I think this is a very interesting book, and it was interesting to read how they came up with their algorithm to measure the significance of historical figures. Obviously I don't agree with every ranking, but I think it does a good job overall, and it's impressive to be able to come up with an algorithm to do this.
The biggest problem I have with the book is the bias towards American figures. The authors acknowledge that the English Wikipedia (their main source of information) is biased towards American figures, but I don't think they really acknowledge the extent of it, and the text of the book is very American-biased as well. There are several chapters devoted to how their system ranks American figures in certain fields, ignoring the rest of the world, and it does very little to dispel the stereotype that Americans think that America is the world.
On the ranking bias, it doesn't seem to take into account how much America has increased as a power over the centuries. It would make sense for twentieth century American presidents to feature more highly in the rankings than older presidents because of America's position in the world. But it seems to view it from an entirely American viewpoint and presidents seem to be ranked in terms of their significance to America.
For example, it has Abraham Lincoln, George Washington and Thomas Jefferson as 5th, 6th and 10th respectively, which I would say overstates their world significance - three of the ten most significant people ever are pre-20th century American presidents according to them. Ulysses Grant is 28th despite having very little resonance outside America, whereas more recent presidents have had more of a global effect and aren't ranked as highly. If another country came to prominence as a world power in the future, would that make their past leaders retrospectively more significant? I would argue not to this extent. I would suggest that the American bias is also why Einstein (19th), who was based in America, is rated as more significant than Newton (21st).
But there are some very interesting discussions and comparisons of many significant figures of the world, and I do think that this book is for the most part an interesting read. I don't think anyone will read it and not find a lot to disagree with, but I don't think anyone could produce a list that wouldn't have this effect. But it does have Napoleon as the second most significant person ever. And he wasn't even American.
This wretched book is largely based on Wikipedia pages for historical figures. Moreover, it is based on only the English-language Wikipedia. Their rankings are patently ludicrous and arbitrary. The authors admit that their book is "Anglocentric" but nevertheless admit non-English-language figures in a meagre, derisive way, so that in the "top 50 literary figures", for example, Oscar Wilde is at number 6 (only someone who knows absolutely nothing about literature would place him in the top 50, and I say that as someone who likes Wilde), while Tolstoy is at number 22 ... two places below Stephen King! Whatever this book is, it is not scientific; or if we say it is, it gives science a very bad name.