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There are numerous examples of findings mathematicians carried out in prisons. Perhaps the most famous is that of the French mathematician ** Andre Weil ** , who developed some of the guesswork enormously influential while serving a sentence in a ** military prison in Rouen ** (France). Another giant of mathematics, Srinivasan Ramanujan, who had no formal training in the discipline, developed the majority of their groundbreaking discoveries in conditions of absolute isolation.

In his autobiography, Weil stated that while he was in prison he was able to achieve a clarity of thought singular. But, is there really a special relationship between ** prisons and mathematics ** ?

The history of ** Christopher Havens ** confirms this possibility.

A conviction for murder

Havens was convicted of murder and sentenced to 25 years in prison in the state of Washington. He discovered his love for mathematics and his gift to them a few months after I entered prison, in an isolation cell. This turn to mathematics and to the research made in January 2020, a scholarly journal of mathematics had published an article in which he was listed as the first author.

In January 2013, my partner, Matthew Charge (which by then was the editor of shipments of the publishing Mathematical Sciences Publishers), a colleague forwarded by e-mail the following letter:

Charge put to Havens in contact with my parents, who are both mathematicians.

A period productivoLa first letter sent by Havens, a prisoner who is serving a sentence in the Prison Department of the state of Washington – Marta Cerruti

at The beginning, my father, Umberto Cerruti, a theorist of numbers that he was a professor of the University of Turin, agreed to assist in Havens only because we asked. He thought that Havens was one of those enlightened to that given by the numbers and end up developing a theory full of holes. To prove to him, he sent her a problem to solve.

My father received as a response, and by mail, a sheet of 120 centimeters and which contained a formula is long and complex. My father got into the computer and, to his surprise, it was discovered that the results were correct!

After this, my father invited Havens to join him to solve a problem of continued fractions on which I was working.

The continued fractions, which were 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 fraction continuous, the sequence becomes something simple and beautiful:

The expression of the number pi as a fraction continues – Wikipedia

The continued fractions exemplify the strength of the theory of numbers, a field in which also belonged the majority of the contributions of Weil and Ramanujan. The theory of numbers has allowed advances in cryptology today, that today is vital to the functioning of banks, financial activity and military communications.

The contribution of Havens, which was published in the journal Research in Number Theory in January 2020, demonstrated for the first time the existence of a series of regularities in the approximation to a vast category of numbers. It is a discovery that could open new fields of research within the theory of numbers. In fact, finding new ways of writing numbers is one of the issues most relevant to a theorist of numbers, although it is not less true that such discoveries may not have immediate application. For example, at this time there are supercomputers that are dedicated only to process billions of digits of the number pi.

Havens has worked on this topic without more tools than pencil and paper; with their peers research exchanged letters that had to cross the ocean.

The conditions in prison

But how was it possible for something to happen as well? Havens explains with his own words: “Less than a year after entering prison, my behavior took me to the hole (the isolation cell). And it was precisely in the hole where my life took a turn, because that’s where I realized that I loved math. I spent about ten hours a day studying ( … ), I Decided to enter the Transition Program Intensive (PTI). It is a programme of one year duration which helps people to maintain mental balance. It is designed to help you effectively that “you pull out the head of the ass.” That became my goal. Eat, math, get me the head of the ass, brush my teeth, rinse my and repeat. It was a very important period of my life.”

After the PTI, Havens sent your request to the magazine math, and my parents began to tutorizarle.

My parents sent lots of books, but the prison had blocked all because of that did not come from a publishing house authorized. Havens began working then with the jail staff to implement the Project of Mathematics in Prison, where we actually taught math to the other inmates. In exchange they were allowed to have a small library as well as a room to be able to receive visits twice per week. That worked, and the prison admitted the entry of the boxes of books.

in order To write this text, I kept three telephone conversations of 20 minutes with Havens (which is the maximum time they let him speak). He used the word education too often: “education was a nuisance to me. I was a student failed — he was hooked on drugs, couldn’t keep jobs, I never called home) (…) The education is very difficult in the prison (…) so now I’m looking outside. I try to build bridges and strengthen my relationships with people outside, because for me, education is that. Every opportunity that I posed is a learning experience, and that is because here it is very unlikely that you have any.”

Havens also sees mathematics as a way of “paying your debt to society”: “I can say with certainty that I have drawn a plan of life in the long term to be able to pay an unpayable debt. I know that it is a permanent plan (…) and that it will never come the day that you can pay off the debt at all. But this is not a bad thing, but inspiring. May sound stupid, but throughout my time I have been accompanied by the soul of my victim; to her I am dedicating my greatest achievements”.

The after math of prison

What is certain is that, despite the fact that there is solid data that support that removed a degree significantly decreases the possibility of relapse, opportunities to go beyond the compulsory education in prison are reduced. And without access to the Internet, the majority of the distance courses to get a degree are out of reach of the prisoners.

At this time, Havens is studying to obtain a bachelor of science degree at Adams State University, which gives you the option of following the course by postal mail. But he already has all the mathematical knowledge that there will require, so that Havens wants to assign you a math tutor with which to establish contact on a regular basis.

When Havens gets out of jail he has the intention of completing the bachelor’s degree, despite the obvious difficulties that, in this sense, he represented his criminal history. You want to start the career of Mathematics, and plans to further transform the Project of Mathematics in Prison in a non-profit organization that helps inmates with talent in this discipline.

** Marta Cerruti, Associate Professor, Materials Engineering, McGill University **

** This article was originally published on The Conversation. **