God of the Mathematicians

Posted on 2012/01/21

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Feature Image - God of the Mathematicians

Statistics

In 1996, a survey was conducted by the Yale historian Edward Larson which asked a sample of scientists about their religious beliefs. The group’s aim was to discover whether religiosity among scientific academics has diminished, compared to results of a a similar survey from 1916.[1]

The study found little change in the spread of response. You’ll be pleased to hear it is not the purpose of this article to free-associate about possible reasons for this.

However, there is a narrower question that might yield to analysis. The research also discovered that, compared to other disciplines, a greater proportion of mathematicians believe in God. Among the general academic populous, around 44.6% of mathematicians affirm a belief in a deity – 4% more than their counterparts in the biological or physical sciences.

Looking at the more accomplished academics, the team conducted a sub-study of members of the National Acadamy of Sciences. As one might expect, they found far fewer believers within this group. However, again, they found the mathematicians had a greater proportion. Around 14% of them believed in a God and 15% (not necessarily in conjunction) believed in immortality. This is double the proportion found in any other scientific discipline within the NAS.

Is there anything different about mathematical investigation, compared to empirical sciences, that might account for this asymmetry in belief?

Theorems

Studying the other pole of religiosity, some prominent mathematicians have been known to have curious relationships with imagined deities. For example, the philosopher Freddie Ayer recounts that:

Someone asked [Bertrand] Russell at some meeting: ‘Lord Russell, what will you say when you die and are brought face to face with your Maker?’ He replied without hesitation: “I should say, ‘God, why did you make the evidence for your existence so insufficient?’ “[2]

Around the same time that Russell was making a very public dismissal of religious speculations, one of his contemporaries at Trinity Cambridge chose to communicate his disbelief by means of  a running joke.

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G. H. Hardy, the mathematicians famed for his collaboration with Srinivasa Ramanujan, was a firm non-believer of any God. He would refuse to step into a religious building, even to vote in the election of a Warden at his undergraduate college.

In moments when explicit confrontations with religion were not available, Hardy would fill the time with a game, aimed at ridiculing the Christian God. Hardy’s caricatured God was omnipotent and omniscient to ‘physical facts’, but unable to influence or know a person’s states-of-mind. Thus, (with a sufficient amount of Cartesian Dualism) it was possible to mislead this God, and defeat his intentions.

In addition, whereas Christians egotistically suppose God listens to their prayers and answer their needs, Hardy supposed God was mostly concerned with trying to ruin his enjoyment of cricket. His God was malevolent, petty, and easily fooled.

When he went to cricket matches he would take what he called his “anti-God battery”. This consisted of thick sweaters, an umbrella, mathematical papers to referee, student examination scripts etc. His theory was that God would think that he expected rain to come so that he could then get on with his work. Hardy thought that God would then have the sun shine all day to spite him.[3]

Other ruses were devised for this continuing feud. For instance:

One of his collaborators, Marcel Reisz, was staying at the place Hardy shared with his sister in London. Hardy ordered him to step outside, open umbrella clearly in view, and yell up to God, “I am Hardy, and I am going to the British Museum.” This, of course, would draw a lovely day from God, who had nothing better to do than thwart Hardy. Hardy would then scurry off for an afternoon’s cricket, fine weather presumably assured.[4]

Another collaborator, George Pólya, recounts (in broken English) that on a visit to Engelberg:

it rained all the time, and there was nothing else to do, we played bridge: Hardy, who was quite good at bridge, my wife, myself, and a friend of mine, F. Gonseth, mathematician and philosopher. Yet after a while Gonseth had to leave, he had to catch a train. I was present as Hardy said to Gonseth, ‘Please, when the train starts, you open the window, you stick your head through the window, look up to the sky, and say in a loud voice: ‘I am Hardy’…[5]

Hardy also once tried a variation of this, in the form of a life-insurance policy:

On each of his regular visits to his Danish mathematical friend Harald Bohr (younger brother of Neils…) , the unswerving routine was to arrive and sit down to construct an agenda for the visit; the first point on it was always ‘prove the Riemann hypothesis‘.

On the return from one such visit, facing a stormy sea passage,he scribbled a postcard and posted it to Littlewood, which read, ‘have proved the Riemann hypothesis’; Hardy, the atheist, reasoned that if God did exist, He would not allow him to die with the unjustified super-reputation that would have resulted in him proving this most sought after of results. Hardy arrived safely in England before the postcard arrived.[6]

Presumably, Hardy thought God had a much higher opinion of Fermat, allowing him to die before demonstrating the proof of his famous ‘last theorem‘.

Sometimes the joke could be presented silently. For example, his aforementioned friend, Pólya, often took walks with Hardy. Discussing mathematics along the way, Pólya couldn’t help but notice that, when they came to a church, if necessary, Hardy would change places so to place Pólya between the two. When asked about this, Hardy said it was just in case God should strike out at him with a lightning bolt.

A tenuous story, too interesting to omit, involves Hardy dining at Trinity during a discussion about propositional logic.

The topic was ‘ex falso quodlibet’ (known today as ‘the explosion principle‘). Known since Aristotle, it serves as a reminder that we all seek consistent assumption. Otherwise, it demonstrates, one can start with two contradictory assumptions and prove any statement one wishes. Sitting amongst the Trinity fellows was a philosopher by the name of McTaggart.

McTaggart is said to have denied the conclusion, saying, ‘If twice 2 is 5, how can you prove that I am the Pope?’ G. H. Hardy answered, ‘If twice 2 is 4, 4=5. Subtract 3; then 2=1. But McTaggart and the Pope are two; therefore McTaggart and the Pope are one.[7]

In some tellings of this story, it was Bertrand Russell or Alfred North Whitehead offering the riposte, although this story, from their contemporary at St John’s, is likely to be the original source. Whoever replied, it is certain that McTaggart was the questioner, especially once you know he was logical handicapped by an expertise in Hegelian philosophy.

I wonder if Hardy consider that this is exactly that blend of logic and semantic sleight-of-hand that is employed by thelogians discussing the nature of the trinity – that millennia-spanning effort to demonstrate, somehow, that 3 can equal 1.

Finally, Hardy once wrote postcard to a friend listing some of his New Year’s resolution. In order of importance:

  • To prove the Riemann hypothesis
  • Make 211 not out in the fourth innings of the last test match at the Oval
  • Find an argument for the nonexistence of God which shall convince the general public
  • Be the first man at the top of Mt. Everest
  • Be proclaimed the first president of the U.S.S.R. of Great Britain and Germany
  • To murder Mussolini[8]
What is curious about this, other than the breadth of ambition, is that Hardy probably wasn’t joking about the possibility of proving the non-existence of God.

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Another mathematician with a quirky view of Le Grand Fromage was Paul Erdös (pronounced Air-Dish – a stern warning to anyone thinking of learning Hungarian). He was extraordinary in many fields, and sometimes it was easy to see the causal link between his achievements. A self confessed asexual, Erdös managed to published around 1525 articles on mathematics – making him seem to be the control test in an alien investigation into the distraction of human sexuality. Clearly the man had plenty of time to sit around and think.

In a 1996 documentary, two interviews with Ronald Graham and Erdös himself presented his peculiar view of God:

Ronald Graham: …He has a perverse view of the almighty, feeling that it’s his job to make people feel unhappy, to annoy them. So, to get even, part of his mission is to annoy, as he calls, the SF…

Paul Erdös: SF means ‘Supreme Fascist’. This would show that God is bad. I don’t claim that this is correct, or that God exists. This is just sort of half a joke. When they ask you, “What is the purpose of life?” I say, “Prove and conjecture, and keep the SF’s score low.” Now the game with the SF is defined as follows: If you do something bad, the SF gets at least two points. If you don’t do something good which you could have done, the SF gets at least one point. And if you are okay, nobody gets any point. And the aim is to keep the SF’s score low.[9]

The SF was also responsible for hiding Erdös’s socks, glasses, Hungarian passport, and kept all the best equations to himself.[10] By ‘best’, Erdös didn’t just mean the ones that solved difficult problems. It was the most elegant solution to all the problems that were supposed to exist in “the book”, and it was the job of mathematicians to figure out what they, despite being denied permission to read it.

“You don’t have to believe in God, but you should believe in The Book,” he once remarked during a lecture.[11]

Proofs

When we compare any group of academics with the general population, they tend to be proportionally less religious – especially in the United States. The astronomer Neil deGrass Tyson points out that, “[f]or reference, 90 percent of the American public claims to be religious (among the highest in Western society), so either nonreligious people are drawn to science or studying science makes you less religious.”[12]

Nevertheless, the proportion of religionist amongst the mathematicians is significantly higher than other ‘sciences’.

I think this curiosity can be explained by noticing it is wrong to assume that mathematics is a science.

Any physicist that has a healthy relationship with experiment will know that their knowledge is fallible. Our best guesses – or theories – are always open to falsification by experiment.

In contrast, mathematicians often consider themselves to be searching for certainties. And they lean towards a Platonic philosophy, believing what they are studying is, in some sense,  ‘real’.

It is the desire to find certainty in reality that leads mathematicians to Christianity, and Christians to mathematics. The same mistake brings about so-called ‘arguments’ for the existence of God, wrongly assuming it is possible to use logic to obtain certain knowledge about the world.

Just a little bit of philosophy can show this position to be incorrect.

The theorems of mathematics are not ‘knowledge’, in the same sense we think scientific theories are knowledge. Instead, consider mathematics to be intellectual technology, and mathematicians as intellectual engineers. They take abstract patterns and try to join them together with logic. These template arguments (or theorems) can then be utilized for various applications: economics, physics, statistics, computer programming, etc. Betrand Russell put it like this:

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true … If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.[13]

References

[1] Larson, E.J. & Witham, L. (3 April 1997) ‘Scientists are still keeping the faith’ Nature 386, 435-436. [See also, Larson letter to Nature (23 JULY 1998) 'Leading Scientists Still Reject God' NATURE 394, 313.]

[2] Ayer, A J. (1988) ‘Betrand Russell’ p 131

[3] C. P. Snow’s introduction to: Hardy, G. H. (1967) ’A mathematician’s apology’ pp 44-45

[4] Kanigel, Robert (1992) ‘The man who knew infinity: a life of the genius Ramanujan’

[5] Alexanderson, Gerald L.(2000) ‘The random walks of George Pólya’ p 72-73

[6] Havil, Julian (2010) ‘Gamma: Exploring Euler’s Constant’ p 215 [I have heard that Hardy often sent message with similar claims before prominent lectures, but the source is unverified.]

[7] Jeffreys, Harold ‘Scientific Inference’ p 18 [For a humorous example of how it doesn't work, see: http://xkcd.com/704/]

[8] Hoffman, Paul (1998)’The Man Who Loved Only Numbers’ p 81

[9] In a documentary about his life, Erdos said: ‘As somebody put it, “he likes girls, but he doesn’t like the thing which they are standing for.” Actually, I have an abnormality. I can’t stand sexual pleasure. It’s a curious abnormality, it’s almost unique.’  From: (1993) N Is a Number: A Portrait of Paul Erdös Directed by George Paul Csicsery

[10] Hoffman, Paul (1998)’The Man Who Loved Only Numbers’ p 4

[11] Schechter, Bruce (2000) ‘My brain is open: The mathematical journeys of Paul Erdős‘ pp 70–71

[12] deGrass Tyson, Neil (1999) ‘Holy Wars: An Astrophysicist Ponders the God Question’

[Appears in (2003) 'Science and Religion: Are They Compatible', Edited by Paul Kurtz and Barry Karr. Prometheus Books (Amherst, NY) pp 73-79]

[13] Russell, Bertrand (1901) ‘Recent Work on the Principles of Mathematics’ [published in International Monthly, vol. 4 1901]