Pure Mathematics

SUMMARY

Jonathan Farley’s main areas of research are lattice theory and the theory of ordered sets.  His main results in these areas include the following: the resolution of a conjecture posed by MIT Professor of Applied Mathematics Richard Stanley in 1975; the solution to a problem posed by Richard Stanley that had remained unsolved since 1981; the solution to some problems from Richard Stanley’s classic 1986 text, Enumerative Combinatorics: Volume I; the solution to a problem in “transversal theory” attributed to combinatorialist Richard Rado that had remained unsolved since 1971; the solution to several problems from the 1981 Banff Conference on Ordered Sets and the 1984 Banff Conference on Graphs and Order;  the solution to some problems of lattice theory pioneer George Grätzer from 1964; the solution to some problems of lattice theory pioneer E. T. Schmidt from 1974 and 1979; and the solution to a problem published in 1982 by universal algebra pioneer Bjarni Jónsson and Berkeley professor (now emeritus) Ralph McKenzie. 

SELECTED PUBLICATIONS

• Jonathan David Farley. “Quasi-completeness and localizations of polynomial domains: A conjecture from 'Open problems in commutative ring theory,” Bulletin of the Korean Mathematical Society 53(2016), 1613-1615. (PDF)
  
  
• Jonathan David Farley and Dominic van der Zypen. “A Problem of Hartmanis on Generalized Partitions,” Baltic Journal of Modern Computing 3(2015), 268-272. (PDF)
  
  
• Jonathan David Farley. “Strictly Order-Preserving Maps into Z, I: A Problem of Daykin from the 1984 Banff Conference on Graphs and Order,” Mathematica Pannonica 25(2014-2015), 17-39. (PDF)
  
  
• Jonathan David Farley. “Distributive Lattices of Small Width, I: A Question of Rosenberg from the 1981 Banff Conference on Ordered Sets,” Mathematica Pannonica 24(2013), 231-242. (galley proofs PDF)
  
  
• Jonathan David Farley. “A Problem (Attributed to Rado) from Mirsky's 1971 Monograph Transversal Theory and a Conjecture from the 1982 Proceedings of the American Mathematical Society,” Mathematica Pannonica 24(2013), 3-14. (PDF)
  
  
• Farley, Jonathan David. “Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order,” Canadian Mathematical Bulletin 54(2011), 277-282. (PDF)
  
  
• Farley, Jonathan David. “Solution to Conjectures of Schmidt and Quackenbush from 1974 and 1985: Tensor Products of Semilattices,” Mathematica Pannonica 22 (2011), 135-147. (galley proofs)
  
  
• Farley, Jonathan David and Ryan Klippenstine. “Distributive lattices of small width, II: a problem from Stanley’s 1986 text Enumerative Combinatorics,” Journal of Combinatorial Theory (A) 116 (2009), 1097-1119. (PDF)
  
  
• Farley, Jonathan David. “Linear extensions of ranked posets, enumerated by descents. A problem of Stanley from the 1981 Banff conference on ordered sets,” Advances in Applied Mathematics 34 (2005), no. 2, 295-312. (PDF)
  

• Farley, Jonathan David and Sungsoon Kim. “The automorphism group of the Fibonacci poset: a ‘not too difficult’ problem of Stanley from 1988,” Journal of Algebraic Combinatorics 19 (2004), no. 2, 197-204. (PDF)
  
  
• Farley, Jonathan David. “Quasi-differential posets and cover functions of distributive lattices. II. A problem in Stanley’s Enumerative Combinatorics,” Graphs and Combinatorics 19 (2003), no. 4, 475-491. (PDF)
  
  
• Farley, Jonathan David and Bernd S. W. Schröder. “Strictly order-preserving maps into Z. II. A 1979 problem of Erné,” Order 18 (2001), 381-385. (PDF)
  
  
• Farley, Jonathan David. “Coproducts of bounded distributive lattices: cancellation. A problem from the 1981 Banff Conference on Ordered Sets,” Algebra Universalis 45 (2001), no. 4, 375-381. (PDF)
  
  
• Farley, Jonathan David. “Quasi-differential posets and cover functions of distributive lattices. I. A conjecture of Stanley,” Journal of Combinatorial Theory (Series A) 90 (2000), no. 1, 123-147. (PDF)
  
  
• Farley, Jonathan David. “Functions on distributive lattices with the congruence substitution property: some problems of Grätzer from 1964,” Advances in Mathematics 149 (2000), no. 2, 193-213. (PDF)
  
  
• Farley, Jonathan David. “Priestley powers of lattices and their congruences. A problem of E. T. Schmidt,” Acta Scientiarum Mathematicarum (Szeged) 62 (1996), no. 1-2, 3-45. (PDF)
  
  
• Farley, J. D. “The automorphism group of a function lattice: a problem of Jónsson and McKenzie,” Algebra Universalis 36 (1996), no. 1, 8-45. (PDF)

Math for Counterterrorism

SUMMARY

Jonathan Farley’s work applying mathematics to counterterrorism has been profiled in The Chronicle of Higher Education, in Science News and Science News Online, in The Economist Magazine, in USA Today, on Fox News Television, and on Air America Radio.  He is Chief Scientist of Phoenix Mathematics, Inc., a company that develops mathematical solutions to homeland security-related problems.

He has had face-to-face meetings discussing math-for-counterterrorism with the Jamaican Minister of National Security, a former Director of the US National Security Agency and a former Deputy Director of the CIA, the director of Homeland Security for the Port of Los Angeles, a former US ambassador to the European Union, a former governor of the US state of New Mexico, a US Air Force general, two US Navy admirals and a former US Director of National Intelligence.

Dr. Farley was a 2007 Proteus Monograph Series Fellow.  In 2005-2006, he was a Science Fellow at Stanford University’s Center for International Security and Cooperation.  Seed Magazine named him one of “15 people who have shaped the global conversation about science in 2005.” He has co-organized five Conferences on Mathematical Methods in Counterterrorism. 

SELECTED PUBLICATIONS

• Farley, Jonathan David (2012).“How Al Qaeda Can Use Order Theory to Evade or Defeat U.S. Forces: The Case of Binary Posets,” in Evangelos Kranakis (Ed.), Advances in Network Analysis and Its Applications (pp. 299-306). Vienna, Austria: Springer Verlag. (galley proofs)
  
  
• Memon, Nasrullah, Jonathan David Farley, David L. Hicks, and Torben Rosenørn, Mathematical Methods in Counterterrorism (Springer Verlag, Vienna, 2009). (cover)
  
  
• Farley, Jonathan David (2009).“Personal Reflections on Beauty and Terror,” in Nasrullah Memon, Jonathan David Farley, David L. Hicks, and Torben Rosenørn (Eds.), Mathematical Methods in Counterterrorism (pp. 385-389). Vienna, Austria: Springer Verlag. (PDF)
  
  
• Farley, Jonathan David (2009).“Two Theoretical Research Questions Concerning the Structure of the Perfect Terrorist Cell,” in Nasrullah Memon, Jonathan David Farley, David L. Hicks, and Torben Rosenørn (Eds.), Mathematical Methods in Counterterrorism (pp. 91-103). Vienna, Austria: Springer Verlag. (PDF)
  
  
• Farley, Jonathan David.  Toward a Mathematical Theory of Counterterrorism: Building the Perfect Terrorist Cell (U.S. Army War College, Carlisle Barracks, Pennsylvania, 2007). (cover) | (PDF)
  
  
• Farley, Jonathan David. “Evolutionary Dynamics of the Insurgency in Iraq: A Mathematical Model of the Battle for Hearts and Minds,” Studies in Conflict and Terrorism 30 (2007), 947-962. (PDF)
  
  
• Lefebvre, Vladimir A.  and Jonathan David Farley, “The Torturer’s Dilemma: A Theoretical Analysis of the Societal Consequences of Torturing Terrorist Suspects,” Studies in Conflict and Terrorism 30 (2007), 635-646. (PDF)
  
  
• Farley, Jonathan David.  “The N.S.A.’s Math Problem,” The New York Times (May 16, 2006). (PDF) “The NSA Is Tap, Tap, Tapping: Spy Agency Misses the Big Picture As It Targets All the Dots,” San Francisco Chronicle (July 9, 2006).
  
  
• Farley, Jonathan David. “The Torturer’s Dilemma: The Math on Fire with Fire,” San Francisco Chronicle (January 8, 2006).
  
  
• Farley, Jonathan David. “Terror and Beauty: The European Institute for Mathematical Methods in Counterterrorism,” Bridges: The Office of Science and Technology’s Publication on Science and Technology Policy (Austrian Embassy in the United States of America, Washington, D.C., 2005).
  
  
• Farley, Jonathan David.  “Breaking Al Qaeda Cells: A Mathematical Analysis of Counterterrorism Operations (A Guide for Risk Assessment and Decision Making),” Studies in Conflict and Terrorism 26 (2003), 399-411. (PDF)

Math and Education

SUMMARY

Beginning the first week the hit television show Numb3rs aired, Jonathan Farley, as well as, soon afterwards, the agent for the company he co-founded, Hollywood Math and Science Film Consulting, wrote the staff of Numb3rs, suggesting that they, in conjunction with the National Council of Teachers of Mathematics, create homework assignments that teachers could use focusing on the math and science in the show.   Nine months later, Numb3rs inaugurated the “We All Use Math Every Day” program, with the National Council of Teachers of Mathematics and Texas Instruments.  This program creates homework assignments that teachers can use focusing on the math and science in the show.  Dr. Farley also used his idea with Dr. Tony Harkin for Flatland the Movie, starring Martin Sheen, Michael York, and Kristen Bell.

Jonathan Farley spoke at the launch of Raytheon Corporation’s math education website, MathMovesU.com.  The only other speakers were Sarah Greenwald, representing Hollywood Math and Science Film Consulting, the late U.S. Senator Ted Kennedy, the late U.S. Congresswoman Jo Ann Davis, Raytheon Senior Vice President for Strategy Bill Lynn (later U.S. Deputy Secretary of Defense), and Olympic gold medalist Apolo Ohno. Seated next to Dr. Farley was U.S. Congressman Silvestre Reyes.

Dr. Farley is also interested in encouraging girls who wish to do mathematics.  He conceived of and co-organized a symposium on women and mathematics at Stanford University’s Institute for Research on Women and Gender (now the Clayman Institute), called “Proof and Prejudice.” 

Television actress Danica McKellar asked Dr. Farley to provide a quote for her New York Times best-selling math book for middle school-aged girls, Math Doesn’t Suck. In her New York Times 2010 best-seller, Hot X: Algebra Exposed, she writes about “the incomparable, brilliant Jonathan Farley.” In her 2012 book, Girls Get Curves: Geometry Takes Shape, she writes about “the immensely gifted Jonathan Farley”.

Jonathan Farley has also worked with the National Action Council for Minorities in Engineering and the Algebra Project.  Jonathan Farley co-founded the consulting group Axum Educational Solutions.    

SELECTED PUBLICATIONS

• Farley, Jonathan David and Héctor Rosario. “A Critique of Monetary Educational Incentives for Elementary and Middle School Students in New York City Public Schools,” Teachers College Record (May 15, 2008) (text).
  
  
• Farley, Jonathan David. “Fix Rochester Schools ‘outside the Box,’” Democrat and Chronicle (May 14, 2008).
  
  
• Farley, Jonathan David. “Improving Math Ed―Bush Right about That: But Where Are the Teachers Coming from?” San Francisco Chronicle (March 12, 2006).
  
  

EDUCATIONAL VIDEOS

• “Oxford alumnus Jonathan Farley promotes a course on logic
  and discrete mathematics".
  
  
• “Of Terrorists and Trees Teaser Trailer".
  
  
• “Of Terrorists and Trees Part 2: An Exploration of Aspects of Graph Theory".
  
  
• “Of Terrorists and Trees Part 3: An Exploration of Aspects of Graph Theory".
  
  
• “Of Terrorists and Trees Part 4: An Exploration of Graph Theory".