阿兰·图灵16岁开始研究爱因斯坦的相对论。1931年,他进入剑桥大学研究量子力学、概率论和逻辑学,这逻辑学是由剑桥大学的怀特海和罗素创立的数理逻辑。德国大数学家大卫·希尔伯特(D.Hillbert)在此基础上,于1928年提出著名的“希尔伯特纲领”,认为《数学原理》所定义的系统既是一致的,也是完备的。换言之,任何系统的完备和一致性,可以由系统本身得到证明。1931年,“希尔伯特 Alain Turing started studying Einstein’s theory of relativity at the age of 16. In 1931 he entered Cambridge University to study quantum mechanics, probability theory and logic, a mathematical logic founded by Whitehead and Russell at the University of Cambridge. Based on this, D. Hamilton, the German great mathematician, put forward the famous Hilbert Program in 1928, believing that the system defined by Mathematical Principles is both consistent and complete of. In other words, the completeness and consistency of any system can be demonstrated by the system itself. 1931, "Hilbert