In the history of mathematics, many discoveries have been by polymaths who were also theologians, especially in the Islamic tradition. So I'm interested in interdisciplinary links between the two fields.
Mathematicians tended to be rationalists vs. emipiricists, therefore many of them were attracted to abstract thought involved in (late) theologies. I can mention Descartes, or Leibniz. Pascal is an interesting example, as he was highly intelligent and rational, nevertheless his conversion was NOT a rational one. I believe that there is relation between religion and mathematics, but only for a very limited group of people. There are atheist mathematicians (e.g. Russell) and theologians who are not attracted to mathematics.
My initial thought is that those who are polymaths make intradisciplinary (their primary field) and extra-disciplinary (in a second field of study) discoveries because they are capable of applying multiple forms of logic or reflection. In other words the polymath is not constrained by the rules of a single academic discipline and are therefore able to ask new questions which lead to new ideas and discoveries.
The mathematician Freeman Dyson writes in "Belief in God in an Age of Science", New York Review of Books (28 May, 1998):
... Western science grew out of Christian theology. It is probably not an accident that modern science grew explosively in Christian Europe and left the rest of the world behind. A thousand years of theological disputes nurtured the habit of analytical thinking that could be applied to the analysis of natural phenomena. On the other hand, the close historical relations between theology and science have caused conflicts between science and Christianity that do not exist between science and other religions ...
Thanks a lot dear Kirk MacGregor for your impressive question, Really, in almost of religions including Islam, there is a relation between theologians polymaths and mathematics, where some times you find a physician and at the same time mathematician, I advice you sir to seek about the number 7 in the Islamic tradition. In the attached link you find a list of the most famous Islamic Scholars.
https://en.wikipedia.org/wiki/List_of_Islamic_scholars_described_as_father_or_founder_of_a_field
Mathematics is the queen of sciences and people believe in science. Religion is a force that unites people who believe in it. Thus, mathematics and religion are united by faith and, perhaps, hope and beauty :)
https://www.researchgate.net/post/Beauty_will_save_the_world?_tpcectx=profile_questions
https://www.researchgate.net/post/Is_mans_power_in_truth?_tpcectx=profile_questions
Difficult to predict a relationship whether empirical or direct. But peace of mind is must. There are persons who are deeply religious and very good in discoveries. The necessary is that knowledge is transferred to future generations. Earlier educated persons were less and education was given only in religious places. So good mathematics came from religious persons. I hope this follows in all cultures as hundreds of years back only few persons were able to read and write. Arabian area was also bridge for business between Asia and Europe and lot of information was exchanged.
Most mathematics, e.g., set theory, involving greater cardinal numbers/degrees of infinity, calculus, topology, chaos theory, and fractals have been proposed by Western and far Eastern thinkers who were non-subscribers to Islam. My proposal for a relationship between mathematics, religion, religious practices, and spirituality (qualitatively and quantitatively different cognitive, emotional, and behavioral phenomena), hinges on forms of Boolean algebra, Aristotelian logic and mathematics in which some axioms and/or operations necessarily are self-referential paradoxes (SRP). The equation, X squared = - 1, is an example. SRP's also appear to be one key for untangling the hard problem of consciousness; quantum mechanics appears to be another.
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