Jonathan Farley, Mathematics

I am a pure mathematician, meaning nothing I do has anything to do with relevance to the real world—but everything to do with Truth.

JONATHAN FARLEY - Associate Professor of Mathematics, Morgan State University

MLK Visiting Professor 2002-2005
Hosted by the Department of Mathematics

Jonathan Farley is Associate Professor of Mathematics at Morgan State University. At the time of his MIT appointment, he was a Fulbright Distinguished Scholar at Oxford University. Main research interests: lattice theory, the theory of ordered sets, and discrete mathematics.

2002-2005 Scholars

Jonathan Farley promotes a course on logic and discrete mathematics

Jonathan Farley is Associate Professor of Mathematics at Morgan State University. At the time of his MIT appointment, he was a Fulbright Distinguished Scholar at Oxford University, one of four Americans to win the award in 2002.  His main research interests are lattice theory, the theory of ordered sets, and discrete mathematics. 

Dr. Farley holds an A.B. summa cum laude (1991) and a PhD (1995) in Mathematics from Harvard University (his undergraduate thesis advisor was Prof. Garrett Birkhoff). Dr. Farley won a Marshall Scholarship to study at Oxford University. In 1994, Dr. Farley was awarded Oxford's highest mathematics awards, the Senior Mathematical Prize and the Johnson Prize, for his research, and received his doctorate (D.Phil. - Mathematics) a year later.

He began his teaching career in 1996 at Vanderbilt University as Assistant Professor of Applied Mathematics, earning tenure in 2003. After writing an article about Confederate remembrance, however, Dr. Farley received death threats from supporters of the Ku Klux Klan, forcing him to leave Tennessee. Journalist Barrett Brown recounts the ordeal in the Guardian and in his book, Hot, Fat, and Clouded.

Dr. Farley’s main research results in lattice theory and the theory of ordered sets include:

  • 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. 

In addition to his academic work, Dr. Farley has written for The Source, Essence, The Guardian, and Time Magazine On-Line. In 2001, Ebony named Dr. Farley a "Leader of the Future" and Upscale Magazine ran a profile of him. Danica McKellar, star of the hit television show The Wonder Years, wrote about “the incomparable, brilliant Jonathan Farley” in her 2010 New York Times best-selling math book, Hot X: Algebra Exposed. Former British Member of Parliament and member of the prime minister’s cabinet, Tony Benn, mentions Dr. Farley in his memoirs.

Dr. Farley has taught at the University of the West Indies, and has been Visiting Professor of Mathematics at Caltech, Science Fellow at Stanford University’s Center for International Security and Cooperation, Visiting Scholar in the Department of Mathematics at Harvard University, and Visiting Associate Professor of Applied Mathematics at MIT.

As an MLK Scholar, he was hosted by the Department of Mathematics. During his three-year tenure at the Institute, Dr. Farley made many strides in his career. He solved a problem posed by Professor Richard Stanley of MIT in 1981 and a problem dating to 1971 posed by mathematician Richard Rado. The Chronicle of Higher Education and Science News Online profiled Dr. Farley's lattice-theory applications to counterterrorism. Seed Magazine named Dr. Farley one of “15 people who have shaped the global conversation about science in 2005.”

At the height of his visit, the Harvard Foundation honored him with the 2004 Distinguished Scientist of the Year Award, a medal presented on behalf of the president of Harvard University in recognition of “outstanding achievements and contributions in the field of mathematics.” On that day, Mayor Michael Sullivan and the city council officially declared March 19 "Dr. Jonathan David Farley Day" in The City of Cambridge. 





Pure Mathematics

  • 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

  • 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

MIT News: Math whiz fights terror with smarts

Cathryn M. Delude, News Office Correspondent 
April 6, 2005

The man who keeps the hit TV show "Numb3rs" mathematically honest is also using a rarified math theory to correct a flaw in standard counterterrorism thinking. A recent visiting professor of mathematics at MIT and a Hollywood math consultant, Dr. Jonathan D. Farley realized that experts could make potentially grave errors by overestimating their effectiveness at breaking up terrorist cells. "They're asking the wrong question and getting the wrong answer," Farley explains.

It's an easy mistake to make, since most government operatives don't use lattice theory to analyze social networks. Lattice theory, which includes Boolean algebra, is Farley's favorite conceptual realm, and his talent at it has earned him great acclaim. (In 2003, he solved a problem posed by MIT's Richard Stanley in 1981.)

He used to joke that it has no practical purpose whatsoever, but after the Sept. 11 terrorist attacks, Farley wondered if pure math actually could save lives. He remembered the opening line in the movie "A Beautiful Mind" about John Nash: "Mathematicians won the war." And, he remembered Palestinian leader George Habash's words: "Terrorism is a thinking man's game."

Being a thinking man, Farley says, "it's better to fight smarter, not harder," and fighting Al Qaeda with abstract theory could more accurately assess our vulnerability to future attacks than current methods. As a bonus, it could also prevent financial resources from being wasted on phantom fears at the expense of real dangers.

"People often view terrorist cells as a graph, with members as nodes connected to each other if they have a direct communications link," Farley says. "But they're leaving out the most important part, the hierarchy," he says. "Terrorist cells have chains of command (partially ordered sets) from leaders to midlevel operatives to the workers who carry out orders."

As simplified examples, the graph theory would conclude that blocking four intersections along Massachusetts Avenue between Kresge Auditorium and Harvard Square could prevent MIT students from driving to the square. But students could use side streets to bypass the blocked intersections.

Likewise, the graph theory would show that capturing four members of a 15-member terrorist cell arranged as a binary tree gives a 93 percent chance the cell has been disabled. Even without knowing the captives' positions in the hierarchy, it's still possible to plug in the "cut sets" that could break the command chain into a probability formula, and that probability is, unhappily, only 33 percent. "Lattice theory won't tell you how to fight the terrorists, but it might tell you if you've won the battle," Farley says.

Farley's hypothesis, published in late 2003, interests several military researchers, including Rebecca Goolsby of the Office of Naval Research. "With covert missions, there's a lot of missing data, and some of it is wrong," she says. "Jon came up with a new approach and drew up good questions" for approaching these "very muddy" issues in an analytical way.

An associate professor of mathematics at Vanderbilt University, Farley was a Dr. Martin Luther King Jr. Visiting Professor in the MIT Department of Mathematics from January 2003 to December 2004. He is also the co-founder of a mathematical modeling consulting firm. "Our ultimate goal is to develop software so that law enforcement experts without these rigorous mathematical skills can ask--and answer--these same analytical questions about security."