## Richard Weller

- Adjunct Assistant Professor of Mathematics and Physics

- AB (Mathematics) Amherst College
- MS (Physics) Maharishi International University
- PhD (Physics) Maharishi University of Management

- Adjunct Assistant Professor of Mathematics and Physics

- AB (Mathematics) Amherst College
- MS (Physics) Maharishi International University
- PhD (Physics) Maharishi University of Management

- Assoc. Prof. of Computer Science and Mathematics
- Paul Corazza has taught at the Maharishi University of Management for twelve years

BA (Philosophy) Maharishi International University, Fairfield, Iowa

PhD (Mathematics) Auburn University

Postdoc (Mathematics) University of Wisconsin, Madison

**Education**

- Postdoc, Mathematics, University of Wisconsin, Madison
- PhD, Mathematics, Auburn
- BA, Philosophy, MIU

**Research papers**

Research in Maharishi Vedic Science, Mathematics, and Computer Science

Published Research in the Mathematics of Infinity (Set Theory)

**Current research interests**

**The Wholeness Axiom and Foundations of Mathematics**. Dr. Corazza has published 15 journal articles concerning large cardinals and the attempt to provide a mathematical foundation for them. Large cardinals are extremely large infinite sets that sometimes arise in mathematical practice. Yet, the standard mathematical foundation cannot account for them — large cardinals are in principle underivable from the ZFC axioms. Corazza’s research begins from the observation that the assertion “there exists an infinite set” is an assertion about the existence of something “local” in the universe. He observes that a proper understanding of the mathematical infinite requires a deeper, “global” expression for the existence of the infinite. Lawvere in 1969 formulated such a global statement, showing that the existence of a certain type of functor j: V -> V is equivalent to the existence of an infinite set (where V is the universe of mathematics). Blass later showed that a somewhat stronger functor of the same type is equivalent to the existence of a measurable cardinal (one of the better known large cardinals). Corazza’s work then extends the properties of these functors to the fullest possible extent. His Wholeness Axiom asserts the existence of an elementary embedding j: V -> V with the additional property (essentially) that the restriction of j to any set is itself a set. ZFC+Wholeness Axiom is sufficient to derive all large cardinals. Inspiration for the Wholeness Axiom derives from Maharishi’s Vedic Science in which it is seen that all expressions in the universe arise from the self-interacting dynamics of wholeness, the field of consciousness itself. In a similar fashion, it can be shown that all sets in the universe are the expression of the dynamics of j: V->V, the wholeness embedding. Moreover, as in Maharishi discusses in his commentary on the Ved, individual expressions arise in the “collapse” of an unbounded value to its point value, and subsequent expansion from point to infinity. In the case of the Wholeness Axiom this is seen by the fact that j has a critical point — a first point moved — and this point gives rise to a compact expression (analogous to the Ved itself) from which all particular sets are seen to emerge.**Self-referral Foundation of Computation**. In Maharishi’s Vedic Science, it is observed that all dynamics in the universe are the expression of self-referral dynamics of the pure field of existence. Nature’s computation is exact and without mistake because it is based on the dynamics of wholeness itself interacting with itself. Mathematically, in a parallel fashion, it can be shown that all computation can be proven to be represented in a recursive algorithm, and all recursive algorithms f are known to have a purely self-referral “definition” in the form F(f) = f, where F is a recursive operator from S to S, where S is the set of all partial functions from N to N. Moreover, these self-referral dynamics are given expression in the untyped lambda-calculus. In the lambda calculus, it can be shown that every term F has a fixed point f — i.e. a term for which Ff=f. Using this fact and the representability of arithmetic in the lambda calculus, one shows that this fixed point point property of terms in fact lies at the basis for all recursion in mathematics and computer science, and therefore at the basis of all computation. Dr. Corazza is in the process of writing a book for a general readership on these topics, and discusses these points in his course on Algorithms.**Design of Rules Engines**. During seven of Dr. Corazza’s years in the software development industry, his work was centered around devleoping a good design for mid-scale rules engines. It has been recognized in recent years that a significant business asset for many modern companies is their business rules. In legacy systems, rules underlying business processes are handled in software implementation simply as if…then statements sprinkled through millions of lines of code. The need to represent rules in an external repository and in a language that lends itself to modification by the nonprogrammer have led to the emergence in recent years of rules languages. Dr. Corazza developed one such language in a recent project for an insurance company, and has more recently upgraded his approach by making use of the Java-certified Jess language. Dr. Corazza teaches a seminar on the Jess language and good rules engine design principles.

**Work experience**

Dr. Corazza has worked as a contractor for Google and e-Trade in Silicon Valley, and at several insurance companies in the United States, with 15 years experience as a Java engineer. Some projects in these roles include:

- Development of a framework for a large-scale, high-volume website to support localization (e-Trade)
- Development of custom tools for managing large-scale localization projects involving 40+ languages, 100+ products, and hundreds of translators and project managers (Google)
- Development of a highly flexible custom rules engine, including a rules language, to support rules management for an enterprise-level customer-service application in the insurance industry (Mutual of Omaha)

**Research**

Fifteen published papers in mathematical logic. One three-part article on a Java framework he created. One textbook on Mathematical Logic and Computability.

- Assistant Professor of Mathematics
- Debra Levitsky has taught at the Maharishi University of Management for seven years

BS, MS, Maharishi International University

PhD, Maharishi University of Management

- Professor of Mathematics
- Dean of Faculty
- Catherine Gorini has taught at the Maharishi University of Management for thirty-five years

AB (Mathematics) Cornell University

MS, PhD (Mathematics) University of Virginia

Catherine Gorini received an Award for Outstanding College Teaching from the Mathematical Association of America in 2001. She has also published many articles on mathematics, especially geometry.

- Maharishi’s Vedic Mathematics
- Using the Transcendental Meditation® technique in the teaching of Mathematics
- Geometry and Symmetry
- Undergraduate Mathematics Education
- Using Geometer’s Sketchpad to study Euclidean Geometry or Analytic Geometry
- Use JavaSketchpad to Create Interactive Geometry Web Pages

- Award for Outstanding College Teaching, Mathematical Association of America, 2001
- Enlightened Educator Award, Maharishi University of Management, 2000

*Facts on File Geometry Handbook*, Facts on File, 2003. Read a review

Geometry at Work, Mathematical Association of America, 2000.

“Maharishi’s Vedic Mathematics: The Fulfillment of Modern Mathematics,” to appear in Samskrita Sangha, 2003.

“Further Steps: Geometry Beyond High School (PDF),” New England Mathematics Journal, May 2003.

“Consciousness: The Last Frontier of Geometry (PDF),” to appear.

*The Natural Role of Mathematics in the Sciences: How Maharishi’s Vedic Science Answers the Question of the Unreasonable Effectiveness of Mathematics in the Sciences,* Modern Science and Vedic Science

*Symmetry: A Link between Mathematics and Life,* Humanistic Mathematics Network Journal.

*Calculus with Dynamic Geometry,* in *Dynamical Geometry*, edited by James King and Doris Schattschneider, 1997

*Using Clock Arithmetic to Send Secret Messages,* Mathematics Teacher, Mathematical Association of America, February, 1996

*An Art Research Project for a Geometry Course,* PRIMUS, Volume 3, Number 4, December 1994

*Where Can a Robot Arm Reach?*, with R. Dettmers, I. Doraiswamy, and C. Toy, COMAP, 1993

*An Integrated Program of Writing and Speaking in the Undergraduate Mathematics Curriculum,* PRIMUS, Volume 1, Number 3, September, 1991.

- PhD, University of Virginia, Robert E. Stong, advisor
- MA, University of Virginia, Edwin E. Floyd, advisor
- AB, Cornell University, Mathematics Major

- Chair of the Department of Mathematics
- Associate Professor of Mathematics
- Anne Dow has taught at the Maharishi University of Management for nineteen years

**Statement of Purpose**

I came to Maharishi University of Management, because:

- I found the students here to be happy, alert, focused, receptive, interested in mathematics, and able to understand their courses deeply. They were clearly realizing their full potential.
- Mathematics was understood here in a much wider perspective. Each topic was seen in its place in relation to the rest of mathematics, to society, to all of knowledge, and to myself. Studying and teaching mathematics in this context gave me great upliftment and a feeling of purpose.
- I found the opportunity to create world peace while teaching in an atmosphere that promotes academic excellence.

**Education**

- BA (First Class Honors in Mathematics) University of British Columbia, Canada.
- MA (Mathematics) University of Western Ontario, Canada.
- PhD (Mathematics) University of Queensland, Australia.
- PhD Thesis: Maximum Principles for Some Quasi-linear Degenerate Elliptic-Parabolic Operators of Second Order. PhD Advisor: Rudolf Vyborny.
- Teacher Training Course in Transcendental Meditation® program, Blackheath, Australia.

**Research Interests**

- Relationship between mathematics and Maharishi Vedic Science.
- Maximum principles and other areas in partial differential equations.
- Fourier analysis
- Effect of Maharishi’s Transcendental Meditation program and Consciousness-Based
^{SM}education on mathematical intuition and the doing and learning of mathematics

**Other Positions**

- Mathematical Editor (Consulting): Illuminations Web-site, National Council of Teachers of Mathematics, 2001–2003.
- Senior Researcher: Integrated Energy Services, Fairfield, IA, 1997.
- Lecturer in Mathematics (Assistant Professor) Department of Mathematics, University of Queensland, Brisbane, Australia, 1985 to 1986.
- Lecturer in Mathematics (Assistant Professor): Division of External Studies, University of Queensland, Brisbane, Australia, 1973 to 1986.

**Awards and Honors**

- Michigan Mathematics Competition, Honorable Mention, 1957.
- German Government Book Prize, University of British Columbia, June 1962.
- Maharishi Award, MIU Relief Effort in Armenia and Russia, 24 June 1990.
- Maharishi University of Management Certificate of Distinction for Academic Excellence in Teaching, 25 June 2003.
- Appreciation Award for Teaching given by the Students of Maharishi University of Management, 9 May 2012.

**Publications**

- P. Corazza & A. Dow: (Editors) Consciousness-Based Education, Vol. 5: Mathematics, Parts 1 and 2. Maharishi University of Management Press, 2012
- Kholodnyi, V.A., and J.F. Price. Foreign Exchange Option Symmetry. River Edge, NJ: World Scientific Publishers, 1998. (I served as a mathematical editor.)
- Preparing the student to succeed at calculus. Modern Science and Vedic Science 6(1995), pp. 96–106.
- A unified approach to developing intuition in mathematics. In R.K. Wallace, D.W. Orme-Johnson and M.C. Dillbeck, eds, Scientific research on the Transcendental Meditation and TM-Sidhi program: Collected papers, Vol. 5 (1990), Maharishi International University, Fairfield, Iowa, pp. 3386–3398
- Strong maximum principles for weakly coupled systems of quasi-linear parabolic inequalities. J. Aust. Math. Soc. 19 (1975): 103–120.
- Three-curves theorems for quasi-linear inequalities. Duke Math. J. 41 (1974): 473–482.
- With R. Vyborny. Elementary proof of Peano’s existence theorem. J. Aust. Math. Soc. 15 (1973): 366–372.
- With R. Vyborny. Maximum principles for some quasi-linear second order partial differential equations. Rend. Sem. Mat. Univ. Padova 47 (1972): 331–351.

**Selected Talks**

- “A Mathematics Course for Majors in Sustainable Living at the Level of Intermediate Algebra”, paper given at the MAA Contributed Papers Session “The Mathematics of Sustainability”, Joint Math Meetings, Boston, January 2012.
- A Unifying Principle Describing How Mathematical Knowledge Unfolds. Paper presented to the MAA Session on Philosophy of Mathematics at the Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America, Baltimore, 13 – 18 January 2003. See summary and accompanying chart (PDF).
- Starting a Course with Wholeness. Paper presented at the Annual Mathematics Conference of the Iowa Council of Teachers of Mathematics, Ames, Iowa, 22 February 2002.
- Beginning a Course with Wholeness. Paper presented at the Joint Meetings of the Iowa MAA, ASA, and IMATYC, University of Iowa, Iowa City, Iowa, 6–7 April 2001. [[handout]]
- Surviving the Explosion of Mathematical Knowledge: A Unifying Perspective for Mathematics. Paper presented at the Annual Mathematics Conference of the Iowa Council of Teachers of Mathematics, Des Moines, Iowa, 31 January – 1 February 2001. [[handout]]
- Keeping Mathematics Unified in the 21st Century. Paper presented at Mathematical Challenges of the 21st Century, Special meeting of the American Mathematical Society, Los Angeles, California, 7 –12 August 2000. [[handout]]
- Some Mathematica Animations for Calculus, Paper presented at the Joint Meetings of the Iowa MAA, ASA, and IMATYC, University of Iowa, Iowa City, Iowa, 16–17 April 1999.[[attach notebooks]]
- Unfolding Every Student’s Mathematical Genius through the Consciousness-Based Approach. Invited Speaker at the Conference on Consciousness-Based education: Awakening the Knower: in the series Conferences for Women, Sponsored by the Ideal Girls School Planning Committee, Livingston Manor, NY, 16–18 August 1996. [[link to CBE]]
- An Intuitive ‘Basis of Belief’ for the Limit Process in Calculus. Paper presented at the Session on Research in Undergraduate Mathematics Education, Joint Mathematics Meetings, Cincinnati, OH, 12 –15 January 1994. [[handout]]
- Preparing the Student to Succeed at Calculus. Conference on the Teaching of Calculus, Harvard University, Cambridge, Massachusetts, 12 –13 June 1992.
- Developing Intuition in Mathematics. Seminar to the Mathematics Department, St. Mary’s University, Halifax, Nova Scotia, Canada, May 1991.
- Effects of Maharishi Mahesh Yogi’s Transcendental Meditation Program on Factors Affecting Success in Mathematics. Joint Meetings of the Iowa Sections of the Mathematical Association of America, the American Statistical Association, and the American Mathematical Association of Two-Year Colleges, Drake University, Des Moines, Iowa, 5–6 April 1991. [[handout]]
- A Unified Approach to Developing Intuition in Mathematics. AMS-MAA Special Session on Research in Undergraduate Mathematics, Joint Meetings of the American Mathematical Society and the Mathematical Association of America, San Francisco, 16–19 January 1991.
- The Role of Intuition in Mathematical Creativity. Invited talk, Yerevan Physics Institute, Yerevan, Armenian S.S.R., February 1990.
- A Unified Approach to Improving Mathematical Intuition. Annual Regional Meeting of the Mathematical Association of America, Iowa Section, Coe College, Cedar Rapids, Iowa, April 1989.
- The Riesz Representation Theorem. A series of 4 talks at the Seminar on Geometric Measure Theory, University of Iowa, Iowa City, Iowa, February/March 1988.
- A Unified Approach to Developing Intuition in Mathematics. Eugene Strens Memorial Conference on Intuitive and Recreational Mathematics and Its History, University of Calgary, Calgary, Canada, July 27 to August 2,1986.
- A Unified Approach to Teaching Mathematics More Effectively. Annual Meeting of the Australian Mathematical Society, University of Western Australia, Perth, Australia, 12 – 15 May 1986.
- A Preliminary Model to Improve Estimation of Prevalence of Malaria. Joint Meeting of the Iowa Section of the Mathematical Association of America, American Statistical Association, and SIAM, Drake University, Des Moines, April 1985.
- Error in Estimating Malaria Prevalence. Statistical Society of Australia, Queensland Branch, University of Queensland, Brisbane, Australia, March 1984.
- The Garki Malaria Project: Improving the Estimate of Prevalence. Department of Biophysics and Physiology, Dalhousie University, Halifax, Canada, May 1983.
- Three-Circles Theorems. Thirteenth Summer Research Institute of the Australian Mathematical Society, University of Queensland, Brisbane, Australia, January 1973.
- Maximum Principles for Quasi-linear Non-hyperbolic Partial Differential Equations. Annual Meeting of the Australian Mathematical Society, University of Newcastle, Newcastle, Australia, May 1972.
- Alexandroff’s Maximum Principle. Tenth Summer Research Institute of the Australian Mathematical Society, University of Tasmania, Hobart, Australia, January 1970.

**Teaching Experience**

- Since 1966 I have taught courses in calculus, linear algebra, abstract algebra, ordinary differential equations, partial differential equations, advanced calculus, real and complex analysis, probability, mathematical statistics, and discrete mathematics at all levels of the undergraduate curriculum.
- From 1973 to 1986 I made a significant contribution to the teaching by correspondence of undergraduate university-level mathematics in the Division of External Studies at the University of Queensland. I wrote complete materials for the independent study of, and taught several times, each of 15 different one-semester subjects.
- I have also taught courses at the graduate level in partial differential equations, mathematical statistics, and real and complex analysis, and have supervised a Master’s thesis on the theory of wavelets.
- I have written syllabi for most of the courses I have taught. At Maharishi University of Management, from 1984 to the present, I developed for my courses Unified Field Charts, main point charts and other materials that relate the mathematical topics taught in class to the rest of mathematics, to the basis of all mathematics in pure intelligence, and to the students themselves