"Fermat's Last Theorem" by Simon Singh

So, is it possible to write an entertaining book about mathematics, in particular, mathematical proofs? Well, it depends. If you have some inclination towards mathematics and the history of science you might really enjoy this book, like I did. It is also great if you want to brush up on some basic math in an entertaining way.

This non-fiction book is about a mathematical problem that dates back to ancient greece, where the Pythagoreans, a secretive "math club" around philosopther Pythagoras, worked on several aspects of number theory. Probably the most important discovery from that time was the theorem about the sides in a right-angled triangle that every kid in school has to memorise: 

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This relation is easy to prove (several proofs are given in the appendix of the book).The more general equation, aⁿ + bⁿ = cⁿ however is not. In fact, for n>2 there is no solution for this equation. Proving this has taken until 1995.
The French mathematician Clement-Samuel Fermat claimed a proof in 1670, but without bothering to actually write it down. It is only due to his apparent genius and other achievements that mathematicians in centuries to follow actually believed Fermat's claim. Ever since, brilliant minds have been unsuccessful in coming up with a proof themselves.
Finally, Andrew Wiles, who had become obsessed with Fermat's last theorem already as a child, and after dedicating his entire career to developing the necessary mathematical tools, solved this problem once and for all in a 100+ page long treatise.

The book takes you through the different centuries and acquaints you with the many great mathematicians who have made significant contributions to number theory and thus provided different pieces to the puzzle. You will enter the oddly fascinating world of mathematical rigour, which yields eternal truths that no other discipline of human thoughts can produce. Mathematical proofs, if done correctly, are valid forever. The pythagorean theorem is a great example for that. Also, you will get to know some of the strangest characters science has known. It is fascinating to see the passion and dedication some people invest in solving problems of "pure thought".

Simon Singh, physicist and journalist, does a remarkable job in recounting the history behind the epic struggle of solving Fermat's last theorem.  If you are interested in learning more about how math works, this book is a great starting point.

"Next" by Michael Crichton

In Michael Crichton's last book before his death in 2008, he attempted to sketch a society a few years from now, taking  the currently available methods of genetic engineering to the "next level". 

While doing this, he is not so much interested in the details of the technologies themselves, but rather in the implications they have on our society. Most of these implications are already manifesting themselves today. Take for instance the legal consequences of patenting anything from genes to entire cells. If you transfer ownership of a tissue sample taken from your body to some institution (under the pretext of advancing medical research) - does this institution own the rest of your body as well? And is it allowed to retrieve these cells from your body (or that of your relatives) in case the original sample was lost? In the novel, this leads to some absurd  bounty hunt scenarios. But gene patents which are in effect today are no less absurd, and fortunately a US court has recently decided that patents on genes are not valid, as genes are so-called "facts of nature" that cannot be owned (NYTimes). Crichton himself was a strong advocate against gene patents. Have a look at this talk he gave in 2006.

Another major theme in the novel is genetic engineering and cross-breeding performed on animals to make them more human-like.  This  implicitly raises questions on ethical treatment of animals, because the boundary between human and animal is more and more arbitrary if any number of genes could be transfered from one to the other. Try to imagine what  happened if a human-chimp hybrid boy was to be adopted by a human family and sent to school along with their own children. You just need to invent some rare gene defect to make it work. Of course some bullying can be expected.

The novel is composed of separate story lines, each of which is concerned with a different aspect of how bio-technologies impact our society. This is interesting in itself, since you can learn a lot and Crichton gives lots of references for the interested reader. But also it s maybe the biggest weakness of the novel. It lacks a coherent story and thus lacks focus. He uses the story to convey arguments in a discussion about how technology will be used in the future. He is not a writer focussing on character development. The technologies themselves are in fact the protagonists of many of his novels ("Jurassic Park" or "Prey" come to mind). 

In summary, it might not be his best novel (in my opinion), but it is definitely a good and entertaining read, especially if you want to engage in the ongoing discussions on gene patents and the like.