The farm

Esteemed Gentlemen, 
I am a poor, young, unemployed person in the business field, my name is Wenzel, I am seeking a suitable position, and I take the liberty of asking you, nicely and politely, if perhaps in your airy, bright, amiable rooms such a position might be free… . Large and difficult tasks I cannot perform, and obligations of a far-reaching sort are too strenuous for my mind. I am not particularly clever, and first and foremost I do not like to strain my intelligence overmuch… . Assuredly there exists in your extensive institution, which I imagine to be overflowing with main and subsidiary functions and offices, work of the kind that one can do as in a dream?—I am, to put it frankly, a Chinese; that is to say, a person who deems everything small and modest to be beautiful and pleasing, and to whom all that is big and exacting is fearsome and horrid.

From “a NY Times photo slideshow of atomic bomb explosions.”

In the book’s strongest sections, the author ties the new vision of the mathematical genius to a foundational shift in mathematical practice. Until around 1800, mathematics was yoked to physics—the mathematician’s role was to solve problems that arose, directly or indirectly, from material experience. Galois, Abel, Cauchy, and Bolyai, despite their disparate politics and biographies, had one thing in common: they represented a new notion ofwhat mathematics was, in which the subject unhooked itself from the physical universe and held itself accountable only to its own logical rules.

In order to make this argument, Alexander needs to go past mathematical biography into mathematics itself. Accordingly, Duel at Dawn features brisk write-ups of the furious battle among the early modern Italians to solve the cubic equation; of the curve described by a hanging chain; of Cauchy’s expulsion of infinitesimals from the calculus; and many more. The reader who is truly unwilling to encounter an equation may have to drape a cloth over these sections, but others will find much to gain from Alexander’s clear and careful exposition. The history of non-Euclidean geometry is handled particularly well, offering many details absent from more casual treatments, and laying the ground for Bolyai’s revolutionary advance.

Ruari McLean, in his groundbreaking study Victorian Book Design and Colour Printing, calls Oliver Byrne’s 1847 edition of The First Six Books of the Elements of Euclid “one of the oddest and most beautiful books of the whole century.” The century was the nineteenth; the publisher was the great William Pickering; the printer, his collaborator and close friend, Charles Whittingham—and McLean was right on the money: indeed it is. Byrne, who wrote a number of books on mathematics and engineering, served as “Surveyor of Her Majesty’s Settlements in the Falkland Islands,” which, in case you don’t know, are in the middle of nowhere in the South Atlantic Ocean. Presumably he had a lot of time on his hands, for in this very beautiful volume, he devised a radical method, which he claims to have tested “by numerous experiments” and with considerable success, to teach the six basic propositions of Euclid. To do so, instead of mathematical symbols, he employs colors and shapes whereby “the Elements of Euclid can be acquired in less than one third the time usually employed, and retention of this memory is much more permanent.

Japanese artist Isao Hashimoto created an animation showing every nuclear bomb explosion from 1945 to 1998.