Harlan J. Brothers

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Harlan J. Brothers
Harlan J. Brothers in 2012.jpg
Harlan J. Brothers in 2012
Residence Branford, Connecticut; United States
Nationality American
Alma mater Berklee College of Music
Gateway Community College
Scientific career
Fields Inventing, Mathematics, Music, Education

Harlan J. Brothers is an inventor, composer, mathematician, and educator based in Branford, Connecticut.

Life and work[edit]

In 1997, while examining the sequence of counting numbers raised to their own power ( {an}=nn ), Brothers discovered some simple algebraic formulas [1] that yielded the number 2.71828..., the universal constant e, also known as the base of the natural logarithm. Like its more famous cousin π, e is a transcendental number that appears in a wide range of formulas in mathematics and physics.

Having no formal college-level mathematics education, he sent brief descriptions of his findings to the host of the National Public Radio show “Science Friday” and also to a well-known mathematician at Scientific American.

His communication with “Science Friday” led to a fruitful collaboration with meteorologist John Knox. Together they discovered over two dozen new formulas and published two papers on their methods. These methods subsequently found their way into the standard college calculus curriculum by way of two popular textbooks on the subject.[2] [3]

Brothers went back to school to study calculus and differential equations. He went on to publish methods for deriving infinite series that include the fastest known formulas for approximating e.[4]

In the summer of 2001, his professor, Miguel Garcia, introduced him to Benoît Mandelbrot and Michael Frame at Yale University. Brothers soon began working with them to incorporate the study of fractals into core mathematics curricula. His current research, begun in collaboration with Frame, is in the field of fractals and music.[5]

Brothers has earned six U.S. patents and is a trained guitarist and composer. He also appeared as guest editor on the NPR show Bruce Barber's Real Life Survival Guide. He currently works as Consulting Director at Forensic Mathematics Services. “Our work is important because e is important,” says Brothers. “We’re not claiming that these theorems represent an advance in the computation of e—we’ve just come up with alternate formulas that may be easier to use in some circumstances. Regardless of whether our work has any actual practical applications, it is already having an impact by sparking the interest of teachers, students, and math buffs around the world. I find this very exciting.”

See also[edit]



  1. ^ H. J. Brothers and J. A. Knox, "New closed-form approximations to the Logarithmic Constant e.” The Mathematical Intelligencer, Vol. 20, No. 4, 1998; pages 25-29.
  2. ^ R. Larson, B. Edwards, and R. Hostetler, Calculus With Analytic Geometry, Seventh Edition. Houghton Mifflin Company, 2002.
  3. ^ R. Larson and B. Edwards, Calculus: Early Transcendental Functions, Fifth Edition. Houghton Mifflin Company, 2010.
  4. ^ H. J. Brothers, "Improving the convergence of Newton's series approximation for e.” The College Mathematics Journal, Vol. 35, No. 1, 2004; pages 34-39.
  5. ^ Fractal Music Workshops, Brothers Technology website

Further reading[edit]

External links[edit]