February 26, 2008

For a layman, mathematics started with the numerals. It is the science of numbers and their operations. We associate mathematics with arithmetic, algebra, geometry, and at advance level to calculus and field of computers. So much so that it is called “Mother of all Sciences”. Mathematics is a thread by which we may know the beyond. It allows us to make some predictions. The eye of mathematics sees deep into the structures of living and nonliving entities. The X-ray machines reveal what is inside our body. There is lot of mathematics that goes in to produce the final images of body. It is said that when mathematics is practiced with great devotion and humility, it involves the transformation of both mind and heart which leads to wisdom.

Minerals, plants, animals and mankind make up our world. The question comes to mind, can we describe material goods and divinity with mathematics? All objects comprise of oxygen, hydrogen, carbon, nitrogen and other elements in proper way and form. In short man is made of matter and energy. Science is developing all the time. Yesterday’s metaphysics is to day’s physics. Some time ago atom was indivisible, today we divide it. Scientists tell us that “nothing can be created from nothing”. In the spiritual field, as is commonly believed, anything can be created by the Supreme will. All that exists can be made to disappear and all that doesn’t exist can be made to appear. Material laws do not apply to divinity. The link between physics and spirituality is found in the depths of mathematics. Just as the mind mediates between body and soul so does mathematics connects physics and metaphysics.

Mathematics is used to explain science phenomenon. Archimedes (250 B.C.) was the greatest scientist and mathematician. He was the first person to explain the law of the lever. . He is supposed to have exclaimed, “Give me a place to stand on and I can move the world”. Similarly Albert Einstein (1905) asserted that the speed of light was the fastest velocity in the universe. He came up with a simple mathematics equation E = m c2 to describe energy in terms of mass and the speed of light. It is termed remarkable because it involves unthinkable element - the speed of light. Speed of light is a big number. A small mass when multiplied by the square of speed of light is equivalent to tremendous amount of energy. According to the present day atomic theory, the atom is the smallest particle of matter. The atom is not a solid particle but consists mostly of empty space. At the centre of atom is the nucleus, which has a positive electrical charge and accounts for more than 99.9 percent mass of the atom. Moving about the nucleus is number of electrons, whose combined electrical charge equals that of the nucleus. The nucleus also consists of other particles namely protons and neutrons. The entire complex structure resembles a miniature solar system. Some time ago atom was thought to be indivisible, today we divided it!

In like manner, 0 and 1 were once simple numerals. Electronic computers now depend on the binary system that comprises of 0’s and 1’s. Every thing we input to or output from computers is binary and therefore explainable in mathematical terms. If we think that universe is governed by the mathematical laws, then we can explain every single phenomenon with some mathematical operations. And the life we live in is the sum total of many such complex mathematical operations. A flower seed that produces petals with six-fold symmetry is in essence a form of life that can be explained with the rules of mathematical operations. If we can build numerous astronomical computers to detect the changes in our universe, we would perhaps be able to establish mysterious links between mathematics and universe. Mathematics is integral to the science of the physical world. When mathematics and science are linked together, they allow us to understand the universe. If we have a question about the universe we may use science and mathematics to find the answer.

There are at least 3000 categories in which mathematics is classified today. This ocean of knowledge is expanding. A good library is said to have about 100,000 mathematics books. And a skilled mathematician (PhD) may know only 10% Math or less. Mathematics has expanded on its own. Algebra came from arithmetic. Geometry utilized arithmetic and algebra. Calculus originated from geometry, arithmetic and algebra. And now we have Topology evolving from geometry and algebra. Every thing that was once mathematics remains mathematics. Knowledge always adds never subtracts

Mathematical thinking starts with review or preview of known mathematics. The actual work in mathematics has an entry phase that begins when we introduce the problem. The problem solving is tackling the problem either by conjecturing or justifying the solution. Finally the review phase reflects upon the achievements and possible extensions.

Are there any questions that science can not answer? Supernatural or divine phenomena are still beyond the human grasp? Some people might think that such things do not exist in reality. The answer lies in realizing the whole universe. There are perhaps areas of nature for which existing models are in the infant stages and therefore we lack full explanations. Science is divided into different branches of disciplines such as physics, chemistry and biochemistry. Physics studies fundamental particles. Chemistry provides insight into elements, molecules and their interactions. The biochemistry gives information on the chemicals involved in the life processes such as DNA, proteins, and enzymes. The biology expands this information on larger structures such as organs in living bodies. Same way zoology relates with the animals while botany deals with the plants. Continuing on we observe that geochemistry is concerned with the elemental structure of rocks and minerals, while geology studies large scale interactions of mineral structures which sometimes result in earthquakes and volcanoes. It means that all objects whether they are minerals, plants, animals, or mankind are related. They all evolve and dissipate in cycles of life and death.

Mineral can be written as

Only

If we describe man with symbol

m m + x m + x + y m + x + y + z

Self awareness can disappear while consciousness continues. Consciousness can disappear while life continues. And life can disappear leaving inanimate body which results into mineral. Thus z = self awareness, y = consciousness, and x = life. Man from a biologist standpoint is flesh and blood, brain and bones, living matter-atoms such as oxygen, hydrogen, carbon and others in a proper way and form. In summary, Man is composed of nearly three- fourth parts of water and other matter which can produce turbulent energy. When man lives he wants to influence his presence in universe created by God.

Just as

Bulb + Power → Light,

So is

Body + Mind → Life

The bulb without power has no purpose; the body without mind is like corpse. The mind is the power in the body. What we do is being determined by our mind. We are nurturing our mind constantly with resources available to power the body.

Master mathematician Prof. V. Kannan [3] of Hyderabad Central University relates math axioms with the faith. He cites mathematics has axioms, which we have to assume to deduce the theorems. Similarly, life becomes more orderly when we accept the axioms of tradition. It is the axioms of tradition that make us a distinct person. Faith is link between man and God.

Professor David Perkins [4], a professor at Harvard University uses the term “Person Plus” to determine that the formal and informal education and training that a person receives, creates a Person Plus. “A teacher in our formal educational system plays a major role in the education of a Person plus” -describes Perkins.

Ramanujan [5], one of the best number theorists who ever lived described math as an art form. He was intensely religious. He often united mathematics and spirituality together. Ramanujan represented zero with the Absolute Reality and infinity with many manifestations of that Reality. Ramanujan felt that each mathematical equation takes us a step closer to understanding the spiritual universe. He once told a friend, “An equation for me has no meaning unless it expresses a thought of God”.

Man created numbers with the divine wisdom. Each number has a destiny or vibration. How we perceive these numbers is matter of faith. Faith is the man’s link with God.

We live in a complex world. The mind has to absorb so much information in so short time. The meditation can stabilize mind before the body gives in. When we meditate we give ourselves up to God so He will guide us. The mind’s neutral zero is to be maintained with such equations as 10-10 = 0, 100-100 = 0. The positive and negative elements responsible for developing mind and body must maintain equilibrium. In this respect Ronald Glasberg [2] has interpreted the complex relationship exhibited by Euler’s equation (also called the equation of spirituality), which provides a simple connection with the divine consciousness. In Euler’s equation the numbers e and are transcendental with infinite decimals while = i is a pure imaginary and yet the exponential growth, (negative unity), so that -1 + 1 = 0 maintains equilibrium or balance in world in harmonious way. Here number 1 stands for the unity of divine consciousness while -1 is negative unity resulting from incomprehensible growth, together they maintain balance. In summary the numbers e,, i, 1, and 0 are important to understanding the meaning of spirituality.

Although science is concerned with the phenomena that we can measure, see and prove, we can not conceive spirituality the same way. The science of spirituality is not a

How are our heart and brains connected with God? We might think that human brain connects human body with God. It is well known that heart begins to beat in the unborn fetes before the brain is formed. Experiments of 20th century indicate that the subatomic electrons are able to communicate with each other regardless of distance between them. The implication is that our heart is connected with its Creator. Some scientists are still closed minded to anything that deals with spirituality, but things are changing at rapid pace. The Quantum physicists are realizing that there are higher realities within infinite dimensions of intelligent vibration energy. Mental illnesses which are attributed to stress and erroneous thoughts are being treated by alternative spiritual methods.

Is the universe, finite or infinite? If the universe were finite we can go on and beyond its boundaries. But, have we seen any boundaries? If the universe were infinite then it would mean that it is limitless and we will see it all only through the eyes of God. We can illustrate this with the solution of the equation:

Can we ever know what the solution is like for infinite value of C?

Understanding God is like immersing oneself into a vector space consisting of polynomials with infinite basis

Our development of science is based on physical observations and therefore its growth is limited. Anything that is not immediately verifiable is eliminated. We are therefore unable to discover the reality underlying the creation which is complex phenomena in nature. The Vedic

In the 1960s scientists and economists warned us about the global food shortages because there isn’t sufficient land to feed a growing population. No one thought at that time of growing food without land. Every field rises and expands horizontally until it saturates the plane, then it is ready for a vertical take off.

Some simple mathematical concepts lead to generalizations as is evident in the study of algebra and geometry. Real number system is generalized to include complex numbers and the Euclidean geometry into non-Euclidean geometries. Such generalizations are observed in spiritual field when for example the love for neighbours is extended to love for all. Professor Sharon K. Robbert [6] has compiled several devotionals connected to the mathematical content through a series of website articles in frame work of Christianity and Mathematics, which in fact is connecting mathematics with spirituality in the larger context. For example the span of vector space with basis

Mathematics can describe with some proximity the many stages of development in nature, as for example, how a tropical storm turns to a hurricane. Group of thunderstorms with winds near 23-39 mph originate a depression. When the winds gear up in the range of 39-73 mph, the depression becomes a tropical storm. A tropical storm then becomes a hurricane, if the same winds gain further momentum and exceed 74 mph. We can like wise look at the human life cycle from the conception to birth and perhaps to death. The fetes starts pounding its heart in the fifth week or so when connection is made with the God, and then the brain starts to develop, the baby is born which turns to a more complex machine the world has seen. It can walk, run, climb, see, hear, smell, taste and feel, and do millions of jobs at the same time! Can mathematics or science fully explain the continuous turn of events in which each turning is perhaps one of the infinite feasible choices? To understand the destiny of our life the mathematics and science would have to connect with the science of spirituality. The ultimate reality can be summed up in the following statements: Out of dust and water we grow and to dust and water we return. Or as they say, the life grows with time and ultimately ends to be born. The meaning of life for us therefore is that we understand the life cycle. Mathematics and science are instruments for understanding universe.

Seed Plant Flower

Winds 23-39 mph Winds 39-73 mph Winds > 74 mph

Conception 10 Weeks Term Complex Human

According to Robert Ellwood [1], we are the product of three Human Eras: The Hunting Era we call the stone- age, or tribal, Agriculture Era that preceded writing, and the Writing Era which introduced actual writings of scriptures. The future of communication now lies in the electronics or paperless age.

The changes of consciousness will take place by communicating with others silently. When we communicate with others silently, we begin to think more and more without words. This will contribute to the understanding of the self, the other, and the cosmos or universe, we are part of.

A human being is a part of a whole called by us

Mathematics plays important role in realizing the science of the physical world. When mathematics and science are linked together, they allow us to understand the universe. In the present time, however, there is a gap between the infinitesimal knowledge of science experiments and the spiritual knowledge of infinite. While some aspects of spirituality can be explained with the present knowledge of mathematics and science, it is difficult to conceive the higher realities within the infinite dimensions of intelligent vibration energy. To understand the destiny of our life the mathematics and science would have to connect with the science of spirituality in more depth.

1. Ellwood, Robert, Next Stages in Human Spiritual Evolution Part 1, from http://www.theosophical.org/theosophy/questmagaine/marapr2001/ellwood/index.html

2. Glasberg, Ronald, Mathematics And Spirituality Interpretation: A Bridge to Genuine Interdisciplinarity, Zygon, vol. 38, no. 2 , (June 2003)

3. Kannan, V., The Hindu, Online Edition of India’s National paper, April 7, 2003

4. Perkins, David, Mind and Body Tools, fromhttp://www.uoregon.edu/~moursund/Math/mind_body_tools.htm

5. Ramanujan, Srinivasa, web citation (biography), fromhttp://www.usna.edu/Users/Math/meh/ramanujan.html

6. Robbert, Sharon K, Christianity and Mathematics Devotional connected to mathematical content, from http://www.trnty.edu/faculty/robbert/SRobbertWebFolder/ChristianityMath/

Mathematics | |||

Tools | Spirituality | ||

Science | |||

(From Infinitesimal Science Experiments to the Spiritual Knowledge of the Infinite)

Spirituality is concerned with matters of the spirit. It is aimed at developing an integral man with deep awareness of his values. Men are like empty jars. Through prayer and chants we fill ourselves with beatitude. Pouring out our disinterested service over society, we empty ourselves so that the divine may fill us again. Filling and emptying ourselves is the process that leads to enlightenment. Spirituality is Life!Mathematics is used to explain science phenomenon. Archimedes (250 B.C.) was the greatest scientist and mathematician. He was the first person to explain the law of the lever. . He is supposed to have exclaimed, “Give me a place to stand on and I can move the world”. Similarly Albert Einstein (1905) asserted that the speed of light was the fastest velocity in the universe. He came up with a simple mathematics equation E = m c2 to describe energy in terms of mass and the speed of light. It is termed remarkable because it involves unthinkable element - the speed of light. Speed of light is a big number. A small mass when multiplied by the square of speed of light is equivalent to tremendous amount of energy. According to the present day atomic theory, the atom is the smallest particle of matter. The atom is not a solid particle but consists mostly of empty space. At the centre of atom is the nucleus, which has a positive electrical charge and accounts for more than 99.9 percent mass of the atom. Moving about the nucleus is number of electrons, whose combined electrical charge equals that of the nucleus. The nucleus also consists of other particles namely protons and neutrons. The entire complex structure resembles a miniature solar system. Some time ago atom was thought to be indivisible, today we divided it!

In like manner, 0 and 1 were once simple numerals. Electronic computers now depend on the binary system that comprises of 0’s and 1’s. Every thing we input to or output from computers is binary and therefore explainable in mathematical terms. If we think that universe is governed by the mathematical laws, then we can explain every single phenomenon with some mathematical operations. And the life we live in is the sum total of many such complex mathematical operations. A flower seed that produces petals with six-fold symmetry is in essence a form of life that can be explained with the rules of mathematical operations. If we can build numerous astronomical computers to detect the changes in our universe, we would perhaps be able to establish mysterious links between mathematics and universe. Mathematics is integral to the science of the physical world. When mathematics and science are linked together, they allow us to understand the universe. If we have a question about the universe we may use science and mathematics to find the answer.

There are at least 3000 categories in which mathematics is classified today. This ocean of knowledge is expanding. A good library is said to have about 100,000 mathematics books. And a skilled mathematician (PhD) may know only 10% Math or less. Mathematics has expanded on its own. Algebra came from arithmetic. Geometry utilized arithmetic and algebra. Calculus originated from geometry, arithmetic and algebra. And now we have Topology evolving from geometry and algebra. Every thing that was once mathematics remains mathematics. Knowledge always adds never subtracts

Mathematical thinking starts with review or preview of known mathematics. The actual work in mathematics has an entry phase that begins when we introduce the problem. The problem solving is tackling the problem either by conjecturing or justifying the solution. Finally the review phase reflects upon the achievements and possible extensions.

Are there any questions that science can not answer? Supernatural or divine phenomena are still beyond the human grasp? Some people might think that such things do not exist in reality. The answer lies in realizing the whole universe. There are perhaps areas of nature for which existing models are in the infant stages and therefore we lack full explanations. Science is divided into different branches of disciplines such as physics, chemistry and biochemistry. Physics studies fundamental particles. Chemistry provides insight into elements, molecules and their interactions. The biochemistry gives information on the chemicals involved in the life processes such as DNA, proteins, and enzymes. The biology expands this information on larger structures such as organs in living bodies. Same way zoology relates with the animals while botany deals with the plants. Continuing on we observe that geochemistry is concerned with the elemental structure of rocks and minerals, while geology studies large scale interactions of mineral structures which sometimes result in earthquakes and volcanoes. It means that all objects whether they are minerals, plants, animals, or mankind are related. They all evolve and dissipate in cycles of life and death.

**Four Great Levels of Being**Mineral can be written as

Mineral can be written as | m |

Plant can be written as | m + x |

Animal can be written as | m + x + y |

Man can be written as | m + x + y + z |

**m**is visible;**x, y, z**, are invisible, and they are extremely difficult to grasp.If we describe man with symbol

**M**, thenAnimal can be written as | M – z |

Plant can be written as | M – z – y |

Mineral can be written as | M – z – y – x |

m m + x m + x + y m + x + y + z

Self awareness can disappear while consciousness continues. Consciousness can disappear while life continues. And life can disappear leaving inanimate body which results into mineral. Thus z = self awareness, y = consciousness, and x = life. Man from a biologist standpoint is flesh and blood, brain and bones, living matter-atoms such as oxygen, hydrogen, carbon and others in a proper way and form. In summary, Man is composed of nearly three- fourth parts of water and other matter which can produce turbulent energy. When man lives he wants to influence his presence in universe created by God.

Just as

Bulb + Power → Light,

So is

Body + Mind → Life

The bulb without power has no purpose; the body without mind is like corpse. The mind is the power in the body. What we do is being determined by our mind. We are nurturing our mind constantly with resources available to power the body.

Master mathematician Prof. V. Kannan [3] of Hyderabad Central University relates math axioms with the faith. He cites mathematics has axioms, which we have to assume to deduce the theorems. Similarly, life becomes more orderly when we accept the axioms of tradition. It is the axioms of tradition that make us a distinct person. Faith is link between man and God.

Professor David Perkins [4], a professor at Harvard University uses the term “Person Plus” to determine that the formal and informal education and training that a person receives, creates a Person Plus. “A teacher in our formal educational system plays a major role in the education of a Person plus” -describes Perkins.

**(Mind + Body) + Education = Person Plus**Ramanujan [5], one of the best number theorists who ever lived described math as an art form. He was intensely religious. He often united mathematics and spirituality together. Ramanujan represented zero with the Absolute Reality and infinity with many manifestations of that Reality. Ramanujan felt that each mathematical equation takes us a step closer to understanding the spiritual universe. He once told a friend, “An equation for me has no meaning unless it expresses a thought of God”.

Man created numbers with the divine wisdom. Each number has a destiny or vibration. How we perceive these numbers is matter of faith. Faith is the man’s link with God.

God | ||||||||||||||||||||

704 | = | GOD, G=7th, D= 4th Letter | ||||||||||||||||||

320 | 384 | while 0 is letter o | ||||||||||||||||||

144 | 176 | 208 | 7 + 0 + 4 = 11 | |||||||||||||||||

64 | 80 | 96 | 112 | |||||||||||||||||

28 | 36 | 44 | 52 | 60 | ||||||||||||||||

12 | 16 | 20 | 24 | 24 | 28 | 32 | ||||||||||||||

5 | 7 | 9 | 11 | 13 | 15 | 17 | Sums of consecutive numbers | |||||||||||||

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Natural Numbers | ||||||||||||

Although science is concerned with the phenomena that we can measure, see and prove, we can not conceive spirituality the same way. The science of spirituality is not a

*normal*science. God is seen as infinite, powerful, perfect and beyond growth. It might appear that we are beginning to control the evolution with our scientific and mathematical progress.How are our heart and brains connected with God? We might think that human brain connects human body with God. It is well known that heart begins to beat in the unborn fetes before the brain is formed. Experiments of 20th century indicate that the subatomic electrons are able to communicate with each other regardless of distance between them. The implication is that our heart is connected with its Creator. Some scientists are still closed minded to anything that deals with spirituality, but things are changing at rapid pace. The Quantum physicists are realizing that there are higher realities within infinite dimensions of intelligent vibration energy. Mental illnesses which are attributed to stress and erroneous thoughts are being treated by alternative spiritual methods.

Is the universe, finite or infinite? If the universe were finite we can go on and beyond its boundaries. But, have we seen any boundaries? If the universe were infinite then it would mean that it is limitless and we will see it all only through the eyes of God. We can illustrate this with the solution of the equation:

**= C**is a finite number**X = C1/C**if C is assumed finite. For example**= 2**, then**X2 = 2**or**X = 21/2**is finite.Can we ever know what the solution is like for infinite value of C?

Understanding God is like immersing oneself into a vector space consisting of polynomials with infinite basis

**1, x, x2, x3,….xn,**…God is an infinite- dimensional being. We can only see Him partially in the lower dimensional planes. His true appearance will remain hidden from us.Our development of science is based on physical observations and therefore its growth is limited. Anything that is not immediately verifiable is eliminated. We are therefore unable to discover the reality underlying the creation which is complex phenomena in nature. The Vedic

*rishis*have considered that the mind, life and matter have evolved from higher levels of consciousness. In the present time, there is a gap between the infinitesimal knowledge of science experiments and the spiritual knowledge of infinite. Discoveries come by intuition from a higher plane of consciousness when the mind is open to new ideas or when the present knowledge is saturated.In the 1960s scientists and economists warned us about the global food shortages because there isn’t sufficient land to feed a growing population. No one thought at that time of growing food without land. Every field rises and expands horizontally until it saturates the plane, then it is ready for a vertical take off.

Some simple mathematical concepts lead to generalizations as is evident in the study of algebra and geometry. Real number system is generalized to include complex numbers and the Euclidean geometry into non-Euclidean geometries. Such generalizations are observed in spiritual field when for example the love for neighbours is extended to love for all. Professor Sharon K. Robbert [6] has compiled several devotionals connected to the mathematical content through a series of website articles in frame work of Christianity and Mathematics, which in fact is connecting mathematics with spirituality in the larger context. For example the span of vector space with basis

**i, j,**or a**i**+ b**j**+ .., is example of the Span of God’s love. And just as a matrix transformation can convert a distorted object into a perfect image, the Holy Spirit produces in mankind a transformation from guilty to innocence. There are spiritual marks that indicate ones loyalty to God or to Satan - in mathematics the value of determinant is critical for the existence of solution which may be either determinate or indeterminate.Mathematics can describe with some proximity the many stages of development in nature, as for example, how a tropical storm turns to a hurricane. Group of thunderstorms with winds near 23-39 mph originate a depression. When the winds gear up in the range of 39-73 mph, the depression becomes a tropical storm. A tropical storm then becomes a hurricane, if the same winds gain further momentum and exceed 74 mph. We can like wise look at the human life cycle from the conception to birth and perhaps to death. The fetes starts pounding its heart in the fifth week or so when connection is made with the God, and then the brain starts to develop, the baby is born which turns to a more complex machine the world has seen. It can walk, run, climb, see, hear, smell, taste and feel, and do millions of jobs at the same time! Can mathematics or science fully explain the continuous turn of events in which each turning is perhaps one of the infinite feasible choices? To understand the destiny of our life the mathematics and science would have to connect with the science of spirituality. The ultimate reality can be summed up in the following statements: Out of dust and water we grow and to dust and water we return. Or as they say, the life grows with time and ultimately ends to be born. The meaning of life for us therefore is that we understand the life cycle. Mathematics and science are instruments for understanding universe.

**Stages of Development****Seed to Flower**Seed Plant Flower

**Tropical Storm**Winds 23-39 mph Winds 39-73 mph Winds > 74 mph

**Human Life Cycle**Conception 10 Weeks Term Complex Human

According to Robert Ellwood [1], we are the product of three Human Eras: The Hunting Era we call the stone- age, or tribal, Agriculture Era that preceded writing, and the Writing Era which introduced actual writings of scriptures. The future of communication now lies in the electronics or paperless age.

**Human Eras: Stone Age****-> Agriculture Era****-> Writing Era****-> Electronics**The changes of consciousness will take place by communicating with others silently. When we communicate with others silently, we begin to think more and more without words. This will contribute to the understanding of the self, the other, and the cosmos or universe, we are part of.

A human being is a part of a whole called by us

**universe**, a part limited in time and space-Einstein, Albert.**Conclusion:**Mathematics plays important role in realizing the science of the physical world. When mathematics and science are linked together, they allow us to understand the universe. In the present time, however, there is a gap between the infinitesimal knowledge of science experiments and the spiritual knowledge of infinite. While some aspects of spirituality can be explained with the present knowledge of mathematics and science, it is difficult to conceive the higher realities within the infinite dimensions of intelligent vibration energy. To understand the destiny of our life the mathematics and science would have to connect with the science of spirituality in more depth.

**References**1. Ellwood, Robert, Next Stages in Human Spiritual Evolution Part 1, from http://www.theosophical.org/theosophy/questmagaine/marapr2001/ellwood/index.html

2. Glasberg, Ronald, Mathematics And Spirituality Interpretation: A Bridge to Genuine Interdisciplinarity, Zygon, vol. 38, no. 2 , (June 2003)

3. Kannan, V., The Hindu, Online Edition of India’s National paper, April 7, 2003

4. Perkins, David, Mind and Body Tools, fromhttp://www.uoregon.edu/~moursund/Math/mind_body_tools.htm

5. Ramanujan, Srinivasa, web citation (biography), fromhttp://www.usna.edu/Users/Math/meh/ramanujan.html

6. Robbert, Sharon K, Christianity and Mathematics Devotional connected to mathematical content, from http://www.trnty.edu/faculty/robbert/SRobbertWebFolder/ChristianityMath/

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