Yet Another Stroll in Plato's Paradise

For the second time in two years, Dr. David Haight, of the History and Philosophy Department at Plymouth State University, has published a possible solution to one of the Clay Mathematics Institute's Millennium Problems. The Clay Prize Problems are a set of seven mathematical problems whose solutions are deemed most crucial to the understanding of mathematics. Each solution is appraised at $1 million.

Haight's recently released article, "Generalizing Riemann: From the L-functions to the Birch/Swinnerton-Dyer conjecture," disproves the Birch/Swinnerton-Dyer conjecture, and is currently being read and evaluated by the general mathematics community.

Haight's first article, "Summa Characteristica and the Riemann Hypothesis: Scaling Riemann's Mountain," published in the Journal of Interdisciplinary Mathematics in 2008, proposes a concise and harmonious solution to Bernhard Riemann's notoriously taunting hypothesis concerning the prime numbers.

The hypothesis, which entails the distribution of the prime numbers, has mystified the luminaries and the bourgeois of pure and higher mathematics for over a century. A successful proof would profoundly influence our understanding of the foundations and philosophy of mathematics.

Dr. Haight's first article, which weaves together a number of vital mathematical ingredients, including Euler's harmonic sequence and Riemann's zeta function, proves that there is a sound and predictable pattern to the distribution of zeta zeros along the one-half critical line, all the way to infinity.

Drawing from his conclusions made in "Summa Characteristica and the Riemann Hypothesis," Haight has recently conquered, in his second article, yet another of the seven Millennium Problems.

His second article, "Generalizing Riemann: From the L-functions to the Birch/Swinnerton-Dyer conjecture," concerns prime numbers involving elliptic curves and functions, which are what many private codes are based on today, including government codes, air traffic controls, and our own online banking information. "If these elliptic functions were to be de-codified or decrypted, these communications would be very seriously compromised," said Haight.

"These codes are based on huge prime numbers, as well as elliptic functions. You take two one-hundred-digit prime numbers, multiply them together, and you get this gigantic number which is not easily, if at all, factorizable back into those two original primes. It's kind of a one-way street," said Haight in a personal interview, "and that's what keeps these codes secure."

The findings in his second article bear good news for the many labyrinths of codes that are built by these elliptic equations and disprove the possibility, as suggested by the Birch/Swinnerton-Dyer conjecture, of there being an all-encompassing formula that would allow for solutions to these functions. Were such a formula or, as Haight says in his article, a "decision-procedure" to exist, the consequences would be inconceivably devastating for our government, our military, and our own security and privacy. "My second paper is a proof showing that this [Birch/Swinnerton-Dyer] conjecture is false, and that, therefore, these codes are secure."

Dr. Haight's first article, "Summa Characteristica and the Riemann Hypothesis," which has been published and open for criticism for two years, is still in the process of accreditation. The Clay accreditation process involves three major phases. The first requires that the proof be published in a peer-reviewed journal. The second requirement is a two-year waiting period, in order for members of the field to examine the proof and possibly challenge it. "There has been no challenge to the proof," said Haight, and "a top expert in the field has seen [the proof], had no critique to make of it, and encouraged me to publish it." 

The third phase, though, remains an obstacle for Haight. "The third step is a huge acclamation from large numbers of mathematicians that, then, the Clay Institute will take into account, and decide whether or not the money will be awarded."

Although the proof itself seems to be flawless, Haight is still experiencing difficulty in achieving this final step. The field of number theorists is small, and Haight, who is not a professional mathematician but rather self-schooled, is "an outsider." "I am not somebody who is a part of this community," he said. "I don't have any contact with them, so I'm at a disadvantage."

Outsider or not, his findings in both his first and his second paper appear promising despite the lack of official accreditation. But the reward for Haight lies not in the acceptance or in the attractive prize sum, but in the sense of harmony and accomplishment he's found since he took on the problem almost ten years ago. "I'm not a mathematician by profession, but by obsession," he said. The problem, when he first encountered it, "got under my skin. I couldn't leave it alone. I had the tiger by the tail. The beautiful forms that these formulas are all about… I felt as if I was in Plato's Paradise."

Dr. Haight's findings, as presented in both "Summa Characteristica and the Riemann Hypothesis" and his second article "Generalizing Riemann," though beyond the grasp of the vast majority of us, are certainly of remarkable stature. If accepted, he will not only be awarded $1 million per article, but his work will greatly contribute to the fields of mathematics, philosophy, and the sciences in their ever-enduring quest to uncover the laws and the patterns, the most precise functions of the elements of universe. 

 "What's missing in mathematics," said Haight, "is the clue to the possible periodicity of the prime numbers," of which he fondly refers to as being the "atoms of mathematics." If his proof of the Riemann hypothesis is accepted and accredited by the Clay Mathematics Institute, then mathematicians will be able to confidently utilize the organized pattern of the primes in uncovering even more mysteries of mathematics. Thousands of mathematical proofs depend on the Riemann hypothesis being true, which is why the Riemann hypothesis is the most statuesque of the Millennium Problems, the Holy Grail of mathematics, and why, according to Haight, "so many have tried to unveil the elegance of prime numbers."