Why I'll Never Be a Good Speller
English spelling is notoriously...arbitrary. Any and all attempts to pin down a spelling rule will be met with at least six different exceptions - and you can be sure that the exceptions will be words that you will actually want to use. A study in English spelling is basically a study in evolutionary history. It's a study of various French invasions and vowel shifts. And, most of all, it's an exercise in brute memorization.
Contrast this with mathematics. Useful mathematical results are derived from previous mathematical results, using nothing but pure logic. A mathematical result is what it is because it had to be that way. A mathematical result simply couldn't be anything else and still make sense. Note that this is, more or less, the exact opposite of what one can say about English spelling conventions.