# MathPath

**MathPath** is a mathematics enrichment summer program for students ages 11–14 (middle school age in the US). It is four weeks long, and moves to a different location each year. MathPath is visited by world-renowned mathematicians such as John H. Conway and Francis Su. It was probably the original, and is still one of the few, international residential high-end summer camps exclusively for mathematics and exclusively for students of middle school age.

## Contents

## History

MathPath was founded in 2002 by George Rubin Thomas, who had previously founded Mathcamp for high school students and has since founded Epsilon Camp for children age 8–11 (in 2011) and Delta Camp for children 6 and 7 (in 2014). His goal was to inspire and advance the most mathematically gifted middle school age students, through a summer camp.

## Story of MathPath

Academic out-of-school-programs for gifted students in grades 7 and 8 have existed for many years. They identified the students and placed them in suitable summer programs. Johns Hopkins University and Duke University have been leaders in the endeavor. Typically they chose students who were in the top 0.5%, 2% and the like from nationally recognized achievement tests.

George Rubin Thomas, a former college professor and then Executive Director of Mathcamp, one of the leading summer programs for mathematically talented high school students, saw the need for an intense program similar to Mathcamp but designed for students in grades 6 through 8. He recognized that, as in music, training suited to the very gifted should be provided at an early age. He saw that such training must go beyond the narrow focus at standard programs for the gifted and talented, and have a balanced approach to the several aspects of mathematical development of the high IQ young student, more balance than can be achieved at problem-solving-focus workshops in the various countries. He first proposed the idea to two fellow mathematicians with whom he ran Mathcamp. They said they did not have the time to be involved in yet another camp and that Thomas could start one if he liked. Starting a large national summer program is financially risky. Thomas, not wanting to jeopardise Mathcamp, struck out on his own. He discussed the idea with many mathematicians, and educators of gifted students. Among those were John Conway of Princeton University and Titu Andreescu, then Executive Director of the American Mathematics Competitions. The encouragement he received prompted him to consult the parents of the very gifted. Their strong endorsement pushed the launch of this summer workshop. The name Mathpath was suggested by Professor John Conway. From the first camp in 2002, Conway has taught at the program. The quality of the program was helped immensely by Professors Stephen Maurer, who joined the program in 2003, and Paul Zeitz, who joined in 2004.

The program is dedicated to nurturing emerging mathematical talent by providing a month-long summer gathering place - a place that has the highest residential standards, instructional programs suited to the extremely gifted, and developmental opportunities, both academic and social.

It was found that a suitable location for a program for the highly gifted young students would benefit from proximity to nature as well as opportunities for weekend trips. Black Hills State University in Spearfish, South Dakota, was selected as a suitable campus for the first camp.

The thrust of the program is four-fold: Teach how to write in mathematics, inculcate the importance of proof, familiarize the heuristics of problem solving, and provide a unified view of mathematics and its culture through its historical development. Some of the world's top experts who educate the brightest young students would teach at Mathpath.

MathPath is now a non-profit organization run by a team of mathematicians and high school and middle school teachers of students gifted in mathematics. Thus, as happened to its sibling program Mathcamp, Mathpath too passed on to the mathematics community.

## Subjects

At MathPath, students learn about many math topics that are rarely taught in American schools, or taught in much depth, such as non-Euclidean geometry, advanced Euclidean geometry, number theory, combinatorics, induction, spherical trigonometry, mathematical origami, and the mathematics of card shuffling. They also learn some history of math and work on mathematical writing. Topics vary somewhat each year, depending on instructor interest. As well, students have the opportunity to prepare for contests such as MATHCOUNTS, AMC, or AIME.

The emphasis throughout is on *enrichment*, not *acceleration*. Thus no effort is made to place students out of their next school course, and when topics are taught which are elective university courses (e.g., number theory) the purpose is to give a good understanding of the issues and key ideas and methods, not to cover the entire university course. Covering a whole university course would be difficult, even an the rapid MathPath rate, since MathPath courses are only a week long.

Although much of the day is spent learning mathematics, there is deliberately more free time than at high school math camps. Also, students regularly go on weekend day trips and visit the surrounding area's attractions.

## Staff

### Regular Staff

Regular staff are those who come almost every year. Usually they come for 2–4 weeks, but a few come for only one week. Most of the regular staff members have an in-camp nickname.

**Silva Chang**(Ms C), University of Colorado at Boulder. As director of the Colorado Math Circle, coach of the Colorado ARML Team, and five-time coach of the Colorado MATHCOUNTS Team, Ms. Chang has mentored and taught MOSP attendees, USAMO qualifiers, and state MATHCOUNTS champions. At MathPath, Ms. Chang has taught two very popular courses, mathematical origami and Mathematica.**John Horton Conway**( Conway) is the inventor of Surreal numbers and Conway's Game of Life, among other things. A professor at Princeton, he comes to MathPath for one week each year.**Thomas Drucker**(Coach D) is a professor of mathematics at the University of Wisconsin and the editor of*Perspectives of the History of Mathematical Logic*. He is an expert on the history of mathematics from the 17th century to modern times.**Alan Q. Lippert**(Mr. L) is a retired mathematics teacher and MATHCOUNTS coach. He was the Academic Director of MathPath in 2003–2005. He used to specialize in MATHCOUNTS and AMC8 classes, but more recently he prefers courses on the mathematics of sudoku extensions like Ken Ken and Kendoku. Also, he is famous for the Problem of the Day, which is always a puzzle problem, sometimes mathematical, sometimes involving physics, and often a general reasoning puzzle.**Stephen B. Maurer**(Mr. M) is a Professor of Mathematics at Swarthmore College. He became Academic Director of MathPath in 2006, and Executive Director in September 2014. He is a former Chair of the AMC and an expert on mathematical writing. At MathPath he teaches courses on mathematical induction, combinatorics, "Linear Set Geometry", and sometimes AMC competitions. He also runs sessions where student solutions to the Qualifying Test are used anonymously to discuss mathematical writing. But watch out! Mr. M sometimes screws up and forgets to remove the name.**Jonathan Rogness**, University of Minnesota, is well known for his beautiful mathematical visualizations, including an award-winning video,*Möbius Transformations Revealed*, which went viral online and has been viewed by nearly two million people. At MathPath he has taught cryptology and the Shape of Space.**Francis Su**(Prof Su) is a professor of mathematics at Harvey Mudd College, Claremont, CA. He teaches about problems relating to probability, shuffling (card tricks!) and social sciences (such as fair division). He typically comes for the first or last week. Now that he is President Elect of the Mathematics Association of America, and then President and then Past President, he may not be able to attend for a few years.**Crispin Sumner**(Kip) is the Camp Director and is in charge of student life and activities, as well as some years being camp champion in doubles pickleball and perennial co-champion in doubles pool. Starting in 2014, he also teaches an advanced course in graph theory.**George Thomas**(Dr. T), Executive Director Emeritus, is the founder of the camp. He teaches courses in Analytic Geometry, Hyperbolic Geometry, Elliptic Geometry and Projective Geometry.**Sam Vandervelde**(Dr. V) is an Assistant Professor of Mathematics at St. Lawrence University, NY, Coordinator of the Mandelbrot Competition, and author of the Circle in a Box pdf and hardcopy book for use in the Math Circle movement. He teaches courses on various topics, usually different ones each year, such as number theory, problem writing, and Ford circles. He will be moving to California in summer 2015 to be the first Dean of Mathematical Sciences of the new Proof School in the Bay Area.**Glen Van Brummelen**(Glen) is an expert in the history of mathematics, especially ancient Greek and medieval Islamic mathematics. In 2009 he published a book on the history of trigonometry, and in 2012 he published the first new book on spherical trigonometry in over 100 years, entitled "Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry", and based in part on the course Heavenly Mathematics that he teaches at MathPath.- John Howe (John) is a retired mathematics teacher at Princeton Day School and is a general administrative Assistant to Kip and Mr M, best known for running the bank, posting the assignment of students to breakout sessions, and taking students to medical care.

### Visiting Staff

Visiting staff are participants for one year or occasional years. Usually they attend for one week, or for a day or two to give a few lectures. Often they are faculty at the host institution or nearby institutions. Below is a sampling of guest staff from recent years. For more recent information see The MathPath Faculty Webpage; A new version with a new year number is put up a few months before each summer's program.

**Gene Abrams**is a Professor of Mathematics at the University of Colorado, Colorado Springs CO. His research interests include Leavitt path algebras and noncommutative rings.**Jennifer Beineke**is an Associate Professor of Mathematics, Western New England College, Springfield, MA is a specialist in analytic number theory.**Andrew Beveridge**is an Assistant Professor of Mathematics at Macalester College, St Paul MN. He studies random walks on graphs as well as structures generated via random processes. He enjoys thinking about problems inspired by massive real world networks, such as the internet.**Owen Byer**, Professor of Mathematics, Eastern Mennonite University, Harrisonburg VA, is an expert in discrete math and geometry, co-authoring the book*Methods for Euclidean Geometry*. At MathPath he has taught breakouts in Affine Geometry and Probability.**Robin Hartshorne**is an Emeritus Professor of Mathematics at UC Berkeley and author of Projective Geometry (1967), Algebraic Geometry (1977), and Geometry: Euclid and Beyond (2000).**Isil Nal**, Harmony School of Excellence, Houston TX, and coach of the 2011 Texas State MATHCOUNTS team that placed 3rd at nationals. At the Harmony School Ms Nal has taught National MATHCOUNTS participants, USA(J)MO qualifiers and MOSP attendees. At MathPath she teachers AMC12, AIME and USAMO courses.**Amelia Taylor**is an Assistant Professor of Mathematics at Colorado College, Colorado Springs CO. She lectures on combinatorics, group theory, and the game Set**John Watkins**, Professor Emeritus of Mathematics, Colorado College. A graph theorist who has also worked on puzzles. He teachers courses at MathPath that use board puzzles, Sudoku and KenKen to teach mathematics, for instance, using material from his book*Across the Board: The Mathematics of Chessboard Problems*.**Paul Zeitz**is a Professor of Mathematics at the University of San Francisco. He is the author of*The Art and Craft of Problem Solving*. At MathPath he has taught such courses as problem solving, combinatorics, and solving the Rubik's Cube.

## Activities

### Typical weekday schedule^{[1]}

- 6:00am Optional activities for early risers: math, jogging, table tennis, etc.
- 7:30 Last wake-up call
- 8:00 Breakfast
- 8:45 Plenary Lecture: The History of Mathematics
- 9:45–11:00 Morning Breakout Session
- 11:00–12:00 Plenary Lecture: Guest Speaker
- 12:00 Announcements
- 12:30 Lunch
- 1:00–2:45 Free Time
- 3:00 Mini-Plenary Lecture: Mathematical Writing
- 3:30–5:00 Afternoon Breakout Session
- 5:00 Wrap-up, Announcements, Problem of the Day
- 6:00 Dinner
- 6:30 Evening Activities (digestion/soccer, basketball, etc.)
- 8:30 Students back in the dorm; math conferencing time
- 9:15 Counselor Meetings
- 9:45 Quiet time, preparing for bed/ showers
- 10:00 Bedtime! (2013)
- 10:15 Bedtime! (2012 and prior)

NOTE: Every year's schedule varies slightly (around 15 minutes). Look on the MathPath website (www.mathpath.org) for the exact schedule for the year.

On Saturday, the afternoon activities are a little different.

- 2:30 Show and tell and voting for breakouts
- 3:30 Fun math activity (such as a math relay race, MathCounts Countdown, QuizBowl, etc.)

On weekends, students usually go on a day trip to the surrounding attractions or participate in other activities, such as biking, white water rafting, rock climbing, or hiking. Chess, ping pong, pool, Rubik's Cube, Set and Magic: The gathering tournaments are played and organized during the students' free time.

## Admissions

MathPath is selective. The primary criterion for admission is the applicant's work on the yearly Qualifying Test. One begins the application process by filling out an online information form. An academic and nonacademic reference are also required. Admission is done on a rolling basis. For details, see How to Apply. Also available: financial aid, merit scholarships for high scores on various competitions, and fee reductions for paying early and for siblings attending in the same year.

## Locations

- 2002 – Black Hills State University, Spearfish, SD
- 2003 – Black Hills State University, Spearfish, SD
- 2004 – Roger Williams University, Bristol, RI
- 2005 – Colorado College, Colorado Springs, CO
- 2006 – University of California, Santa Cruz, CA
- 2007 – Colorado College, Colorado Springs, CO
- 2008 – The University of Vermont at Burlington
- 2009 – Colorado College, Colorado Springs, CO
- 2010 – Macalester College, St. Paul, MN
- 2011 – Colorado College, Colorado Springs, CO
- 2012 – Mount Holyoke College, South Hadley, MA
- 2013 – Macalester College, St. Paul, MN
- 2014 – Mount Holyoke College, South Hadley, MA
- 2015 - Lewis & Clark College, Portland, OR
- 2016 - Macalester College, St. Paul, MN

## References

- ↑ "A MathPath Day". MathPath.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>