Davies On the Unreasonable Effectiveness of Mathematics

Last updated on: February 18, 2018 at 5:34 pm by Andrew

Davies On the Unreasonable Effectiveness of Mathematics 2018-02-18T17:34:52-05:00 Andrew

LOGO Patheos Explore the world's faith through different perspectives on religion and spirituality! Patheos has the views of the prevalent religions and spiritualities of the world.

In Mind of God, agnostic physicist Paul Davies explores a number of deep questions, one of which takes aim at Eugene’s Wigner’s question on the “unreasonable effectiveness of mathematics” in describing the natural world. Restated by Einstein, “how is it possible that mathematics, a product of human thought that is independent of experience fits so excellently the objects of physical reality?”

He presents various perspectives on the “is mathematical invented or discovered?” question. For many with Platonic leanings, mathematics is obviously discovered. Here Davies lays out the thought of Roger Pemrose, with things like complex numbers and “the Mandelbrot set”, along with his mathematical breakthroughs on black holes and space-time singularities, that mathematics is certainly discovered.

He also provides the counter argument that mathematics is invented, just the way our cognitive faculties express scientific truths abstractly. This may sound initially attractive, that mathematics is the language we’ve invented for this abstraction, so no wonder why it’s incredibly effective. But something seems awry there. In Davies’ words:

“So is the success of mathematics in science just a cultural quirk, an accident of our evolutionary and social history? Some scientists and philosophers have claimed that it is, but I confess I find this claim altogether too glib, for a number of reasons. First, much of mathematics that is so spectacularly effective in physical theory was worked out as an abstract exercise by pure mathematicians long before it was applied to the real world. The original investigations were entirely unconnected with their eventual application… And yet we discover, often years afterward, that nature is playing by the very same mathematical rules that these pure mathematicians have already formulated. (151)

He continues:

The mystery becomes even deeper when we take account of the existence of mathematical geniuses… The astonishing insight of mathematicians such as Gauss and Riemann… Probably the most famous case is that of the Indian mathematician S. Ramanujan… Born in India in the lat nineteenth century, Ramanujan came from a poor family and had only a limited education. He more or less taught himself mathematics and, being isolated from mainstream academic life, he approached the subject in a very unconventional manner… To this day nobody really knows how he achieved his extraordinary feats… “(153-154)

The challenge for mathematics being an invented language to describe empirical facts is that mathematics is time and time again in front of empirical discovery and/or intimately connected or adding to empirical discovery. This not only returns us to Einstein’s question (“how is it possible that mathematics, a product of human thought that is independent of experience fits so excellently the objects of physical reality?”), but seems to further distance us from the mathematics is just invented solution. Restated by Mario Livio (for a deeper dive, check out my review of Is God a Mathematician):

“It is difficult to see how this ability could have led to abstract mathematical theories of the subatomic world, such as quantum mechanics, that display stupendous accuracy… Researchers use mathematical models to product new phenomena, new particles, and the results of never-before-performed experiments and observations. What puzzled Wigner and Einstein was the incredible success of the last two processes. How it is possible that time after time physicists are able to find mathematical tools that not only explain the existing experimental and observational results, but which also lead to entirely new discernment and new predictions?”

Personally, alongside Davies (and Livio), I find the mathematics is just invented solution extremely wanting. At the same time, I agree that a Platonic realism of mathematics is also problematic (mathematical truths in a separate immaterial realm). Holding an Aristotelian realism (metaphysically, morally, and mathematically), which I do, I find an extremely balanced alternative of both Platonic realism and irrealism. There is mathematical ontology in matter (again, not in some Platonic realm, nor just invented by our minds). Like with morality, we don’t invent it. There is intrinsic value in nature. We have the ability to abstract this knowledge epistemologically from nature because it’s in nature ontologically.

Image credit:

Author: ASU / Tom Story

Source: Wikimedia Commons

Quote Bank

Previous Post

February 12, 2018

From Evangelical to Progressive

Next Post

February 25, 2018 MLK Jr on a Christian Humanism

Browse Our Archives

Select a Category Book Reviews Deep Scene Breakdown Deep Song Breakdown Events with Adam Lee Iron Heart Musings Podcast Quote Bank

Select a Month January 2026 September 2025 August 2025 June 2025 March 2025 February 2025 November 2024 August 2024 April 2024 March 2024 February 2024 January 2024 December 2023 September 2023 August 2023 April 2023 March 2023 February 2023 December 2022 October 2022 September 2022 August 2022 June 2022 May 2022 April 2022 March 2022 February 2022 January 2022 December 2021 November 2021 October 2021 September 2021 February 2021 January 2021 December 2020 November 2020 August 2020 June 2020 March 2020 December 2019 November 2019 October 2019 September 2019 August 2019 June 2019 May 2019 March 2019 November 2018 October 2018 August 2018 July 2018 June 2018 May 2018 April 2018 March 2018 February 2018 January 2018 December 2017 November 2017 September 2017 August 2017 May 2016 April 2016 November 2015 October 2015 August 2015 July 2015 June 2015 May 2015 March 2015 January 2015 December 2014 November 2014 October 2014 September 2014 August 2014 June 2014 May 2014 April 2014 March 2014

TAKE THE

Religious Wisdom Quiz

Where did Jesus spend forty days being tempted by the devil?

Select your answer to see how you score.

Sea of Galilee The wilderness Jerusalem Nazareth