It is synonymous with the highest honor in the computer field, but it may be a strange name for the broad masses of people. 1936, 24-year-old Turing published this paper which influenced the construction of computer science. The title of this paper "computable number and its application in entscheidungssprout" concisely reflects the main idea of this paper, that is, to study computable number and its judgment. And this book revolves around the content of this article and the introduction of related things. The purpose of this paper is to prove that the viewpoint of a top mathematician is wrong. Therefore, Turing made a thorough study of calculation, what is calculation, how to define calculation, whether there are uncountable problems, whether it can be judged whether the problem is computable and so on. Then, by conceiving a machine that can run various algorithms, he gave a concise and wonderful proof with reference to Godel and Autol.

Even so, I was just confused and dizzy after reading it. Generally speaking, in order to prove the hypothesis put forward by Hilbert, Turing "has a decision-making procedure that can tell us whether an argument can be proved by these axioms (the decision-making procedure it refers to is a clear calculation process, which is what we now call an algorithm). He believes that inputting axioms and possible conclusions in this process should tell us whether this possible conclusion can be proved by these axioms. ), defines the calculation, designs such a decision-making program (Turing machine), and then proves the error of Hilbert's hypothesis by proving that there are problems beyond the computer's solving ability. Through contradiction proof (Bertrand Russell's Barber Paradox), it is proved that the stopping problem and the accepting problem are undecidable (some Turing machines can accept their own codes, others can't, but no Turing machine can distinguish the two situations).

After reading it, I lost more than half of my brain cells. However, on the whole, it is definitely easier than reading the paper directly, because the author also provides relevant knowledge background introduction, which is a rare book to understand that paper.