IndexIntroductionDavid Hilbert's 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 was a good mathematician of his era. It was a great invention. He was famous for his ability to solve difficult statements. According to him, one algorithm can solve all the theorems in the world, but at the beginning of the 20th century it was considered wrong by a great mathematician, the logician Sir Alan Turing. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay David Hilbert Program One of the major problems in the early 20th century was paradoxes (it was a major problem at that time). At that time people did not know the term mathematicians. At that time it was very difficult to solve a huge amount of problems and this was the main reason why people thought that all the statements given by mathematicians were not true. Hilbert was subsequently forced to accept the statements that were axiomatic. We can say that axiomatic statements are those statements that we can say are true. Then, with the use of axiomatic statements he claimed that his statements are coherent (coherent statements are those statements that are free of contradictions). He took a large number of axiom statements and said that these statements are consistent, which means that they are true. Using axiomatic statements he provided his program for solving problems. After some time, the theorem introduced by David Hilbert was considered wrong because after some years a scientist named Godel said that this theorem is impossible. Then at that time many contradictions occurred 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 which is a procedure in which there are two possibilities. Using an algorithm, it can be true or false at the same time but not both. The subtle procedure says that if we have some garbage input and we need to fix it, then there will be two possibilities. The response of that input using the algorithm will be in two words. They will be "Yes or No" (True or False, 0 or 1). Making a decision using this procedure is called a decision procedure. We can easily understand the term decision procedure with an example. This procedure is very useful for solving problems. Using this decision procedure we can also solve the problem of any value. This procedure helps us save time and says the algorithm of this problem may or may not be possible. Let's take an example in high-level language. Suppose we have many inputs and we need to perform some mathematical operations in our program with these inputs. To solve this type of problem we have to create an algorithm that will decide whether we can solve these inputs or not and in the end we will get two answers, the answer will be Yes or No. The procedural lines that define the problem are so-called decision procedure. 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 age of mathematics reached its peak in 1930 because at that time Alan Turing and Kurt Godel proved that David Hilbert was wrong about who was the great mathematician of his era. This proves that this was the beginning of the modern world, or a new emerging field of mathematics. The effect of Godel and Turing's leaps forward from the Hilbert program in the 1930s is best understood in light of the foundation of.