KDP for an e-book; CreateSpace for print. Doesn't matter if your friend's book is one of a kind or not ... it can be pure shyte and he can still publish if he wants. And he needs to get off his derriere and set up his own account for publishing and putting in banking and tax info.
I'd caution you against setting up an account for your friend. There is tax info involved, payments to bank accounts or by cheque, etc. Are you prepared to deal with being the middle man, and the financial aspect of it? (That's if the book sells. Naturally, we'd all like the praise we think we rightly deserve, but there are millions of books on Amazon, so few get any recognition whatsoever). If your friend is able to do it themselves (or you can help walk them through it), it would be far less complicated for you.
Mathematics is one of my great passions. I wish him good luck with this book.
With that said, I think you're opening up a big can of worms if you're going to be in charge of his account. Do you really want that responsibility in the coming years? For example, dealing with the taxes, or any changes in his banking, address, etc?