Luisella showed me several beautiful flavors of number theory, but when she introduced me to continued fractions, I was hooked. I remember getting stuck on a problem – now tell me if this has happened to any of you – FOR OVER A YEAR, only to learn that the solution didn’t even exist in the terms that I was looking for! But it’s these types of problems which teach us the most.. This was the first time I had ever truly been in awe of my failures. I say this because between sending my findings back and forth to Luisella in Italy, I had sent an original closed form for a certain type of continued fraction. It was a piece of new math, and it caught the attention of Umberto Cerutti, Luisella’s husband… and it was beautiful. And I’ve learned a beautiful life lesson. In the midst of our failures, we find the seed of success.
My next letter from Italy was from Umberto. In his response, he suggested I partake a research involving the general Hurwitz continued fractions I was becoming very intimate with, and a certain transformation. I dove in. I worked my ass off. Then research I did gave several original formulae for different closed form sets of leaping convergents to more Hurwitz continued fractions. Umberto has since made me a member of his research team, where I have the honor of working with 3 brilliant minds.
My involvement in the mathematical community has since exploded. Luisella and Umberto are my mentors. I’ve met them and several of their colleagues in person at the math events put on by the Prison Mathematics Project, the program I started. There are articles being written about me. As well, I’m currently involved in writing an expository article for a magazine catering to the history of mathematics. I don’t doubt my future anymore… and the support I get from the mathematical community drives me and fuels me. We create a synergy.
I once decided that I’d set a 25 year goal.. to make some beautiful math and publish it. The idea being that I would truly give the victims of my crime the justice they deserve by contributing something permanent to the world… It seemed fitting since I had permanently taken something that I cannot give back. I set my goal high. After all, I am only the “institutionally challenged”. And it frustrates me to see so many of us with the same notion that we are only what we are.. because we can do so much more. Why dumb it down to what the public perceives of us? You know, It has only been three years since setting that goal. The research suggested to me by Umberto has come to fruit. The name of the paper is “On non-linear leaping convergents of a linear fractional transformation of Hurwitz continued fractions”. At this moment it is in the publication process where the referees are pouring through the work. It’s a joint paper, and it’s under review for publication at a journal of number theory in Tokyo, Japan. And this is only one of many. One of the few lessons I’ve learned from the school of hard knocks, that didn’t hurt, was that you can’t set your goals high enough. Your limit is here ( in your head). Because if we don’t set our goals to reach the moon, then we’ll never truly get a good look at the stars.
Before I sign off, I have one last thing to say.. contrast is a powerful thing. The biggest function of my past is the contrast it shows from what I was to what I am. But we can’t use our past for much more than contrast and memories. The thing is, we are not our past.. we are not our future. We are what we are right now. And the future is only an inductive step away.. so if we want to shine in the future, then we must learn to shine in our present.