One of the joys of continuing to try to educate oneself throughout life, even as one grows old, is that you’re for ever extending your vocabulary.
My maths education ended at fourteen, when I had done my O levels and entered the classical sixth. I’d had a good grounding in arithmetic, algebra and geometry, extending to trigonometry and calculus. But I have always felt a bit ignorant about, for example, such matters as exponentials and complex numbers and calculations involving them. I can’t process e and i as easily as I can π, sin θ, and x-1.
Recently, beguiled by Prof. Brian Cox’s eloquent and engaging television programmes, I embarked on his recent book, coauthored with Jeff Forshaw, The Quantum Universe (subtitle: everything that can happen does happen).
So I was looking forward to some challenging new ideas that I might struggle to understand. I hadn’t quite expected, though, that within the first dozen pages I would come across a word I had not met before: ansatz, explained as an ‘educated guess’.
Now Ansatz is the sort of German word that I know passively, though I would not claim that it belongs to my active vocabulary. I would take it in my stride if I encountered it in the middle of a German text, perhaps einen neuen Ansatz (zu etwas) machen, ‘make a fresh attempt (at something)’. On looking it up I find that it has a whole range of specialist and technical meanings that need not detain us here.
But as an English word, how would I pronounce it? The trouble with knowing German is that I immediately think to myself ˈanzats. I map a onto a and syllable-initial prevocalic s onto z. This is not appropriate for English, where a maps onto æ and syllable-initial s onto s. I have to force myself to anglicize the pronunciation to the ˈænsæts that British mathematicians would probably say (or possibly the ˈɑːnsɑːts that I imagine American math (sic) specialists might prefer).
The only English dictionary I have to hand that contains the word is the on-line OED. which confirms ˈænsæts as the pronunciation. There’s a Wikipedia article on the subject, but it shows no pronunciation.
And what would we say if there were more than one ansatz? What is its plural? Again, my German is good enough to expect it to be Ansätze ˈanzɛtsə (yes, I’ve checked, it is). But when we borrow occasional German words into English we don’t usually at the same time borrow their plural forms: though we may sometimes refer to a wunderkind ˈwʌndəkɪnd in English (cf German ˈvʊndɐkɪnt), we never speak of wunderkinder, and we get embarrassed about what to call the Länder of the Federal Republic. So I suspect that if you make more than one ansatz in mathematical discourse they’ll be ansatzes ˈænsætsɪz.
A few more pages later in the book, I did have to skip over Schrödinger's equation. (In calculus I didn't get as far as partial differentials.)