Commenting on Cantor

Pulling from the book, The Book of Nothing, by John D. Barrow, Georg Cantor is quoted as saying,

“Because of this extraordinary position which distinguishes mathematics from all other sciences, and which produces and explanation for the relatively free and easy way of pursuing it, it especially deserves the name of free mathematics, a designation which I, if I had the choice, would prefer to the customary ‘pure’ mathematics”

Our labeling of math as “pure” and alternatively, “applied” has been existence for more than 100 years.  I’m not sure who labeled it thus.  Certainly those partaking in “pure” research present and past hold their heads a little higher because they feel they are doing something more noble and righteous than the sell-out applied mathematicians- who are obviously not interested in mathematics for mathematics’ sake.   But that doesn’t mean it wasn’t the applied mathematicians trying to segregate themselves from the abstract to show that they were dealing with something which actually made sense in our world.

Let me paint a possible picture for you. Back in 1900, the Applieds are spending their time trying to convince congress that their calculations guarantee the success of a flying hot hair balloon made of metal. Congress recently heard from a Pure trying to get funding about one infinity being larger than the other.  This sadly puts them off from all mathematicians, because the mathematicians speak in tongues no one can understand.  Now the, trying to split themselves from their jargon-filled brethren, Applieds point furiously to the  Pures to say, “Nay! Do not lump me in with those loonies! I am not a Pure, I am an Applied and I assure you that my math connects with reality!”

Idyllic Galileo

Back in the Renaissance scientists were allowed to be such poets!  The breath of study was more liberal arts degree than pre-med.  Which is to say, the romantic mathematician is much more my style than not.  And so it is not at all surprising, but beautifully eloquent all the same, that I like to return to these poet mathematicians to hear their devout praise.  In the words of Galileo:

“The human intellect does understand some propositions perfectly, and thus in these it has as much absolute certainty as Nature itself has.  Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows them all.  But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty.”

G. Galileo, Dialogue Concerning Two World Systems,
transl. S. Drake, California Univeristy Press,
Berkeley (1953)

A call to read

I’ve been traveling quite a bit in the last week or so visiting lots of old friends and such.  And I have noticed that my mathematically inclined friends often have similar books on their bookshelves.  This seems like a great idea.  Perhaps everyone should own Rudin and baby Rudin Analysis.  But there are other books that everyone also seems to have;  God Created the Integers, The Golden Ratio, and Flatland are the three most common books on a mathematicians shelf which contain more history than mathematics.  There are several other common books, Through Euclid’s Window, The Man who Loved only Numbers, and Letters to a Young Mathematician among them.  Perhaps you know of others?  What do you have on your bookshelf for the literary inclined mathematician?

I think it is wonderful that the math culture has created this rich and enduring volumes about the giants whose shoulders we stand apon as mathematicians.  But what I find truly amazing is that so many of my collegues purchase these books but never actually read them!  And so I say to you; Read!  These are excellent books worthy of your time.  Take a break from the latest episode of Numb3rs and pick up a book for a couple hours.  You will be richly reward with fascinating stories of all the mathematicians who came before you.  It’s a great culture we young mathematicians enter into and it is wonderful that authors are starting to research and put together vibrant windows into our culture.