Emil Post And His Contributions To Computability Theory

Post,one of the founders of computability theory,made significant contribution to computability theory in mathematics.His lifelong research process is worthy of future generations.He asserted the incompleteness theorem more than ten years before G?del,and almost simultaneously proposed a computational model equivalent to the Turing machine at the same time as Turing.But the god of destiny did not give him too much care,his lifelong accompanied by mental illness.Despite this,he relied on his own tireless efforts to eventually take a place in the academic world.The analysis of Post's work and life can provide a new perspective for understanding the early development of computability theory.On the basis of sorting out a large number of related literatures,this paper combs its contribution in the field of computability theory by combining Post's life experience with research work.The main contents are as follows:Firstly,according to the ups and downs of Post's life,this paper restored and analyzed his lifelong research experience.Using the method of staging of mathematics,his life was divided into four stages: the period from birth to the doctoral period,the frustration period during the post-doctoral period,the turning period of return to the academic world,and the peak period of the help of the noble.Secondly,through the study of the original literature,a detailed analysis of Post's research work from the doctor to the postdoctoral stage.With the help of historical restoration,this paper explored the research process of his incomplete assertions,and analyzed the correspondence between G?del and Post and the reasons why Post is not widely praised.Finally,from the perspective of computability theory,the similarities and differences between Turing machine and Post-machine are explored.Combined with the historical background of Post's research,this paper restored the research process of Post-machine at the same time as Turing,and analyzed the relationship between Post-machine and the decision problem.