This page explores some ways of finding spiritual values in mathematics, including Vedic Mathematics and a foundational theory based on Vedic Mathematics. ↖

Vedic Mathematics is the mathematics of the ancient Vedic tradition of India. The Vedic tradition is an all-encompassing field of knowledge that is currently being revived through Maharishi Vedic Science. Vedic Mathematics has many definitions and many aspects, ranging from the governing intelligence of the universe to the familiar procedures of practical calculation.

Maharishi’s Absolute Theory of Defence—Sovereignty in Invincibility  •  mumpress.com/government-administration/a14.html  •  A 668-page book by Maharishi Mahesh Yogi, the founder of the Transcendental Meditation program. This book describes how the principles of modern science and Maharishi Vedic Science can be used to create invincibility for any individual and any nation. It contains 90 pages on Maharishi Vedic Mathematics and 33 pages on modern mathematics.  •  In this book, Maharishi describes Vedic Mathematics as the mathematics of the Veda, the mathematics of the governing intelligence of the universe, which calculates instantly, without steps, in a way which is both orderly and evolutionary, on the level of wholeness rather than parts.

Summaries of Published Sources by Maharishi Mahesh Yogi on Mathematics, including modern mathematics and Vedic mathematics  •  PDF file  •  200K  •  Summaries of sections of publications and press conferences in which Maharishi Mahesh Yogi has addressed any subject in modern or Vedic mathematics.  •  Revised 1 February 2012.

Is Consciousness a Number? How Maharishi Vedic Mathematics Resolves Problems in the Foundations and Philosophy of Mathematics  •  PDF file  •  100K  •  How Maharishi Vedic Mathematics resolves problems in the foundations and philosophy of mathematics. Based on my Masters thesis for a degree in Maharishi Vedic Science at Maharishi University of Management.  •  Revised 8 January 2005.

Vedic Mathematics: The Cosmic Software For The Cosmic Computer, Dr. Narinder Puri and Dr. Michael Weinless  •  PDF file  •  100K  •  A paper presented at the National Council of Teachers of Mathematics Annual Conference, Chicago, IL, 1988. Computation using the sūtras of Vedic Mathematics, with examples, and its connection to the development of consciousness, as described by Maharishi Vedic Science.

Vedic Maths India  •  vedicmaths.org  •  One of several sites on the system of calculation known as Vedic Mathematics, or Sūtra-Based Computation. This system is based on 16 sūtras or aphorisms and was first published in 1965 by Swāmī Bhāratī Kṛiṣhṇa Tīrtha, Śhaṅkarāchārya of Govardhan Maṭh, Puri, in the east of India. This system uses sūtras and alternative methods of calculation to do arithmetic and other calculations in a way which is easier, more creative, and more enjoyable.

Sūtras of Vedic Mathematics  •  PDF file  •  100K  •  The 16 sūtras and 16 upasūtras, in Sanskrit and in English translation by Swāmī Bhāratī Kṛiṣhṇa Tīrtha. An alternative system of calculation using these sūtras is outlined in Swāmī Bhāratī’s book Vedic Mathematics. The sūtras can be applied to any branch of mathematics to make it easier and more rewarding. ↖

Numeristics is an alternative, number-based foundational theory for mathematics. Using tools from Vedic Mathematics and other sources, numeristics provides practical, intuitive procedures for developing mathematical structures from a basis in what Vedic Mathematics describes as the absolute number or zero. An extension of numeristics, equinfinitesimal analysis, provides procedures for doing calculus by operating within zero.

Numeristics: A Number-Based Foundational Theory of Mathematics  •  PDF file  •  100K  •  Inspired in part by the recent revival of the Vedic tradition of India, as expressed by Maharishi Mahesh Yogi in his Vedic Mathematics. This paper gives the fundamental ideas of numeristics as they apply to arithmetic and elementary algebra. Numeristics includes an alternative approach to analysis called equinfinitesimal analysis, described in the paper below.  •  Revised 27 February 2011.

Equinfinitesimal Analysis: A Numeristic Approach to Calculus  •  PDF file  •  100K  •  Extends the concepts of numeristics to analysis. It develops a theory of analysis based on infinitesimals which are all exactly equal to zero, and infinite values that are their reciprocals. Concepts derive from Maharishi Mahesh Yogi’s Vedic Mathematics, Charles Musès’s analysis of zero and infinity, and Abraham Robinson’s non-standard analysis. This theory uses multiple levels of sensitivity to evaluate equality and defines derivatives and integrals solely in terms of elementary arithmetic operations.  •  Revised 28 February 2011.

Divergent Series: A Numeristic Approach  •  PDF file  •  200K  •  Infinite divergent series can generate some striking results but have been controversial for centuries. The standard approaches of limits and methods of summation have drawbacks which do not account for the full range of behavior of these series. A simpler approach using numeristics is developed, which better accounts for divergent series and their sums. Numeristics is introduced in a paper above.  •  Revised 7 December 2010. ↖

There is much that is beautiful in mathematics. Here are some forumulas and figures that I particularly like.

Beautiful Arithmetic  •  PDF file  •  100K

Beautiful Algebra  •  PDF file  •  100K

Beautiful Trigonometry  •  PDF file  •  200K  •  I took a particular liking to trigonometry. This document is a fairly comprehensive collection of trigonometric formulas.

Beautiful Calculus  •  PDF file  •  100K ↖

Quotations by Kurt Gödel, recorded by Hao Wang in his biographies of Gödel and by Rudy Rucker in one of his books.

Gensler’s Gödel’s Theorem Simplified: Summary and revisions  •  PDF file  •  200K  •  A summary of Harry Gensler’s book on Gödel’s famous incompleteness theorem. Gödel’s theorem is widely regarded as technically difficult, but Gensler has developed an admirable framework for a simplified approach which still retains the theorem’s essence. Gensler develops a set of forumulas which go about 90% of the way towards proving the theorem. This document hsa a revised set which provide the other 10%. ↖