Recently I wrote about my impression of a predominance of religious worldviews and practices among the most celebrated mathematicians. I concluded by indicating that I wouldn't be surprised if religious worldviews were more conducive to great advances in maths and other disciplines, because of the way that faith and imagination are involved in discovery. Today I'd like to explore some slightly more specific ideas about how that might work. This is very tentative, largely because I'm clearly not one of those mathematical geniuses myself! But I want to share some ideas and see what others think.
A key to progress in many scientific disciplines seems to be the positing of connections between different concepts. For example, one of the founding moments in physics came from supposing that celestial and terrestrial bodies moved according to the same laws (Newton); much later came the idea that light might be a form of wave-motion (Maxwell); biology, meanwhile, progressed with the idea of natural selection as an analogue of selective breeding (Darwin), and later with the idea that some processes in living cells might be modelled as chemical reactions in test-tubes. Not all of these ideas are necessarily completely reliable or true, but they have still aided deeper and richer understanding. Progress has also come from looking for numerical descriptions of phenomena: scientific laws that can account for relations among certain quantitative variables.
Within maths itself, advances have come with making connections from numerical to spatial concepts, such as with the development of irrational and complex numbers and, later, the formalisation of number systems as sets. This 'bridge-building' might also be seen as relaxing constraints - as with the development of non-Euclidean geometry by Gauss and others. Constraints on our thinking are an important part of an academic 'discipline', yet there is clearly some knack of recognising when and how it might be productive to relax a certain constraint and posit a connection between supposedly-disparate concepts. But relaxing a constraint is not necessarily enough on its own: a certain imagination is also required in order to conceive of a connection.
When and why do certain thinkers manage to posit connections that turn out to be real, in some sense? Perhaps - and this is only a suggestion - it depends on an appropriate kind of faith. Faith complements imagination (isn't that how we start to pray for something to happen?), bringing a sense of actuality to what we might playfully imagine. And well-placed faith is indeed "the reality [Gk: hypostasis] of things hoped for" (Heb 11:1).
To be more specific, I'm suggesting that holding certain worldviews, not least Judaeo-Christian ones, may lead people to expect connections between diverse domains of the cosmos, and hence between corresponding areas of knowledge. Dick Stafleu points out that "the unreasonable effectiveness of mathematics" in the sciences, as Eugene Wigner notably called it, is not so unreasonable at all if one has this kind of worldview. It's a realist worldview, and one that shuns the materialism that makes it difficult for thoughts to correspond logically with reality.
Mathematics seems to be one field where materialism has had relatively little traction (as explored by John Byl in The Divine Challenge), and we might postulate that unproductive worldviews have, to some extent, been weeded out of the discipline by a kind of natural selection. But my hunch is that the prominence of religious affiliations among some of the most celebrated mathematicians may point to the positive compatibility of certain kinds of non-reductionist worldviews with the way the world is: specifically, with a universal joined-up reality, a cosmos that is designed to have a deep, multifaceted harmony and that ultimately rewards those who expect, and look for, its connectedness.
The Christian tradition certainly encourages us to look for connectedness. At a personal level, we know the Gospel of redemption and reconciliation. But at a cosmic level, surely God's plan to bring all things together under Christ hints at a far wider interconnectedness in all of creation? Could this possibly help us also to serve and glorify God by being better scholars?
Are there any ways in which your faith has helped you to persevere in looking for an academic connection of some sort? Have you proposed a bold hypothesis, or been vindicated in casting off a constraint?