On the sources of genius

Portraits of Euler, Gauss, Cantor, Ramanujan, Noether, Hilbert, Godel

[Portraits of (L-R) Euler, Gauss, Cantor, Ramanujan, Noether, Hilbert and Gö​del from the public domain]

In teaching elementary probability and statistics to undergraduates, I've been reading about some of the great mathematicians who are commemorated in the names of functions and constants. This has led me to ponder the role of religious worldviews in mathematical genius, and it's on that topic that I'd like to share a few thoughts today.  I hope that some readers here may have further knowledge and ideas to share.

My reading started with Leonhard Euler (1707-1783), the Swiss mathematician for whom the number e (about 2.7) is named and who is widely considered the most prolific mathematician of all time.  A recent article in Faith And Thought by JW Montgomery focuses on Euler's biblically-rooted Christian faith and engagement in apologetics.  I then moved on to read about Carl Friedrich Gauss (1777-1855), the German for whom Gaussian distributions are named and who is sometimes considered the greatest mathematician since antiquity for his wide-ranging contributions.  Gauss was a Lutheran and seems to be a believer; he is said to have declared, upon solving a particularly difficult problem, "Finally, two days ago, I succeeded – not on account of my hard efforts, but by the grace of the Lord."  Another Lutheran, Georg Cantor (1845-1918), also appears in some lists of the top ten most important mathematicians of all time, for his contributions to the understanding of kinds of infinity.  Philosophical considerations arising from Cantor's work were the occasion for strong claims that he made defending God's independence from even such mathematical realities as infinities – and he claimed that the theory of transfinite sets was revealed to him by God.  Earlier than all three of these, there's also Isaac Newton (1642-1727), a unitarian believer in the Christian tradition, whose contributions to mathematical physics are well known. 

So far these are all men of the Enlightenment, and the strength of Christian faith among them might be thought of as incidental.  But it seems to me that cultic religious worship and beliefs are oddly prominent in the most notable mathematicians from other cultures as well.  Pythagoras of Samos (c.570-495 BC) founded the Pythagroean cult in which it is said that certain integers were worshipped – although there seems to be some doubt as to how much of both the mystical and the mathematical ideas attributed to Pythagoras were really his own. And jumping forward to modern times, Srinivasa Ramanujan (1887-1920), the Indian whose career is depicted in the film The Man Who Knew Infinity, was a devout Hindu who attributed his spectacular insights to direct revelation from his family goddess.  Given the tortuous path by which Ramanujan's genius came to be appreciated on the international stage, one wonders how many other great mathematicians are being consigned to ignominy!  Similar concerns may be raised concerning women, at least up to the 20th century – and Emmy Noether (1882-1935), sometimes considered the most important woman in the history of mathematics, was Jewish. 

I'll conclude my brief survey with two final European men.  The celebrated German mathematician David Hilbert (1862-1943) was raised a Calvinist in the Prussian Evangelical Church but became agnostic.  But ironically, his vision of establishing the autonomy of mathematics independently of any philosophy or religion was capsized by the young Austrian Kurt Gödel (1906-1978), a Bible-reading theist.  Gödel's incompleteness theorem (1930) "ended a half-century of attempts... to find a set of axioms sufficient for all mathematics" [1].

What do I take from my brief dip into mathematical biography?  I'm not sure I could persuade a skeptic that religious worldview or adherence is a prerequisite for great mathematical genius; I daresay there are good counter-examples out there.  But there is at least food for thought here.  In contemporary philosophy of the sciences (broadly construed) there is great emphasis on the justification of a theory and very little on how it was discovered.  Even scientific–​historical studies rarely shed great light on this.  Of course there won't be any simple recipe for making great discoveries, but I'm sure that worldviews – and hence religion – play a crucial important role in the thought of great scientists, and a fortiori in the case of mathematicians.  After all, it takes faith to search for what no-one has seen before, and imagination to see it.  I'll return to this in a follow-up post.

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[1] Wikipedia article on Gödel, accessed 25/11/19

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