Jonathan Julián Huerta y Munive is currently a Mexican Mathematics undergraduate student in the Benemerita Universidad Autónoma de Puebla (BUAP), but he previously tried Mechanical and Physics Engineering in the Instituto Tecnológico de Monterrey. After realizing that the applied approach to mathematics was not what he enjoyed the most, he decided to study pure mathematics, which he has done ever since. His main area of interest is Model Theory along with Mathematical Logic, subjects that he has started to study recently. At the time of this writing, he is studying many-valued logics and first-order languages, but his main goal is to start developing innovative model structures with applications in economics, computer science, and physics.
Jonathan is also passionate about teaching and has had professional experience as an English as a Foreign Language teacher and as a mathematics tutor. As a personal project he has been teaching mathematics for free to people interested in passing their Standard Admission Tests. His favorite hobby is learning, but he also enjoys swimming, playing basketball, playing the guitar, the piano, and the flute, and most importantly, singing in the shower.
Project: Research on the Capacity of Axiomatic System's to Prove Theorem's through Computational Methods
Axiomatic systems, at least in Classical Propositional Calculus, can be said to be both complete and consistent at the same time. However, when one chooses to work in higher-order logics, Gödel's Incompleteness Theorem asserts that those types of systems cannot satisfy both properties, i.e., no matter how consistent a high-order system is, it will always be incomplete. According to Stephen Wolfram in his book A New Kind of Science, it is possible to model axiomatic behavior with Multiway String Systems using an approach similar or identical to the systems that define axiom rules for strings. With that idea in mind, my research project consists of generating a certain set of strings and doing an empirical study of the behavior of those systems by applying the referred transformations. If one accepts the premise that some axioms prove different numbers of theorems, it is possible to measure how "good" an axiom is, i.e., how many theorems it can prove. The main objective is to eventually answer these questions: Given a set of string replacement rules, is there a systematic way to find axioms that are powerful? How much incompleteness is there in different axiom systems and how does the action of adding axioms reduce incompleteness?
Favorite Four-Color, Four State Turing Machine