The Greatest Mathematician

Some years ago a large black Labrador retriever named Bridger entered my life. Bridger is a good friend; he takes me for walks – quite energetic walks at times – and has improved my skill at throwing frisbees no end. We communicate as best we can given that his verbal skills are almost as limited as my olfactory skills.

I am familiar enough with his habits, his various tricks for begging food (and snatching unguarded food given the chance), his ardent pursuit of small game that seldom has much to fear from him, his eagerness to go on walks, and his desire to go hunting. Although I enjoy his company until recently I had taken him for granted at a fundamental level. After all, as a friend once remarked, he’s just a dog.

My thoughts on this took a turn recently. Like most dogs, Bridger spends a good part of his time laying around waiting for his humans to do something interesting. I got to wondering about what he might be thinking about as he lay there.

Sometimes it is quite obvious. For example, when some of his begging does not produce the desired results, he has a way of plopping onto the floor that shows exactly what he thinks of that. Once down he lies there and pouts.

At times he lies there and watches you, obviously in hopes that you are going to do something, anything. At other times his eyes are half-glazed, as though he were in some trance of exquisite boredom.

It is those trances that intrigued me. Whatever is he thinking about in those trances? Some might think that he isn’t thinking of anything in particular, that, after all, he is just a dog. It might be so. Since he doesn’t speak, at least in the kinds of words that we use and understand, how would we ever know?

It occurred to me, though, to think about what I do in similar circumstances. To ask, that is, what I think about when I am constrained to do nothing but wait on events not under my control, to sit and gather by patience.

In my case the answer is simple – I think about things, stories and essays I might write, or mathematical problems. The casual observer observing me might well suppose that I’m mindlessly half asleep with nothing more in mind than keeping my head from falling in my lap. The casual observer would be wrong.

This habit of conducting one’s intellectual labors whilst appearing to be mindless is one of the annoying characteristics of authors and mathematicians – annoying, that is, to those who must deal with said gentry. Mathematicians and authors, however, see no problem with such behaviour.

You see where I am going with this. I am certain you do. Bridger spends much of time in just that state of being that is so characteristic of mathematicians, or, dare I say it, characteristic of other mathematicians. Our Lady of the Large Black Dog has suggested that his thoughts whilst lazing are fixed on the next bird and the next rabbit that he hopes to encounter.

I dare say that she is right in part – after all, he is a dog, Still I am persuaded that that is not the entire story. I am confident that the majority of his lazing about time is spent doing mathematics. I don’t think he spends it creating fiction – he lacks the verbal skills. However a lack of verbal skills is no bar to being a mathematician. Indeed it has never been a bar to being a mathematician of the first rank.

It may be that he is a paltry mathematician of no particular skill. It may be so, but I prefer to think that modest exterior (actually a quite handsome exterior for a dog) conceals the mind of the greatest mathematician in the world. It could be so. I imagine him as having retraced the work of Galois while a puppy and having long ago disposed of the Riemann zeta hyphothesis. These days he is happily unifying general relativity and quantum physics. The physics mean nothing to him, but the mathematics is entrancing.

No doubt you think this to be a mere crotchet, an idle and rather silly fancy on my part. Consider this, though. It could be so – the world’s greatest mathematician might be laying at your feet, apparently sleeping by the fire. The sad thing, or perhaps the glorious thing, is that we shall never know.