A prison inmate contributes to a major discovery in mathematics

Washington: Christopher Havens, a prison inmate at Washington Department of Correction, serving 25 years sentence has done something astonishing. Due to his craze for mathematics, he became part in publishing a three-author article in the journal Annals of Mathematics.

In USA, the access for books to prisoners are extremely restricted evenif the prisoners place a large demand in their interest in books and journals. The guidelines are byzantine, and prisoner rights organizations hold up restricted access to books as an example of a violation of the First Amendment.

Havens used to teach himself Calculus and Number theory, while in prison. It was then Havens decided to send a request to Prof. Marta Cerruti’s partner for the annual subscription of the journal Annals of Mathematics. Cerruti’s father being a number theorist eased the matters in Haven’s favour.

Cerruti’s father gave him a problem to solve, to test his expertise. “To his surprise, my father got a 120 cm long paper piece in the mail, where we found complex math formulae. And the answer was surprisingly correct”, Cerruti said. Thus, Havens contributed his skill and a paper ‘“Linear fractional transformations and nonlinear leaping convergents of some continued fractions” was published.

Number theory deals with study of integers and processing using integers. It is a part of discrete mathematics, which examines countable numbers like integers rather than continuous topics like calculus. Continued fractions are a fun special case of, for example, irrational numbers like π that can be represented with complicated fractions that also repeat. Instead of a series of digits that continue after a decimal point, they are ‘fractions in fractions.’ These get smaller and smaller and eventually converge into approximations of the irrational numbers they can represent.

In their paper, Havens, Cerruti, and two other mathematicians study a linear transformation of an infinite continued fraction and draw conclusions from their findings. Then they apply those findings back to (relatively speaking) famous continued fractions. Havens said: “It is designed to effectively aid you into ‘taking your head from your backside.’ This was my schedule. Eat, math, remove my head from my backside, brush, rinse, repeat. It was an important time in my life.”