This is a book for a wide audience. Not the right place for maths. But Piketty is a very respected researcher (at home and internationally), with an excellent grasp of the state of the art in econometric and economic modelling ('math'). Read his papers if you mistrust text and graphs.
I'm aware of who Piketty is. That's why I'm so surprised that he wrote such a voluminous tome with so little point. Last week before I read the book, I assumed it was just vapid reporters misunderstanding him.
If he has a paper which clearly and succinctly summarizes the point book, please point it out. Cause the book doesn't even contain a hint of that.
I haven't said anything about clearly and succinctly though; I do not know if that kind of material exist. I believe the book to be a mix of original material, existing research (as linked above), and most of all the fruit of many years of productive research on these topics.
You are of course free to not buy Piketty's thesis based on his book alone; however, to convincingly build your case to convince others, it looks like you may have to absorb a fairly considerable body of knowledge.
On a more personal note -- while I am an economist by training (doctorate obtained in early 2010s in a top 10 uni), my field was quite far from Piketty's, so I am not in a position to know with any confidence whether he's right or wrong. (I would say though that his position certainly has merit and deserves the attention it is getting.) That being said, I maintain that Taleb shows himself as disconcertingly naive and frankly quite condescending to think that he can dismiss years of research in a few witty disparaging paragraphs. (Possibly without reading the book, almost certainly without reading the research, and very definitely without looking at the raw data.)
On the other hand, Taleb has made a literary career out of busting unsound social science. He has quite a lot of practice at it. So a few disparaging paragraphs is just the surface.
What is really need is a rebuttal/response to Taleb's probability based argument.
https://docs.google.com/file/d/0B8nhAlfIk3QIbzRrRkhhc1RNY0U/...
So far as I can tell (I'm only halfway through Piketty) he has no math. Just a bunch of pretty graphs and lots of words.