Tuesday, March 21, 2006

Cole's Paper on M67

As promised, here is the delightful story from 1903 of F. N. Cole and M67, that is, the "Mersenne number" M67 which is 267-1, and Mersenne's claim that it is prime. Not only does it show how persistence pays off, but it also demonstrates that knowing how to add and multiply can be very important!
Dr. Thursday

...In 1903 F. N. Cole (1861-1927) proved that M67 is not prime.
I should like here to preserve a small bit of history before all the American mathematicians of the first half of the twentieth century are gone. When I asked Cole in 1911 how long it had taken him to crack M67 he said "three years of Sundays." But this, though interesting, is not the history. At the October, 1903, meeting in New York of the American Mathematical Society, Cole had a paper on the program with the modest title On the factorization of large numbers. When the chairman called on him for his paper, Cole - who was always a man of very few words - walked to the board and, saying nothing, proceeded to chalk up the arithmetic for raising 2 to the sixty-seventh power. Then he carefully subtracted 1. Without a word, he moved over to a clear space on the board and multiplied out, by longhand,
193,707,721 x 761,838,257,287
The two calculations agreed.
Mersenne's conjecture - if such it was - vanished into the limbo of mathematical mythology. For the first and only time on record, an audience of the American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.

[Eric Temple Bell, "The Queen of Mathematics" page 503 in The World of Mathematics Vol. 1.]


At 22 March, 2006 16:53, Anonymous Anonymous said...

Dear Doctor,

I looked for "The World of Mathematics" by E.T. Bell at Amazon but couldn't find it. Do you have any clue as to where else I might buy it?

At 23 March, 2006 17:15, Blogger Dr. Thursday said...

That particular essay is by Bell, but this four-volume collection called The World of Mathematics has the subtitle:
"A small library of the literature of mathematics from A'h-mose the Scribe to Albert Einstein, presented with commentary and notes by James R. Newman."

It was published by Simon and Schuster (NY) in 1956, and I found mine in a used-book store.

BUT! it has been reprinted by the amazing Dover publications. Note: I have no connection with Dover, except that I am a very satisfied customer, and pleased to inform you of the great service they render to Chestertonians (they print Manalive!!!) and scientists (they print Madame Curie's doctoral thesis!) and so many other scholars, artists, and interested children like me.

You can see their entry for this work here.

At 23 March, 2006 23:23, Anonymous Anonymous said...


Thanks for clearing that up.

I did find that volume but was confused as it didn't make sense the way I read your attribution. My error.

I did add it to my ToBuy list.


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