A Tenuous Analogy

Let me offer you three words -- inaccessible, hardship, and beauty -- and ask you if there's anything that can tie these words together. Based on my experience there are two seemingly unrelated topics that come to mind: Antarctica and higher mathematics. I was introduced to the latter as an undergraduate math major over forty years ago and again as a graduate student just a few years ago. As for Antarctica I learned about the heroic age of exploration in the 1980's, and had the fortune to visit the continent in 2010.

Inaccessible - unreachable, remote, unattainable.

Many people consider higher mathematics as inaccessible. Certainly you need an aptitude for it, but it does exist. In 2008 over 1,360 Phds* were awarded in mathematics in the United States. The interior of Antarctica is nearly inaccessible. You have to be well-prepared and well-motivated to go there. However, around 1,000 people winter in Antarctica every year including 50 at the Amundsen-Scott South Pole Station.



Hardship - a condition that is difficult to endure; suffering; deprivation.
There's no doubt that the exploration of Antarctica involved hardship. Consider the tragic ending to Robert Falcon Scott's expedition to the South Pole in 1912. I can't cite a case of death while exploring mathematics, but certainly there have been nervous breakdowns and possibly suicides.

The one thing math researchers and explorers have in common is the intense need to know the unknown. Apsley Cherry-Garrard, a member of Scott's support team, had this to say about polar exploration:

Polar exploration is at once the cleanest and most isolated way of having a bad time which has been devised... There are many reasons which send men to the Poles, and the Intellectual Force uses them all. But the desire for knowledge for its own sake is the one which really counts and there is no field for the collection of knowledge which at the present time can be compared to the Antarctic. Exploration is the physical expression of the Intellectual Passion.

I think you can substitute "mathematic exploration" for "polar exploration" and maintain the meaning of the quotation.

Beauty - the quality present in a thing or person that gives intense pleasure or deep satisfaction to the mind, whether arising from sensory manifestations, a meaningful design or pattern, or something else.

I can attest to the beauty of the Antarctic Peninsula. The snowscapes are gorgeous; the icebergs are magnificent. Many mathematicians, scientists, and engineers laud the beauty of mathematical forms that contain deep symmetry and internal elegance.


Here are mathematician Bertrand Russell's words on this kind of beauty:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet
sublimely pure, and capable of a stern perfection such as only the greatest art
can show.

Here substitute "icebergs" for "mathematics" and again the meaning is preserved.

It would be silly to suggest that a heroic polar explorer would make a good mathematician or vice-versa. I count myself as neither an explorer nor a mathematician, yet I am fascinated by both species. The best I can do is explore words, make an analogy, and hope the analogy works.

*Phd's awarded in the United States in mathematics and statistics in 2008.