Natural Science

Mathematics and the Mind of God

By: Dr. Deborah Arangno

“The invisible things of Him, from the creation of the world, are clearly seen, being understood by the things that are made”
(Romans 1:20)

Mathematics surrounds us.  And the mathematical reality of the universe permits us – through our reason and intellect – to discover the work of creation and the Creator Himself.

Crystal structure is mesmerizingly mathematical in design.  Crystallography can be best studied using the mathematical theory of algebraic geometry, all crystals belonging to one of 230 known spatial symmetry groups, referred to as Federov Groups (see E.S. Federov, “The Symmetry & Structure of Crystals.  Fundamental Works”, Moscow, 1949).  This includes the mind-boggling fractal patterned symmetry of snowflakes.

The patterns of conic sections – circles, ellipses, parabolas – appear frequently in Nature.  Ellipses govern the motion of planetary orbits, tree rings are perfectly circular, parabolas underly the design of the Human eye in focusing light and making sight possible (inspiring us to design lenses and satellite dishes according to the same mathematical principle), as well as describe the trajectory of projectiles in free fall.

Among a vast number of examples, we discover trigonometric functions in sinusoidal systems which are harmonic such as sound or light.  The sine function perfectly models all wave motion, and all oscillating or periodic systems, from the behavior of a spring to the motion of a pendulum, as well as vibrational or rotational systems, and the phenomenon of harmonic resonance.

Myriad other regular geometric shapes abound in Nature.  Honeycombs are perfectly hexagonal; surface soil erosion causes perfectly tessellated rectangles; the refraction of light into rainbows follows the perfect arc of a circle; and the cycloid, or brachistochrone, provides the path along which an object under the influence of gravity travels fastest between two points.

There exist countless examples of spheres and other 3-dimensional geometric structures in Nature – fruit, seeds, planets, rocks.

Moreover, the patterns and rhythms of Creation obey mathematical laws in their frequency and regularity, from the night/day cycle of the Sun, to the seasonal changes of the year, and all biological functions of the human body – including everything from gestation, to the circadian rhythms, and the cycle of cell generation and destruction.

Familiar to many is the Fibonacci sequence, discovered by Leonardo di Pisa (aka Fibonacci).  This sequence can be generated after the initial terms of zero and 1, by taking the sum of the previous two terms to generate each successive term: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…

We see the Fibonacci numbers in the structure of the Nautilus shell, the arrangement of seeds in the head of the sunflower, and the electron patterns in the structure of the nucleus of the atom. The Fibonacci sequence corresponds to the pinnation of ferns and the spiral arrangement of leaves around a plant’s stem, which as Fred Willson observes is “a pattern which assures that each leaf will receive its maximum exposure to sunlight and air without shading or crowding other leaves” 1.

He further points out that “not only do we discover this pattern in leaf arrangements, but it is also commonly found in the arrangement of many flower petals. Examples: a lily has 3 petals, yellow violet 5, delphinium 8, mayweed 13, aster 21, pyrethrum 34, helenium 55, and michaelmas daisy 89. With such a great variety of spiral ratios in leaf and petal arrangement, no one has any reason to get bored with God's creation.” 2.

Moreover, the ratio of each successive pair of terms in the Fibonacci sequence produces a sequence of proportions 3/2, 5/3, 8/5, 13/8, 21/13,…  each of which yields a quotient approaching the “golden ratio” phi = 1.61818…  This golden ratio is observed in countless examples in Nature in a wide range of structures – from the design of DNA, to the symmetries of pinecones and plants, and even the shape of spiral galaxies such as our own Milky Way. An excellent visualization of this pattern is given in the video “Nature by the Numbers” 3.

The golden ratio is crucial to all the best human works of art and engineering, from the Pantheon and the Taj Mahal, and the Great Pyramids, to the masterpieces of da Vinci and Vermeer, to the music of Beethoven, Bach, and Chopin.

Truly these examples – all around us – illustrate that the Universe was created by a Mathematical Genius, indeed a loving and poetic Creator.


  1. Fred Willson, “Shapes, Numbers, Patterns, and the Divine Proportion in God’s Creation”
    Institute for Creation Research, December 1, 2002
  2. Ibid

Dr. Deborah Arangno has a Ph.D. in Pure Mathematics and Graph Theory from Utah State University. Her research interests include Graph Theory, Mathematics, and Philosophy. She is currently an Associate Professor at Holy Cross College at Notre Dame where she holds the Father David Tyson Endowed Chair of Natural and Quantitative Sciences, and is the Director of Mathematics and Computer Science.


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