Joël : the book you love is by S.D. Silvey, not Sylvey.
David Williams "Weighing the Odds" is a book about probability and statistics by a distinguished probability theorist. He has a great sense of humour and the book is a lot of fun. The exercises can be demanding, but they are also interesting. (I have latex solutions to many of them if you want to ask me after first trying an exercise.) Professional statisticians think this book is more maths than stats, but it does contain a lot of stats. It's an introduction that will hold your attention if you put effort into the exercises. It's aimed at advanced undergraduates, but in my opinion is also very suitable for research mathematicians (though I have my doubts as to its suitability for a professional probability theorist).
After reading and enjoying this book, a mathematician will find it much easier to get to grips with a good book on stats. But there's no substitute for trying to handle large amounts of real data, when nothing works out as it "ought" to. Learning stats without handling data is like learning maths without working out anything for yourself---it's too easy to kid yourself that you understand.