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Okay, lets start by setting expectations: The advertising blurb mentions ‘the life of Archimedes’, suggesting a big, dense, fictional biography via novel. No, this is a tight fairly plot-focused lighter novel taking place over maybe a single year (probably not that long).

As such, some of the most famous incidents of his life are outside the scope of the novel.

Overall, anything outside the central focus of the novel tends to be a bit simplified, and kept in relatively modern terms.

But, outside of that, this is up to Bradshaw’s usual quality. While the most famous incidents aren’t here, plenty is. There are eleven known texts by him that survive today, and bits of pretty much all of them are in here. (Since this is fairly early in his life, generally in the guise of ideas that he is starting to work out, and would presumably get formalized into his works later.) Archimedes himself is presented as unworldly, the son of a mathematician who is somewhere on the high-functioning side of the autism spectrum.

The central binding plot pillar of Syracuse being at war with Rome, and allied with her usual enemy Carthage is just one element of any that drags him into the world of practical machines—and and other grounded realities. The entire family setting around him is fiction—we just don’t know enough about him—but are essential parts of the plot. Also essential is his manservant and effective keeper when Archimedes can’t be bothered with things like money.

As with all her books, The Sand Reckoner is a very deeply character-driven book, and the cast of characters is a bit wider than normal while retaining all the charm and driven personalities of her other books. Like The Beacon at Alexandria, one of the central pillars of the book is the love of a subject. There it was medicine, here it is mathematics. And in both that love is part of the core of book, and help make it shine.

This book gave me a bad impression early on when the introduction states, “All the land taken from Mexico, historians now acknowledge, could have been acquired peacefully through diplomacy and deliberate negotiation of financial recompense.”

That’s a rather big pill to swallow. David M. Pletcher did indeed make this argument in a 1975 book (footnoted in this text), but I’m not sure how many people would agree with him, especially in 2012, when this book was written. And in fact, in the main part of the book, when Greenberg gets to it, she acknowledges that just paying Mexico for a huge swathe of its territory was pretty much impossible. Sadly, there’s also no direct engagement with the contention implied in A Country of Vast Designs that Polk was attempting to get a peaceable settlement by playing the same game of brinkmanship that he pulled off with Great Britain over the Oregon Territory. (Admittedly, the other only came out four years before this book, which would be a fairly short turn around time to talk directly to that idea.)

What we do have is an attempt to look at the Mexican-American War through the viewpoints of five people. The problem is only two were directly involved (one killed in action, and one forced through the treaty of Guadalupe Hildago), two peripherally involved, and while Polk was central to the war, he was also physically a long way away from it. So, if you want to understand the actions of the war itself, this book isn’t a great place to go, and when it is talking about that, it’s actually detracting from central parts of her book.

Greenberg is much more critical of James Polk than Merry’s Country of Vast Designs (fine enough), but you also don’t get to know nearly as much about him here, and she could really have used a better look at just how disruptive Buchanan’s actions in the cabinet were.

John Hardin is the surprise star of the book. He was a successful Illinois politician, who’s falling out with Lincoln could have permanently derailed Lincoln’s career. But he gave up his position to support patriotic fervor and went to war. His regiment was shot to pieces at Buena Vista, and he returned home for a state funeral.

Nicholas Trist pretty much single-handedly held the peace process together, and against Polk’s orders produced a treaty that no one could refuse. Merry’s book is longer and more detailed in general, so his treatment of Trist is similarly more detailed there, but there’s plenty here too.

Henry Clay’s involvement in the book is about as outsized as his entire career was. While there’s a lot of attention on the personal side, he’s also part of the political anti-war movement that Polk stirred up with his heavy-handed actions against Mexico. I would have liked to see a bit more coverage on that, though what we get is good.

Abraham Lincoln is the least present of the five people focused on in the book, despite being one of the three to make the cover blurb. There’s no accounting for fame. That said, the end of the book very much leans on him, presenting a speech from Clay that Lincoln attended on his slow way east to take his seat in the House of Representatives. Lincoln had generally stayed away from the subject of the Mexican-American War, and had concentrated his political energies on economic matters. But after this point, he becomes one of the more fiery anti-war persons in the House, making some fame with his “Spot Resolutions” (if Mexico attacked Taylor’s army on American soil, show me the spot on which it happened). The stance may well have sunk what few chances Lincoln had in politics in the short term, but also seems the start of the more morally involved career we see later.

In all, this does add up to a fairly good book. The parts do generally weave together well, and there’s a lot here, even if a lot of it doesn’t get very well developed. If you’re interested in the war itself, look elsewhere, but this shows a lot of the tensions the war generated in the United States.