There are numerous examples of mathematical findings made in prisons. Perhaps the most famous is that of the French mathematician André Weil, who developed enormously influential guesses while serving time in a military prison in Rouen, France. Another mathematics giant, Srinivasan Ramanujan, who had no formal training in the discipline, developed most of his revolutionary discoveries in conditions of complete isolation.
In his autobiography, Weil claimed that while in prison he was able to achieve singular clarity of thought. But is there really any special relationship between prisons and mathematics?
Christopher Havens' story confirms this possibility.
A conviction for murder
Havens was convicted of murder and sentenced to 25 years in prison in Washington State. He discovered his love for mathematics and his gift for it a few months after entering prison, in an isolation cell. This shift to mathematics and research prompted an academic journal of mathematics in January 2020 to publish an article in which he was listed as the first author.
In January 2013, my colleague Matthew Cargo (who was then the shipping editor for Mathematical Sciences Publishers), was e-mailed the following letter by a colleague:
"To Whom It May Concern: I would be interested in receiving more information regarding a subscription to Annals of Mathematics for my personal use. I am currently serving a 25-year sentence in the Washington State Department of Prisons, and have decided to use this Time to be a better person. Since my interest is numbers, I am studying calculus and number theory. Could you please send me some information about your mathematical publication? Christopher Havens, # 349034PD: I am self taught, and I often get stuck a lot time with certain problems. Do you know of someone with whom I could establish a correspondence relationship, on the assumption that I would send postage-paid postal envelopes? There are no teachers here who can help me, so I often spend hundreds of dollars in books that then don't contain the help I need. Thank you. "
Cargo put Havens in touch with my parents, who are both mathematicians.
A productive period
At first, my father, Umberto Cerruti, a number theorist who was a professor at the University of Turin, agreed to help Havens only because we asked him to. He thought Havens was one of those enlightened people who gets hit by numbers and ends up developing a theory full of holes. To test him, he sent him a problem to solve.
In response, my father received, by post, a 120-centimeter sheet containing a long and complex formula. My father put it in the computer and, to her surprise, found that the results were correct!
After this, my father invited Havens to join him in solving a continuous fraction problem he was working on.
The continuous fractions, discovered by Euclid in the year 300 a. C., allow to express all the numbers through sequences of whole numbers. For example, the number pi is the ratio between the value of the circumference of a circle and its diameter: 3.14159 ... The sequence of numbers that follow the first digit is infinite and totally chaotic. But expressed as a continuous fraction, this sequence becomes something simple and beautiful:
Continuous fractions exemplify the strength of number theory (the branch of mathematics that studies the properties of numbers), a field to which most of Weil and Ramanujan's contributions also belonged. The number theory has allowed advances in cryptology today, which today is vital for the operation of banks, financial activity and military communications.
Havens' contribution, which was published in the Research in Number Theory magazine in January 2020, demonstrated for the first time the existence of a series of regularities in the approach to a vast category of numbers. It is a discovery that could open new fields of research within number theory. In fact, finding new ways to write numbers is one of the most relevant questions for a number theorist, although it is no less true that such discoveries might not have immediate application. For example, right now there are supercomputers that are dedicated to processing billions of digits of the number pi.
Havens worked on this subject with no tools other than pencil and paper; With his research partners he exchanged conventional letters that had to cross the ocean.
Conditions in prison
But how could something like this happen? Havens explains it in his own words:
"Less than a year after entering prison, my behavior led me to the hole (the isolation cell). And it was precisely in the hole where my life took a turn, because there I realized that I loved mathematics. about ten hours a day studying (…) I decided to enter the Intensive Transition Program (PTI). It is a year long program that helps people maintain mental balance. It is designed to help you effectively to "Get your head out of your ass." That became my goal. Eating, math, sticking my head out of my ass, brushing my teeth, rinsing and repeating. It was a very important time in my life. "
After completing the PTI, Havens sent his request to the math magazine, and my parents started tutoring him.
They sent him tons of books, but the prison blocked all of them because they did not come from a licensed publisher. Havens then began working with prison staff to launch the Prison Math Project, in which he effectively taught other inmates mathematics. In exchange, they were allowed to have a small library as well as a room to receive visits twice a week. That worked, and the prison admitted the boxes of books.
To write this text, I had three 20-minute phone conversations with Havens (which is the maximum time they allowed him to speak). He used the word education very frequently:
"Education was a nuisance for me. I was a failed student (I was hooked on drugs, I couldn't keep my jobs, I never called home) (...) Education is very difficult in prison (...) So now I'm doing it looking outside. I try to build bridges and strengthen my relationships with outsiders, because for me education is that. Every opportunity that comes to me is a learning experience, and it is because here it is very rare that you are not presented with any " .
Havens also sees mathematics as a way to "pay your debt to society":
"I can say with certainty that I have drawn up a long-term life plan to be able to pay an unpayable debt. I know that it is a permanent plan (...) and that the day will never come when I can pay off the debt at all. But This is not a bad thing, but an inspirational one. It may sound stupid, but throughout my sentence the soul of my victim has accompanied me; to her I am dedicating my greatest achievements. "
Mathematics after prison
The truth is that, despite the fact that there are solid data that guarantee that obtaining a degree significantly reduces the possibility of recidivism, the opportunities to go beyond compulsory education in prison are limited. And without access to the Internet, most distance courses to earn a degree are out of reach for prisoners.
Right now, Havens is studying to earn a Bachelor of Science from Adams State University, which gives him the option to follow the course by mail. But he already has all the mathematical knowledge that is required of him there, so Havens wants to be assigned a math tutor with whom he can make regular contact.
When Havens is released from prison, he intends to finish his degree, despite the obvious difficulties that his criminal record will entail in this regard. He wants to start his Mathematics career, and he also plans to transform the Prison Mathematics Project into a non-profit organization that helps talented inmates in this discipline.
Marta Cerruti is an associate professor of Materials Engineering at McGill University.
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