Sep 20, 2012 | By

Do The Puzzles of Mathematics Prove God?

Mario Livio’s book “Is God a Mathematician?” (2009) provides a delightful history of mathematics and its many heroes, but fails to answer the question posed in the title. Dr. Livio does address directly the slightly different question of whether mathematics is a human creation, or a human discovery. In other words, is mathematics absolute, and therefore potentially a “creation of God”, or is it invented, a kind of technology resulting from human endeavor. While mathematics and the physical world are very different things, I think it’s clear they are both a “creation of God.”

As humans, we are provided with many perceptual/intellectual gifts – one is the ability to distinguish one object from another – another is to sense length, breadth and depth (space)– a third is to leap from the things we see to abstract concepts that we can then manipulate as tools to predict what we have not yet perceived. The mathematics of numbers arises as abstractions from the distinction between objects. The mathematics of geometry arises from abstractions concerning the behavior of shapes in space. Remarkably, if we follow certain logical rules (which also seem to be an intellectual gift to the human mind) in manipulating these abstractions, we precisely and correctly determine the behavior of the physical world.

It is not surprising that this ineffable relationship between abstract mathematics and the “real” world, which Dr. Livio refers to “the unreasonable effectiveness of mathematics” (attributed to Eugene Wigner 1902-1995), has given rise to deep philosophical speculations. Livio gives credit to Plato (ca. 428-347 BC) for the concept that mathematics exists in an independent and ideal world of mathematical forms and perfect truth, a philosophy known as Platonic Idealism. In the subsequent millennia, mathematicians, philosophers, astronomers, and physicists have wondered about this mystery and many have reached different conclusions. A number of 20th century mathematicians hold that mathematics is created through the idealizing and abstracting processes practiced by humans and does not exist otherwise (Livio attributes this view to Sir Michael Atiyah and others). Many, however, including Albert Einstein can be found in the puzzled camp: “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality.” (Cited by Livio on page 1)

As a student I was drawn powerfully to mathematics and its clear exploration of what I felt was absolute truth – an immediate and self-evident truth, quite apart from the physical world with its vague, complex and messy behaviors. So my first observation in response to the debates explored by Livio is that mathematical truth does not depend on the physical world per se. Any distinct objects, in any universe (real or imagined), are countable and subject to the laws of arithmetic. From these laws, through processes of definition and logical steps (in which each statement is a tautology of the former statement), all of mathematics can be “discovered”. All of those discovered truths are true when proved – significantly, they always will be true, and, more importantly, they were always true even before a mathematician proved them.

Admittedly, this is outright Platonism, but it comes very close to the position espoused by renowned physicist and mathematician Roger Penrose (1931- ), so I am in good company. Penrose (according to Livio) postulates three different “worlds” – the conscious world (us), the physical world and the mathematical world. He then offers three mysteries – (1) the physical world seems to obey the laws of the mathematical world; (2) conscious minds have somehow arisen out of the physical world; and (3) these conscious minds are able to discover and reveal the mathematical world. Livio also quotes Penrose (page 3) as saying, “No doubt there are not really three worlds but one, the true nature of which we do not even glimpse at present.” I don’t know whether Penrose was intentionally ironic in his statement, but it does resemble a somewhat feeble attempt to explain the mystery of a Divine Trinity.

Livio takes a more nuanced stance in his conclusion – that mathematics is both discovered and created. While there are fundamental truths that apply to our physical universe, much of what mathematicians do is to create and explore invented conceptualizations that, arguably, would have no being except for the efforts of humans to explore them.

In the end, Livio does not tackle the question posed in his title – “Is God a Mathematician?” It is, rather, simply used as a rhetorical device (probably picked by the publisher to boost sales). Notably, it does appear that many of his modern counterparts hold fast to non-deistic explanations and, indeed, some are directly hostile to the concept of God as accepted by most major religions. After all, God is not a particularly “testable” phenomenon and as Livio notes (page 252) “scientists have selected what problems to work on based on those problems being amenable to a mathematical treatment.”

The other difficulty with Livio’s title is that it poses the question in a somewhat anthropocentric way by implying that God’s thinking process is like ours. In fact, if you believe that God is the creator of the universe including the laws of mathematics, then his relationship to mathematics is quite different from ours. We discover mathematics – God created mathematics.

The bottom line, as unsatisfying as it may be, is that if you believe in a God as infinite creator of the universe, then it is easy to accept the notion that He created mathematics, and the puzzles of Penrose are easily resolved. If you do not believe in God, then you will continue to conclude, as he does, that the physical world, the conscious world and the mathematical world have a “true nature of which we do not even glimpse at present.”

6 Responses to “Do The Puzzles of Mathematics Prove God?”

  1. […] It seems quite remarkable to find these odd pieces of mathematical complexity theory including fractals, power law distributions, scale-free, small-world networks, and self-organizing behaviors throughout the different branches of science. These are beautiful examples of what Eugene Wigner in 1960 called “the unreasonable effectiveness of mathematics in the natural sciences”. Physical reality seems to conform to mathematical principles or, to express it differently, mathematics seems to constrain the forms which physical reality displays. In this sense, then, mathematics is a metaphysical necessity of the physical universe. (see: Do the Puzzles of Mathematics Prove God) […]

  2. Stephen H. Smith, M.D. says:

    What a wonderful article…but Matthew has me worried. If the “higher” angels understand numbers in a “much more profound way” I am doomed to the lowest natural heaven at best. I love the very end of the piece where you state in so many words that without a belief in God one will necessarily be very limited in understanding the deepest working of the natural world. And, this is what Ian Thompson asserts; quantum physics is essentially at a dead end without enjoining a “theistic” approach ( and this extends to ontology in general as well as psychology).

  3. George Gantz says:

    Mathematics is an idealized form of the order of the universe, so you could say that its creation is a manifestation of Divine Truth. Our understanding of mathematics and its ordering of the physical world is on the natural level. A more profound spiritual understanding would perhaps entail an ability to perceive the purposes of the ordering principles of mathematics. This could be things like the emergence of the cosmos, matter, life and consciousness from complexity, or the purpose of numbers in human life. A simple example: 10 and 100 are interesting numbers, but they also correspond to an ordering principle from the Word regarding human society – humans are built for small intimate groups of about ten and larger close communities of about 100.

  4. Matthew says:

    Thanks George for the interesting read. I believe that Emanuel Swedenborg spoke of the idea that the “higher” angels understand numbers in a much more profound way that the “lower” angels. This is specifically in relation to numbers and measurements mentioned in the Bible: ages of people when they died; generations; measurements of the ark and holy city New Jerusalem. These numbers and measurements all represent spiritual realities that the angels understand in a profound way. Here’s one question I’ll throw out there: If God created mathematics, WHY did He create mathematics? God must have a reason/use for everything He does. Thanks again for the stimulating thoughts.

  5. admin says:

    Paul – I wonder what mathematics looks like from God’s infinite perspective? There’s a lovely little book by Swedenborg on The Infinite that talks about the process of creation from the standpoint of the Infinite being “finited”. It seems that separations and distinctions (the source of number – arithmetic – mathematics) would be nascent and unmaterialized in the Infinite prior to creation, but fully functional once the “finiting” is in place.

  6. Paul Therrien says:

    HI,

    I think that GOD did create “mathematics” but not necessarily the way we have conceptualized it…It might be conceptually different to GOD meaning the whole of creation must be taken into consideration to understand what “Mathematics” really is. We as humans tend to be myopic as opposed to God who sees the whole of creation simultaneously outside of time as one working unit. Thanks for the article…

    Paul

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