A Report on My ARF Fellowship

August-December 2011 and February-June 2012

By Esperanza Buitrago-Díaz

First of all, I would like to thank all the Advanced Reasoning Forum members who approved and supported my visit. As I will explain, the visit and fellowship was one of the most enriching experiences of my life, which is also why this report is so hard to write. I have learned so many things that I have a hard time listing them here. However, I’m going to try in the best way I can.

When writing my objectives for my fellowship application, I never imagined completing them as successfully as I have. Actually, I never thought that I was going to achieve so much more than them, on so many different levels: personal, academic, professional, social, etc. I feel like I grew in many different dimensions.

On an academic level (which was the level I was going after) I studied:

• Propositional Logics written by R.L. Epstein,

• Algebraizable Logics by Don Pigozzi and W.J. Blok,

• Roger Maddux's logic seminar

• About algebras of logics by Maddux and Richard Kramer

• Modal Logics seminar notes by Maddux and Richard Kramer

Later, I read

• Classical Mathematical Logic by R.L. Epstein

• Computability by R.L. Epstein

There, the experience of reading with the author and being able to discuss the deep ideas in his work, rather than just reading the books and solving the exercises, has helped me to grow as mathematician and understand that these areas—algebra, logic, and their connections—are what I would like to keep studying.

Besides the books and articles I studied, I learned important things about myself that will guide my future academic studies:

• Why I want to continue studying mathematics

• Why I want to research the mathematical and philosophical aspects of logic

• Where I want to work, and where I see myself after a Ph.D. program

• Why, where, when, and how to choose a Ph.D. program

• How to prioritize study, research, and life

• How learning a new language is a matter of words, grammar, gestures, and history

• How to prepare for exams and apply for universities

But also, I learned many things that are important to my life:

• Family is not a matter of blood, it is a matter of company, of being generous with those who are and aren’t generous with us. And generosity is emotional, is based in friendship, and is about helping each other.

• Family is what dogs teach us to be. Actually, they teach us more than about family, they teach us about life.

• Farming

• Being active in a community, defending and listening to opinions

From the ARF fellowship, I got a lot of different things:

• People who I can consider my family, my friends, my community

• Animals, and how to take care of them

• A new language and a new culture (American culture and many aspects of it)

• When to wait and how to work at a professional level in life