Benjamin’s Homepage

A treble clef with quarter notes: b c d e f g a b

I hight “Benjamin”. I manipulate software. My email address is benjamin at this domain.


Assorted quotes from the math world

Inquiring minds must know!—Mikhail Kapranov

Apparently readers seek vengeance on other readers when they turn into authors.—Iacopo Barsotti

Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.—Leopold Kronecker

[Pu] was recalled to the mainland after the communists ousted Chiang Kaishek in ’49. Pu was henceforth confined to research in fuzzy topology in the service of the people.—Horowitz, Katz, and Katz

There are crystals of all kinds of substances: sodium, sulfur, modules, rings, relative schemes, etc.—Grothendieck

An alternative approach is to use [Grothendieck] universes, but this requires assuming additional set-theoretic axioms. The reader is invited to ignore such questions.—James Milne

…standard methods are stymied by the possibility of an exceptional zero, violating the Riemann hypothesis, lying very close to 1. Such a zero does not exist—but this cannot be proved. The usual proof of Linnik’s theorem…establishes an ‘exceptional zero repulsion’ principle, akin to proving that at most one of Santa Claus and the Tooth Fairy exist.—Frank Thorne

The geometry of Banach spaces lies in darkness and has attracted the attention of many talented research mathematicians.—John Bligh Conway

The problem is most easily grasped when stated in the language of cricket.—Hardy and Littlewood

The mathematics that comes from the ‘baroque’ inbreeding of the work of people with bad taste is often ugly and doomed to quick oblivion. The instinctive good taste of the geniuses who led the way is needed to guide the rest of us, and when we don't let it, we get generalization for the sake of generalization. We get what I have heard Zygmund call centipede mathematics (remove 99 legs and see what it can do); we get the elaborate elaborations of Baire category theory in fuzzy topological semigroup.—Paul Richard Halmos

Je me détourne avec effroi et horreur de cette plaie lamentable des fonctions continues qui n’ont point de dérivées.—Charles Hermite


$$\lim_{s\to 1}\frac{L_E(s)}{(s - 1)^r} = \frac{2^r\Omega\#Ш(E/\mathbb{Q})R(E/\mathbb{Q})\prod_pc_p}{\#E_{\mathrm{tors}}(\mathbb{Q})^2}\style{font-size: 250%; color: red;}{?}$$