“Mathematician” has more phonemes than “musician.” You can count them when you see how they are written in IPA (the International Phonetic Alphabet). В принципе, это то же самое, что и транскрипция, как на tophonetics.com. One letter in IPA represents one sound. Count the letters, and you’ll count the number of phonemes. But note that symbols such as ‘ and . are not letters, so don’t include those in the count! Mathematician has 11 letters in IPA /ˌmæθ(.ə)məˈtɪʃ.ən/ Musician has 8 letters in IPA /mjuˈzɪʃən/

I count 8 for musician: m - y - u -z - i - sh - i - n (sorry, I never learned those symbols like ʃ and ə, but you get the idea)