About Charybdis and Scylla Academy

About Charybdis and Scylla Academy

Charybdis and Scylla Academy is a home school in San Jose, California, which has filed a private school affidavit (PSA) with the State of California each year since 2007. We follow the classical model of education, with respect to the scope of the California curriculum. Neil Bickford is the only student. Neil has studied history, literature, science, mathematics, foreign languages, and art, as reflected in his transcript. All courses were taught to mastery (as shown by essays, discussion, and/or presentations) and/or to the completion of the resource, so there are no formal grades. There are grades for courses at San Jose State University, which are included on his transcript.


Why We Homeschool

Neil is academically precocious and the San Jose Unified School district had difficulty serving him at his level. Homeschooling allows us not only the freedom to let Neil work at his academic level, but also gives Neil the time to go into depth on subjects of interest. Neil has also had the freedom to travel extensively, and this has allowed him to attend recreational math conferences; tour national parks, including Yellowstone and Gettysburg; and most recently, explore NASA’s Johnson Space Center, the Very Large Array, and the Petrified Forest.


Pedagogy and Curriculum

Charybdis and Scylla uses a variety of learning methods and resources, as described below. Most courses have been taught at a college level. Whenever possible, courses have included hands-on work and presentations, such as battle recreations for history, 3D printing puzzle prototypes with mathematical algorithms, and the extraction of DNA sequences for biology.


Private tutoring: Neil has had weekly tutoring sessions year-round with mathematician Bill Gosper. This has allowed Neil to explore his passion and interest in mathematics and computer science in depth, meet and work with other notable mathematicians, and fostered some of his most notable accomplishments, such as (for a time) holding the world record for calculating the continued fractions of Pi, presenting at Gathering 4 Gardner recreational mathematics conferences in 2012 and 2014, and contributing to the New York Times’ Numberplay blog.


San Jose State University: The mathematics department at San Jose State University has allowed Neil to audit mathematics courses, and he enrolled as an Open University student for Linear Algebra. Additionally, he has been a member of the university’s juggling club and game development club.


Online Courses: Neil has completed several Coursera courses, as well as MIT Open University molecular biology course, and a Thinkwell Physics 101 course. Most of these courses included quizzes and tests; the Thinkwell course scored his results; the Coursera Image & Video Processing course awarded him a certificate with distinction.


DVD/Audio Courses: The Great Courses have provided lectures and syllabi for a general literature course (“A Day’s Read) and a poetry course (“How to Read and Understand Poetry”). In addition to doing the required reading, Neil wrote essays based on the material of each lecture. The Great Courses has also provided our Latin 101 course, which has exercises accompanying each lecture.


Other: Other courses have been book based, with reading and discussion of each chapter, and appropriate worksheet work, essays, and labs based on the material. In some cases, such as AP literature, a syllabus created by another teacher has been adapted to fit our schedule and resources. The first semester of his public speaking course was at a local homeschool co-op; drawing and painting instruction was provided by a local community center adult-level course.


Vocational: Neil goes to work 7 hours a week as a production assistant. He has written macros to facilitate data integration, as well as done lighting and filming for commercial video.


Standardized Test Results

Charybdis and Scylla Academy currently boasts the highest SAT scores of any academic institution in the State of California.[1]



Critical Reading           800

Mathematics                800

Writing                         800


SAT Subject Tests

Math 2                         800

Biology                                    700


Advanced Placement Results

Calculus                       5

Computer Science        5


Awards and Distinctions

National Merit Semifinalist


“Random” mathematics blog, nbickford.wordpress.com, 2009-present; covered topics include cellular automata, Minsky-Trinsky Circles, Hilbert space-filling curves, sliding block puzzle algorithms and more

Record computation of the continued fraction of Pi to 458 million terms, October 2010 – see http://mathworld.wolfram.com/PiContinuedFraction.html


Presentation: “Marble Runs and Turing Machines” at Gathering 4 Gardner 11, Atlanta, Georgia, March 22, 2014


Presentation: “Reversing the Game of Life for Fun and Profit” at Gathering for Gardner X, Atlanta, Georgia, March 2012


Guest contributor New York Times Wordplay blog: “Numberplay: A Triplet of Time Puzzles,” May 5, 2011, wordplay.blogs.nytimes.com/2011/05/30/numberplay-a-triplet-of-time-puzzles/


Lissajous animation for New York Times Wordplay column, January 1, 2014, wordplay.blogs.nytimes.com/2014/01/06/2013



[1] Heh, heh. There is only one student, and he did well on his tests. As with his record on the continued fractions of pi, this may be short lived, but we’re enjoying it while we can.

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