It’s December, the semester is winding down, we all need a break from deep thinking about hard math. So this week I have some extra special brain candy I’ve been saving up for you, in the form of a Tumblr, Math Professor Quotes.
You can browse by subject, or just take your time and scroll through them all, but either way, prepare to give up at least 15 minutes of your life. It’s fun. I always find the number theory quotes extra hilarious, but having just taught discrete math this semester, these were giving me the giggles extra hard.
I myself have always been a fan of the $2 words injection and surjection, not because I’m a fancy pants who drinks from a frosted mug — I prefer my beer in a can, thanks — but just because (for unclear reasons) I hate the word onto. I mean, how can onto even be a word? It doesn’t have the heft that I need such an important piece of terminology to bear.
I do always feel silly talking about pigeons and holes. Do pigeons even live in holes? And even if they did, are they tame enough to be placed into the holes by a handler? Anyways, some of these quotes hit really close to home, and I start to wonder, have I said that before? If not, I should really start saying it.
I totally agree about ‘onto’, but ‘pigeonhole’ is at least historically and etymologically sound: pigeons are kept in a grid of shallow, rectangular, open-fronted boxes, and that really is where we got the term ‘pigeonhole’ for the grid of shallow, rectangular, open-fronted boxes that internal mail goes into.
When I’ve seen the pigeonhole principle discussed it has more often been in terms of mail into pigeonholes, not pigeons, which sounds less silly but relies on people knowing the term ‘pigeonhole’ for mail boxes.
“Epsilon is doomed to go to zero” — Hermann Weyl (1885-1955)
Sourcing: In 1971, I took complex variables from Henri Frederic Bohnenblust (1906-2000) at Caltech, who had worked with Weyl at Princeton, and told us this quotation. I still tell this to my students in Urbana, keeping the direct tradition alive.
Interesting discussions!
Do you have a clue of the origin of pigeonhole principle wording in English? In French we use the “drawers principle”: if you put n>m pairs of socks in m drawers, then one drawer will contain at least 2 pairs. It seems that the drawer principle wording comes from the German mathematician Dirichlet, and we keep this wording in French (“principe des tiroirs”) today, like in Polish or Italian.
In French we only use surjection, injection and bijection… I don’t know if it is because we drink more wine then beer! Anyhow trying to write math in my mathcounterexamples blog I had (and still have to…) to discover a lot of different wordings between French and English. Like onto, one-to-one… By the way what would be your recommendation between one-to-one, onto vs. injection, surjection in a blog?
Also one big difference is the use of increasing, non-decreasing… Which have different interpretations.
Injection or 1-1, onto or subjective, everyone knows both words. Just like we might “ask a question” or “make an inquiry”; we put chicken on the BBQ while we eat poultry at the restaurant with the white linen tablecloths. In English, when we wish to sound sophisticated and intelligent, we use words which come from Latin (usually via French), and when are just being ourselves we use words that are short and simple, usually of Germanic origin. “Bijective” is used more often than “one to one and onto” because “one to one and onto” is long and awkward. You can use whichever terms you prefer for your blog.
“Increasing” and “non-decreasing” are just precisely what they say. x1 < x2 < x3< … is an increasing sequence; x1 <= x2 <= x3 <= … is non-decreasing. There are different interpretations of these words in French?