Three years ago, Christopher Havens, who has been sentenced to more than 20 years in prison for murder, announced his discovery of number theory in his cell. He and his three co-authors showed that important classes of fractions often maintain a regular structure after being algebraically transformed. Havens’ work was unusual in another way. Although he did not have access to a computer, it was common for mathematicians to program computers to tackle such aspects of computation. So he painstakingly pieced together his research by hand.
Havens and co-founded nonprofit invented a computational programming platform built around highly restricted, text-only email, one of the few technologies people in prison have access to. And as the facility begins to offer new opportunities, more and more inmates are grappling with advanced mathematics to make their years in prison meaningful.
Havens dropped out of high school in sophomore year and began studying math in a cell. “It brings out the worst in a lot of people,” he says. “There’s fluorescent lights right above you that never go out, even when you sleep. They’re screaming. There [are] They’re the ones who just get up and kick the wall. ” To escape the confusion of day and night, Havens began solving problems. Math Puzzles: First a Sudoku, then a packet of algebra problems slipped under the cell door by prison officials. “I went crazy for days and days,” he says. “I would have dreamed of it.” By the end of the months spent in what prisoners call a “hole” in a cell, he was “knee-deep” in calculus and would finally publish it. Havens says he was getting into the deaf field, namely number theory and research. Integers and relationships between them.
But even if you get out of solitude, self-taught math in prison means you’re stuck not only with the problem, but where to look for the solution. “Imagine no professors or anything,” says James Conway III, who studies measurement theory—an extension of his intuitive ideas about length, area, and volume—from an Ohio death row inmate. “You are alone.” So after Mr. Havens was released from the hole, he wrote to a journal published by Princeton University and the Institute for Advanced Study in Princeton, New Jersey, seeking a mathematician to correspond with. A few months later, a group of researchers returned from Turin, Italy, initially providing guidance and eventually, when Havens’ years of mathematical quest had pushed him to the brink of discovery, his first I wrote the question “how is the continued fraction” with the question behind the paper. f converted by the operation (of + b) / (reference + d)?
continued fractions look mathematical matryoshka A series of dolls are arranged such that one doll is nested inside another, or that doll is nested inside another, and so on. In this case each doll is an integer added to a fraction whose denominator is the next smallest doll in the sequence. Although a “universal” solution to the transformation question sent to Havens by the Turin researchers has not yet been found, Havens discovered a particular kind of transformation formula from patterns of hand-computed continued fractions. A long chain of these fractions could stretch across his fifteen feet of notebook pages covering the wallpaper in his cell. “It took us over two years to actually do the math,” says Havens.
But for those incarcerated, the pen and paper days of tackling 21st century problems may be over. Havens co-founded the Prison Math Project (PMP), a national non-profit organization to help other people in prison overcome the challenges of studying math in prison. Advised by UCLA computer scientist Amit Sahay, the project already pairs 171 inmates from 27 states with mentors to tackle subjects ranging from combinatorics to abstract algebra. One of his participants, his Travis Cunningham, is preparing to submit his work in mathematical physics for publication. Most recently, the project developed a system that allows incarcerated mathematicians to write computer programs using only the rudimentary “e-mail” system available to those in prison.
Performing hundreds of memorized calculations per second, computational programming is a valuable tool for solving problems across many areas of advanced mathematics. The Prison Math Project’s programming platform, called the PMP Console, acts as a go-between so that incarcerated people can write computer code without computer access. A prisoner emails a code from a tablet or kiosk to the console, and a cloud-based system extracts the program, runs it in an isolated digital environment, and automatically returns the results.
Havens is already working with mathematician Carsten Elsner of the University of Economics and Applied Sciences in Hannover, Germany, to test the console in a new study. These latest projects are primarily driven by specific continued fractions, in which nested integers form the sequence 1, 2, 3, . . . , says Elsner. “We gave [this fraction] German name BraidThe name, meaning “braids,” comes from a speculation that Mr. Elsner and Mr. Havens are trying to prove. Braid Generates a twist pattern in which the sequence 1, 2, 3, … alternates with the sequence 1, 1, 1, 2, 1, 3, 1, 4, ….
But the name also has a symbolic meaning. In German folklore, a traveling nobleman falls into a swamp, sinking deeper and deeper until the mud nearly swallows him whole. To escape, he pulls himself out of the swamp with his braids. Elsner “proposed”Braid” Because of how numbers twist around the real number line, and in a way, my life has had that same winding journey through mathematics,” says Havens. Havens ‘intensively dealt with’ [Zopf] That’s when I started studying mathematics,” Elsner added. “He tried to communicate his results to other mathematicians and start a better life for him.”
Inmates are interested in PMP consoles, but “I would definitely go that route if I could,” says Conway, but the system faces major obstacles to widespread adoption in U.S. prisons. . Sending email in prison can cost up to 50 cents, but inmates earn only up to 52 cents an hour on average. And even if the prisoner can afford to send the code to the console, the message may never be delivered. “[Prisons] There’s a perfectly reasonable rule that you can’t send encoded messages,” Sahai says. “And, of course, what that means is an encrypted message.”
help may come. Securas Technologies, a leading prison email provider, is “exploring the possibility” of incorporating the console into its approved educational platform, which includes free “electronic messaging between students and instructors.” Securas spokesman Jade Trombetta said.
Ultimately, though, the Prison Mathematics Project isn’t a technology company, regardless of whether the console is widely adapted. It is a anchorage point for prisoners who weave their own mathematical lifelines. “My life was chaos and destruction until I started studying math,” says Cunningham, who is serving a life sentence for a DUI death. “When I got my first textbook on partial differential equations, I learned what love is.”
Over the past six years, Cunningham has developed his original “love” for partial differential equations into his own work on scattering theory, a framework for explaining the effects of collisions between free systems, such as particles and waves. rice field. Led by mathematicians trained at the Massachusetts Institute of Technology, his work provides new details about how “resonances”, the physically significant afterimages of collisions involving particles and waves, arise. discovered.—Distributed in a simplified quantum-mechanical setting. Mathematics “changed everything for me,” says Cunningham.
For Havens, that change is at the heart of justice. “Justice is not what happens after a person who has committed a crime has been in prison for ○ years,” he says. “Justice comes when you begin to fix the causes that have led you [to prison] in the first place. Some of the debt, Mr. Heavens puts it, is “infinite debt” that can never be paid off in full, but more and more people in prison turn to math to get out of the swamp.
