One of my favorite books when I was growing up was the Mathematics volume in the LIFE Science Library. I didn’t own the book, but my uncle did, and I’d browse through the book whenever I visited him. I was too young at the time to understand much of what I was reading.

One of the pages that stuck in my mind was a photo of Samuel Eilenberg. His name meant nothing to me at the time, but the caption titled “A subway topologist” caught my imagination.

… Polish-born Professor Samuel Eilenberg sprawls contemplatively in his Greenwich Village apartment in New York City. “Sometimes I like to think lying down,” he says, “but mostly I like to think riding on the subway.” Mainly he thinks about algebraic topology — a field so abstruse that even among mathematicians few understand it. …

I loved the image of Eilenberg staring intensely at the ceiling or riding around on a subway thinking about math. Since then I’ve often thought about math while moving around, though usually not on a subway. I’ve only lived for a few months in an area with a subway system.

The idea that a field of math would be unknown to many mathematicians sounded odd. I had no idea at the time that mathematicians specialized.

Algebraic topology doesn’t seem so abstruse now. It’s a routine graduate course and you might get an introduction to it in an undergraduate course. The book was published in 1963, and I suppose algebraic topology would have been more esoteric at the time.

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For daily tweets on topology and geometry, follow @TopologyFact on Twitter.

Take a look at this short story named “A Subway Named Möbius”, by A. J. Deutsch:

http://westongeometry.pbworks.com/w/file/fetch/61244911/SubwayNamedMobius.pdf

A citation from the story:

” “And you call yourself a mathematician, Professor Tupelo!” he said.

Tupelo almost laughed aloud. The incongruous, the absolute foolishness

of the situation, all but overwhelmed him. He smiled thinly, and said: “I’m no

topologist. Really, Mr. Whyte, I’m a tyro in the field—not much better

acquainted with it than you are. Mathematics is a big pasture. I happen to be

an algebraist.” “

Hard enough to challenge a mathematical topologist,

Simple enough that a slime mold can solve it.

https://www.youtube.com/watch?v=GwKuFREOgmo

I remember reading that as a kid and going to the dictionary to look-up “abstruse.”

Also, “Bourbaki” intrigued me for years, until I could look it up on the internet. :-)

The picture I remember best from that book is that of the colossal German farmer, along with a picture of the food he consumed in a day. I don’t have the book to hand, but I think the purpose was to illustrate the nature of a function.

That first paragraph is something I could have written from my own life, save that the book that fascinated me the most was “The Universe”.

I can still remember where my uncle kept the series: in a little built in bookcase to the right of the fireplace in the parlor; and the smell of lavender (he was a typical unmarried Irish bachelor and lived with my grandmother) and the unspoken understanding that I wasn’t to submerge myself in the books until after supper.

John Tukey also liked to think lying down:

John W. Tukey: His Life and Professional ContributionsYes! I so vividly remember that photograph. When I went to visit my

cousins, who had a copy, that was the book I turned to.

The book is easy to find at jumble sales like Brisbane’s LifeLine Bookfest. Of course I now have a copy.

I suspect that the photo was important to many who later became mathematicians. For myself, it was a glimpse of a world where one could actually be relaxed (look at his pose) about comtemplating advanced mathematics. It was a contrast to the anti-intellectual attitude of most of my circle at that time – an attitude that I still encounter.