Table of contentsIntroductionDavid Hilbert programWhat was the decision procedure?Godel's theoremTuring's theoremIntroductionOne of the great mathematicians, whose name was David Hilbert, introduced a program in 1890.David Hilbert was a German scientist and a good mathematician of his time. It was a great invention. He was famous for his ability to solve difficult statements. According to him, a single algorithm can solve all the theorems in the world but it was considered erroneous at the beginning of the 20th century by a great mathematician, the logician Sir Alan Turing. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get the original essay David Hilbert Program One of the main problems of the early 20th century was paradoxes (this was a serious problem at that time). At that time, people did not know the term mathematician. At that time, it was very difficult to solve a large number of problems and this was the main reason why people thought that all the statements given by mathematicians were not true. After this, Hilbert was forced to take the statements which were axiomatic. We can say that axiomatic statements are those statements that we can say are true. So, using axiomatic statements, he said that his statements are consistent (consistent statements are statements that are free from contradiction). He took a lot of statements of axioms and he said that these statements are consistent, which means that they are true. Using axiomatic statements, he gave his program for solving the problems. After some time, the theorem introduced by David Hilbert was considered false because after a few years, a scientist named Godel declared that this theorem was impossible. Then, at that time, many contradictions were replaced, and then Alan Turing and Godel proved that this theorem is impossible. What was the decision-making procedure? I can define the word decision procedure as follows: It is a procedure in which there are two possibilities. Using an algorithm, it can be both true or false, but not both. The thin procedure states that if we have unnecessary inputs and we need to resolve them, there will be two possibilities. The response to this input using the algorithm will be in two words. They will be “Yes or No” (True or False, 0 or 1). Deciding using this procedure is called decision procedure. We can easily understand the term decision procedure by a given example. This procedure is very useful for troubleshooting. Using this decision procedure we can also solve the problem of any value. This procedure helps us save time and indicates whether the algorithm for this problem may be possible or not. Let's take an example in high-level language. Suppose we have a lot of inputs and we need to perform a mathematical operation in our program with these inputs. To solve this type of problem we need to create an algorithm that will decide whether we can solve these inputs or not and at the end we will get two answers, the answer will be Yes or No. The lines of procedure that define the problem are called decision procedures. Furthermore, there are two other possibilities, one is decidable (if the answer is possible) and the other is undecidable (if the answer is not possible). We can say that the era of mathematics reached its peak in 1930 because at that time Alan Turing and Kurt Godel proved David Hilbert wrong who was the great mathematician of his time. This shows that.