Just a short post to point out the possibilities of writing cardinals in a more modern typeface. Pick your favourite solution from this list. The following compares the Euler math font version from the AMS with the FDSymbol version at the TeX.SE answer.
My goodness, I didn’t realise this was still online (pretty, but short…). Sadly the Dropbox link (not hosted by me) has rotted, though I’ve still got a copy of the files. I should re-post that here someday.
ICM 2018 | "A lot of the time, when you do Math, you're stuck. But you feel privileged to work with it. You have a feeling of transcendence and feel like you've been part of something really meaningful." Akshay Venkatesh, 2018 Fields Medallist. #ICM2018#ICM2018Rio
I’m trying to track down a picture of Benacceraf in his younger days, to illustrate a seminar on the history of numbers for undergraduates. Ideally close in time to his famous essay What numbers could not be. I found two photos from Princeton University Philosophy department from the late 60s and 70s respectively, but the people in them are not personally identified. The photos can be seen at this History of Science and Mathematics Stackexchange question, where I invite answers, or let me know in the comments.
I’m standing with Williamson in his office at the University of Sydney, on the seventh floor of the Carslaw Building, looking down at the campus’s historic sandstone quadrangle. The Carslaw is renowned by staff and students as being the university’s ugliest building, an antipodean approximation of a KGB regional headquarters. “The standard joke is that the best thing about working in Carslaw is that you don’t have to look at it,” Williamson says. His office is similarly unappealing – essentially a concrete bunker with bad carpet – and yet it has everything a mathematician might need; a whiteboard, marker pens, a computer, and most important of all, a couch. “When I moved in here, I told them ‘I need a big couch!’ ” he says. “As opposed to things like medicine and science, which require specialised equipment – microscopes, X-rays – mathematicians can do most of their work with a pencil and paper. Really, you spend most of your time sitting around talking.”
Fortunately, Williamson is a good talker – jaunty and light, his sentences tripping along before ending with an upward inflection, like a little trampoline kick-out off the final syllable. He’s a little goofy. He smiles a lot; his eyes go wide. You get the sense that inside his head is a banging dinner party where all these brilliant ideas are elbowing one another to get out and roam around. Turning on his computer, he talks me through a slide display about representation theory – his area of expertise – and how it can, via spectral analysis of fundamental frequencies, explain why a whistle sounds different to a violin, and why, consequently, you’d rather listen to a concerto played by violins than a concerto played by whistles. An intriguing-looking textbook lies open on his desk, the pages crammed with cryptic glyphs and a photo of a Mayan pyramid. There’s also a stack of shiny new books. “Our latest publication,” he says, handing me one. I turn it over and read the back cover. “In this book,” it says, “we conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block.”
I want to ask: what is a “functor”? Who is Hecke? And why is the word diagrammatic in brackets? But instead, I ask: “Where can we get a sandwich around here?”
“What I care most about are definitions. For one thing, humans describe mathematics through language, and, as always, we need sharp words in order to articulate our ideas clearly. (For example, for a long time, I had some idea of the concept of diamonds. But only when I came up with a good name could I really start to think about it, let alone communicate it to others. Finding the name took several months (or even a year?). Then it took another two or three years to finally write down the correct definition (among many close variants). The essential difficulty in writing “Etale cohomology of diamonds” was (by far) not giving the proofs, but finding the definitions.) But even beyond mere language, we perceive mathematical nature through the lenses given by definitions, and it is critical that the definitions put the essential points into focus.
Unfortunately, it is impossible to find the right definitions by pure thought; one needs to detect the correct problems where progress will require the isolation of a new key concept.”
Harris was asked to write a draft for New Scientist about Scholze’s work, but they were after something far too low-brow in the end. I have only seen a couple of good articles in there about serious mathematical topics (one on Woodin’s “Ultimate L” was reasonable, but gave really no decent mathematical information about the topic) and wouldn’t have expected Harris, not an easy writer even for mathematicians, to be the best fit for their intended audience.
Tim Gowers has posted about a new journal, Advances in Combinatorics, that is a) open access, b) free to publish in for authors. It is aimed at good (but not absolute, Acta/Annals top-tier papers). I heartily endorse this new journal.