One of the most common approaches for people writing about Thomas Piketty’s blockbuster book “Capital in the 21st Century,” about global inequality, has been to critique his theories and predictions while effusively praising his data collection. Mr. Piketty, after all, did yeoman’s work compiling data from tax and other records to try to determine a history of wealth inequality around the world.

But now The Financial Times is throwing doubt on the data at the core of Mr. Piketty’s work, in a blockbuster report that will open a new debate on how reliable the book’s excavation of historical patterns of income and wealth truly are. At issue: Is the most influential economics book of the year built on bad math?

“The central theme of Prof Piketty’s work is that wealth inequalities are heading back up to levels last seen before the first world war,” writes Chris Giles, the economics editor of The Financial Times. “The investigation undercuts this claim, indicating there is little evidence in Prof Piketty’s original sources to bear out the thesis that an increasing share of total wealth is held by the richest few.”

Here is a detailed walk-through of the problems Mr. Giles alleges, and Mr. Piketty’s detailed response. We have contacted Mr. Piketty, a French economist, and his publisher, Harvard University Press, for further comment. May 24 update: In an e-mail to me Saturday morning, Mr. Piketty wrote: “Of course I welcome open debate and new series. This is why I put everything online.”