From Hilbert Problem to Turing Machine: The Marriage of Mathematics and Computation At the beginning of the 20th century, mathematician Hilbert attempted to establish a complete, compatible, and decidable formal mathematical system. However, G ö del solved the first two problems, while the third problem, which is the determinacy problem, remained unresolved. The mystery of determinability The decidability problem refers to whether there is a universal mechanical method that can determine the truth or falsehood of any mathematical proposition in a finite number of steps. This problem attracted numerous mathematicians, including von Neumann and Church. Von Neumann proposed that perhaps the determinacy of mathematics could be proven through mechanical processes. Qiu Qi used the lambda calculus and independently solved this undecidability problem. Turing's groundbreaking contribution Inspired by von Neumann, Turing proposed the concepts of "computable numbers" and "computable sequences", and ultimately proposed the famous "Turing machine" model. A Turing machine is an abstract computational model that can simulate any computational process by reading and writing symbols on paper tape. Turing published a paper titled 'On computable numbers and their applications in decision problems', proving that Hilbert's decidability problem is undecidable. This achievement not only solves mathematical problems, but more importantly, it lays the theoretical foundation for the development of computers. The Marriage of Mathematics and Computation Before the invention of Turing machines, the application of mathematics was mainly limited to theoretical research, such as law deduction in physics and quantum physics calculations. Mathematicians mostly perform symbolic operations on paper, lacking practical applications. The emergence of Turing machines led mathematics from the abstract world of symbols to practical applications. Mathematical symbols can represent operable numbers and symbols, while Turing machines guide computers to apply these symbols. The Turing machine, as a bridge between abstract symbols and the physical world, achieved the union of mathematics and computation, ushering in a new era of computer science.