so the mathematical level plays a crucial role in the development of artificial intelligence. However, if we define "desired AI" as AI that fully mimics human thinking and behavior, then the current level of mathematics really cannot reach this goal. Because human thinking and behavior are very complex, involving many social, cultural, historical, psychological and other factors, current mathematical models and algorithms cannot fully simulate these factors. If we define "desired artificial intelligence" as intelligent machines capable of accomplishing specific tasks, such as autonomous driving, speech recognition, image recognition, etc., then the current level of mathematics is already able to support the development of these applications. With the continuous development of technology and algorithms, we are also expected to achieve more advanced AI applications in the future. The view that "it is impossible to produce the desired artificial intelligence with the current level of mathematics" needs to be analyzed and discussed according to specific scenarios and definitions.
