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“God is a mathematician of a very high order, and He used advanced mathematics in constructing the universe.” Nobel Prize winner Paul A.M. Dirac
Mathematical descriptions of reality are fantastically accurate. We have discovered a universal framework, providing insights into the deepest mysteries of reality and Maths lie at its foundations. Every invention, every advancement owes mathematics a debt of gratitude and, in reality, all of science relies on the assumption that we live in a mathematically imbued universe. Its theorems led to the discovery of Einstein’s general theory of relativity. British physicist Sir James Jeans remarked, “The universe appears to have been designed by a pure mathematician. ”[1] Mathematics is the crystallisation of logic with Physics being the application of those mathematics in the real world.
Yet mathematics being so accurate and effective at describing nature presents us with a puzzle. In 1960, the Nobel Prize-winning physicist and mathematician Eugene Wigner, published a paper that stunned the western scientific community. He called it the “Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner realized that the universe does not have to exhibit the mathematical structure that it does and why does mathematics work? He wrote “the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” [2]
Mathematics, though an abstract discipline, reveals a profound alignment with physical reality in ways that show intentional correlation. Why would equations developed to solve abstract problems correspond so precisely to the behaviour of particles, galaxies, and everything in between? This remarkable applicability of mathematics implies a pre-established harmony between the human mind and the universe, as Wigner wrote that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and has no rational explanation"[3]. Albert Einstein echoed this sentiment, “The eternal mystery of the world is its comprehensibility. The fact that it is comprehensible is a miracle.”[4]
Even more astonishing is that a mathematical framework can predict the behaviour or uncover the existence of physical phenomena before they are observed. How is it that a mathematical theorist like Peter Higgs can sit down at his desk and, by pouring over mathematical equations, predict and expect the existence of a fundamental particle?
The ability of mathematics to predict physical phenomena long before their experimental confirmation reveals a profound connection between abstract mind and physical reality. Here are some examples:
- The Discovery of Neptune: Using Newton’s law of gravitation, Urbain Le Verrier and John Couch Adams noticed unexplained deviations in planet Uranus's orbit. Independently, they calculated where an unknown planet, Neptune, should be, leading to its discovery precisely were predicted by German astronomer Johann Galle.[5]
- Electromagnetic Waves: James Clerk Maxwell's equations unified electricity and magnetism, predicting the existence of electromagnetic waves. Heinrich Hertz’s experiments later confirmed these waves, establishing the basis for radio, light, and other wave technologies.[6]
- The Higgs Boson: In 1964, Peter Higgs along with other physicists, developed a theory that a field permeating space (the Higgs field) imparts mass to particles. Nearly five decades later, experiments at CERN's Large Hadron Collider confirmed the Higgs boson.[7]
- The Expansion of the Universe (1922): Alexander Friedmann solved Einstein’s equations to show that the universe might be expanding, a prediction later supported by Edwin Hubble’s observations of redshifts in distant galaxies, proving an expanding universe.[8]
- The Structure of DNA: The mathematical analysis of chemical bonding and symmetry contributed to James Watson and Francis Crick’s double-helix model for DNA, later confirmed through X-ray crystallography.[9]
- Black Holes: Karl Schwarzschild found a solution to Einstein’s equations predicting dense, collapsed regions where not even light could escape, leading to the concept of black holes, later observed indirectly through gravitational waves and X-ray emissions from nearby matter.[10]
- Gravitational Waves: Einstein’s theory predicted ripples in spacetime from massive bodies in motion. In 2015, the LIGO collaboration detected these waves from merging black holes, confirming the prediction.[11]
- The Periodic Table: Dmitri Mendeleev arranged elements into a table, predicting properties and behaviours of elements not yet discovered, all later confirmed with the identification of elements like gallium and germanium.[12]
Let’s take one example of the many we could analyse. The example from physicist Sir Roger Penrose, who has made significant contributions to the study of cosmology and the nature of the universe. Penrose estimated the probability of the universe’s initial low-entropy state occurring randomly to be 1 in (larger than the number of atoms in the observable universe). To put it in perspective, this probability is far smaller than the chance of picking a specific atom out of all the atoms in the observable universe. That is just once, they try picking the correct atoms, sequentially millions of times. It is mathematically impossible.
In his book Man Does Not Stand Alone, A. Cressy Morrison points out that, “So many essential conditions are necessary for life to exist on our earth that it is mathematically impossible that all of them could exist in proper relationship by chance on any one earth at one time. therefore, there must be in nature some form of intelligent direction. If this be true, then there must be a purpose."
Atheists often use this example of extreme improbability to support their view, “If six monkeys sat at typewriters and banged on the keys for billions of years, it is not unlikely that in the last pages they wrote we would find one of the sonnets of Shakespeare. This is the case with the universe that exists now. It came about as the result of random forces which played with matter for billions of years.”[13] Khan comments, “Any talk of this nature is utter nonsense. None of our branches of sciences — until the present day — know what type of accident could produce such a great reality with all its wonder and beauty.”[14]
1. If God did not exist, the applicability of mathematics would be just a lucky coincidence.
2. The applicability of mathematics is not just a lucky coincidence.
3. Therefore, God exists.
[1] Jeans, James. The Mysterious Universe. Cambridge University Press.
[2] Wigner, E. P. "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Communications on Pure and Applied Mathematics.
[3] Wigner, E. P. "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Communications on Pure and Applied Mathematics,
[4] Einstein, A. "Physics and Reality." Journal of the Franklin Institute.
[5] Le Verrier, U. J. J., & Galle, J. G. Discovery of the planet Neptune by the method of mathematical prediction. Royal Astronomical Society
[6] Maxwell, J. C. A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society.
[7] Higgs, P. W. Broken symmetries and the masses of gauge bosons. Physical Review Letters
[8] Hubble, E. P. A relation between distance and radial velocity among extra-galactic nebulae. Proceedings of the National Academy of Sciences.
[9] Watson, J. D., & Crick, F. H. C. Molecular structure of nucleic acids: A structure for deoxyribose nucleic acid. Nature.
[10] Schwarzschild, K. On the gravitational field of a point mass according to Einstein’s theory.
[11] Thorne, K. S. Gravitational Waves: A New Window to the Universe. Journal of Modern Physics.
[12] Scerri, E. R. The Periodic Table: Its Story and Its Significance. Oxford University Press.
[13] J. Monod, Chance and Necessity.
[14] W. Khan, God Arises: Evidence of God in Nature and in Science.
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