A young, Argentinian mathematician visiting the UK is drawn into a murder mystery when his landlord (a woman who had worked as a code breaker during World War II) is killed. A clue and the words "The first in a series" are left in the mailbox of Oxford maths professor Arthur Seldom, who plays Holmes to the Argentinian's Watson. As it turns out, Seldom is a logician who has published a book on the difficulty of predicting the next term in a mathematical sequence. (In fact, it is important to note that there is no unique right answer to such questions.) So, one would think that Seldom would be the ideal person to find a serial killer who leaves mathematical clues. Unfortunately, he is also an expert on Gödel's theorem and knows that it may not be possible to resolve the mystery at all!
This book was very popular in its original Spanish, and has been translated and released in many others. However, reviews of the English version seem to be mixed. Some claim that the characterizations and writing are poor, while others claim that the reviewers who are complaining simply don't get it.
I can see why the reviews have thus far been mixed. Although it seems to be quite well written to me, a reader who is not interested in mathematics may miss some of the most interesting parts. In particular, the importance of Gödel's theorem may limit the appeal of the book to general audiences. It turns out that the character of Seldom has proved a result in mathematics that is analogous to Heisenberg's Uncertainty Principle in quantum mechanics. In particular, in this (fictional) theorem of Seldom, it is shown that any axiomatic system has a "macroscopic" domain where true statements can always be proved and a "microscopic" regime in which the "uncertainty principle" applies and Gödel's observation that some true statements are unprovable takes effect. Since Martinez is a logician himself (click here to see a list of his papers if you subscribe to MathSciNet), it is not surprising that this is an intriguing (if not entirely believable) piece of fictional mathematics. But, Seldom goes further, applying the same idea to other fields involving logic, including philosophy and even criminal law.
The book mentions Andrew Wiles' proof of Fermat's Last Theorem (which the book perhaps more accurately but less standardly calls "Fermat's Last Conjecture"). As it turns out, Seldom is one of the organizers of the session at Cambridge in which Wiles announces his proof and this is a running subplot. However, I was rather disturbed by the claim in the book that one of the characters (a Russian mathematician) originally proved a key step in achieving the results but gets no credit for it since the result is stolen by another mathematician (an unnamed student of Seldom's) who wins a Fields Medal for it! Now, whichever version of the story you believe (one side claims that the Russian's proof had a flaw in it while the Russian himself says that its only flaw was that it was not in English), this is unlike any true story of plagiarism in mathematics that I have ever heard and I fear that it is insulting to the field of mathematics and to the Fields medal to suggest that such an act of plagiarism could not only occur but be so rewarded.
My only real complaint about the book is that the plot becomes so contrived that it is difficult to believe. There are so many unexplained coincidences that one must accept to believe the story as told that it becomes almost a fantasy in the end. Now that I think about it, several other (nonmathematical) books I've read by authors from South America seem to be like that...perhaps it is just their style!
The 2008 film adaptation starring Elijah Wood and John Hurt was very faithful to the book. Since I have already discussed the book, I will focus on the differences. The main character became an American rather than an Argentinian and "Fermat's Last Conjecture" mysteriously became "Bormat's Last Theorem", even though everything indicates that it is still FLT (e.g. references to elliptic curves, Taniyama Conjecture, 1993, Cambridge, etc.). It is not surprising that some things were left out of the film, such as any discussion of Seldom's Theorem. Also, for some reason, the apparent sexism of the movie bothered me more than the book. All of the mathematicians and academics shown are men, and the two young women are there essentially as sex objects. Moreover, it bothered me that the sex and freedom that they represented was presented as being somehow incompatible with the intellectualism and mathematics of Seldom. Of course, like the book, the film seems unconcerned with the unlikely coincidences that the plot depends on. Finally, there were a few scenes in which the dialogue was a bit stilted. Despite all of these complaints, I thought it was a good film, interestingly directed and thought provoking, and worth seeing.
Two of the mathematician characters seem to be quite a bit "crazy": a student of Seldom's who becomes convinced (from anomalous experiments with children about logical series) that he should lobotomize himself with a nail gun. Also, the Russian character who claims to have played an unacknowledged role in the proof of Fermat's/Bormat's Last Theorem seems quite a bit "unhinged". So, I'm checking the "insanity" box in the list of motifs below.
Contributed by
Alejandro Satz
I have read "The Oxford Murders" in the original Spanish, "Crimenes imperceptibles". (I am an Argentinian student doing a PhD in Mathematical Physics in Britain, so naturally the book had a special appeal to me). It is a good mystery with a surprising double twist at the ending, although critics may have a point in that the character construction is not very deep. It has lots of mathematical references: Godel's Theorem, the Pythagorean sect, Fermat's Last Theorem (which yes, is proved by Wiles during the timeline of the book), Wittgenstein's philosophy of mathematics, and more. A good read.

Contributed by
allcarbon
I enjoyed the book too  its well written and concise (like many mathematical solutions). I only wish there was more of an introduction or preface that described what to read next for the nonprofessional mathematicians who want to read more about the theorems/concepts mentioned in the book. Perhaps other readers can help on this one.
Now for the main reason that I am posting this review: it is driving me nutty not to know the answer that Seldom intended to the M heart resting on a underline 8 ... what is next in this series (as we know from the book there is rarely just a unique one answer)?
Its especially hard as I know that the book hints that "the" answer is very simple! "Symmetry" is also mentioned in the book as the key to the solution  despite knowing both of these, I cannot predict what would be the most obvious choice for the next in the series.
Someone please suggest some solutions with reasons of course!

I am quite certain that I know the answer the author intends for the "M heart 8" puzzle, though a key point of the book is that there is no one "right answer". However, I do not want to just give it away since it would spoil the fun. Instead, I will offer three clues. If, after these three clues, you still need further assistance, just click here for even more help. Here are the clues:
 The next symbol in the sequence would again look like an M, but this time with a horizontal bar through the middle that just touches the point of the "v" shape.
 Symmetry is very important. Each of these symbols is symmetric about some axis, and you need to make use of this symmetry.
 As the book says, the sequence is very simple. In fact, it is one of the simplest sequences you know...it's just been "dressed up" a bit so that you don't recognize it.
Well, that's it. I think you should be able to get it now with those clues...but give yourself some time to relax and think about it. Remember, mathematicians sometimes have to spend years working on a difficult problem! 
Contributed by
Anonymous
Finished this book (novella?) yesterday and found it a really good read both for the story and the settings. I agree there are an unbelievable number of coincidences but the whole is very involving. Perhaps it had special appeal because I studied maths at Oxford!

Contributed by
Ros
As a nonmathematician, I found the frustration and challenge of trying to grasp the mathematical concepts a pleasing metaphor for the "whodunnit" puzzle. But the mathematical content was also a smokescreen to compensate for the under developed characters, most significantly that of the grand daughter.

Contributed by
Anonymous
i read the book very quickly, but i had the distinct impression that we (the readers) were supposed to understand that the solution to the murders was not as Seldom finally confessed ...that if we had been reading closely we would be able to infer another ending... can't be bothered working it out myself...but if there are any clever sticks out there who have any ideas i would be interested in hearing them.
J

Contributed by
Sandro Caparrini
Here is what I've found in the `News' section of the latest issue of
Shivers, a British magazine dedicated to horror movies:
"Spain's Tornasol Films is backing the second Englishlanguage foray of Spanish
cult director Alex de la Iglesia, the man behind Accion Mutante and Day
of the Beast. Oxford Murders is a serial killer thriller set against
the esoteric world of mathematics at Oxford University. The bloody thriller is
based on an awardwinning novel by Argentinian writer Guillermo Martinez,
himself a former mathematics student at Oxford. De la Iglesia's first English
language film was Perfect Crime, still unreleased outside Spain where he
recently won a topo director award at the Sitges Fantasy Festival. He is
currently working on the Oxford Murders script with his longtime writing
partner Jorge Guerricaechevarria."
Sounds interesting!

Contributed by
Sam Burne James
I maybe got slightly bogged down with the maths, because it's something i have only slightly more than a passing interest in so the book maybe wasn't the natural thing for me to read. Otherwise, I found it very unique and a good work overall, hence my vote of 3 out of 5  although i'd have given it 3.5 if i could!

Contributed by
Caroline Hunt
Addendum to your math fiction list: The Oxford Murders is now available in this country and in Canada (MacAdam/Cage, 2005). As of its last listing, prospective readers would have to get the U.K. version—but not any more.
It also seems to have won something called the Planeta prize, but I don't know what that is.
Speaking as definitely a “general reader,” I did not find the mathematical content at all offputting (as at least one of your reviewers thought likely). Everything was well within the range of what any ordinary person would know.
Not as good as the fractal book, though.

Contributed by
Anonymous
Well, I think the book is very good. I read a lot of comments about it and I donÂ´t understand why most of people try to find something wrong or something out of order. In my experience those things occurs when something is good. Why donÂ´t people try to find something wrong in a novel by Agatha Christie, or Conan Doyle, or even Poe? For me is very important that this is a mystery novel written before those great writers and before a thousand of good mystery novels and there is no copy in the way the mystery is solved, I mean that there is nothing that we can find in another mystery novel written before, and that is a great thing.
I have to say that I am from Argentina and perhaps I am not been impartial, but before my patriotism I am a reader.
Sorry for my bad english.

Contributed by
simon
The whodunnit is as easy as one two three

Contributed by
Gireesh
An excellent read and very thought provoking  especially the section on logical reasoning tests. That section also made me realise that the answer to the M heart 8 puzzle is not necessarily what has been suggested here. I guess you need to be in "prime" form to see other solutions!

Contributed by
Vaughan Pratt
BTW What did the author intend us to get out of the sequence (1, 3, 9, > 81)? It looks like powers of three, except that the third power is missing, or is it the squares of powers of three with an extra term of 3 > thrown into it? Either way, it doesn't quite make sense to me.
Right. I think he started out with powers of 3 and then when he got to 9 he thought he'd squared 3 (as opposed to multiplying 3 by 3) which switched him to that rule instead. Very cute example of someone remembering what he was doing by looking only at the most recent step and reconstructing the rule each time, which at 3 > 9 was ambiguous. Since 9 > 81 is unambiguous (multiplying by 27 being very unlikely) the next number has to be 6561.

Perhaps this sequence was intended to disturb since it looks so close to being sequential powers of 3. But, of course, there are lots of things it could be. My problem with these sorts of questions may be that I have too good of an imagination and can generally think of many possibilities with no clear "best" answer. For instance, {1,3,9,81,...} could be the powers of three with every fourth element skipped. (So the next term could be 243.) It could be the sequence {a_{1}, a_{2}, a_{3}, ...} where a_{i}=3^{p(i)} and p(x) is the polynomial (x^{3}6x^{2}+17x12)/6. (Then the next term would be 6561.) It could be that {f_{1}, f_{2},...} is the Fibonacci like sequence in which f_{i+2}=1+f_{i}+f_{i+1} that starts with f_{1}=0 and f_{2}=1 so that f_{3}=1+0+1=2 and f_{4}=1+1+2=4 and then the sequence here is 3 raised to the power of this sequence. (Then the next term would be 2187.) Another one is that the sequence could start with an arbitrary a_{1} (which in this case is 1) and then the rule is a_{i+1}=a_{i}*3^{(i2)!}. (In that case, the next term would be 59,049.) Or perhaps, as you've suggested, the author intended to be doing something much more obvious and just made a mistake.
Contributed by
Vaughan Pratt
I see what you mean about having "too good of an imagination," that's quite an impressive list of possibilities, albeit somewhat contrived. Here are two more, both relatively natural I think.
1. Number of labeled trees with 3colored nodes. (There is 1 empty tree, one onenode tree A (A being the label, not the color) hence 3 colorings, one twonode tree AB hence 9 colorings, and 3 threenode trees ABC, BAC, ACB each having 27 colorings. There is only one unlabeled threenode tree, which is the smallest size of tree where labeling makes a difference. These are trees in the sense of connected acyclic undirected graphs, enumerated for n >= 2 by n^(n2), not rooted oriented trees of the kind computer scientists are used to.)
This example is also good to keep in mind, with 2 colors instead of 3, whenever someone throws you the sequence 1, 2, 4, 24, 256 and you find yourself scratching your head about that factor of 3 in 24now you know.
2. He originally had just 3,9,81 but then had to prepend 1 following the rule of prepending 1 when not already there used by Neal Sloane in the 1970s for submitting sequences to his Encyclopedia of Integer Sequences, now at
http://www.research.att.com/~njas/sequences/Seis.html
Sloane seems to have dropped this rule completely since if you submit 3,9,81,6561 it gets the right answer but if you prepend 1 per the old rule and ask about 1,3,9,81,6561 it fails to recognize it. However if you then drop 6561 it gets the tree enumeration above, which I wish I'd come up with. :)

Contributed by
Hauke Reddmann
T.O.M. (German "Die PythagorasMorde") makes up a nice
study in unintended selfreferentiality. I seldom read crime novels
because my instinct always knows the murderer way before my
logic, this book making no difference (I even correctly
doubted whether a murder happened at all). So my only
joy is finding out the "why" at the end (and bitching that the
solution is a nonsequitur, relies on too many coincidences
or both). In fact, Martinez describes a minority of guys
who constantly fail at IQ number series tests because they
find some creative solution not intended. He must mean me 
when Martinez came up with "the tetrakys" I began to hum
a song by "2 Live Crew" ;) because I had something complete
other and completely logical in mind. And that even considering
there will be a tetrakys on the cover of my Great Forever Unfinished
Novel [tm] so I should have known better!
Conclusio: I'm still waiting for a worthy successor to
"Landscape With Dead Deans" when it comes to crime&university.

Contributed by
Peter Matthews
Re ‘M heart 8' how about —
M encloses no spaces,
Heart encloses one space
8 encloses two spaces
So the next one must enclose three spaces — so two intersecting circles.

Peter, I guess the point of the sequences in the book is that there is no one correct answer for the continuation of the first few terms in a sequence.
So, it is not surprising that you are able to come up with an alternative. Indeed, the number of distinct regions enclosed by the lines does increase by one each time in the sequence given.
Note, however, that the second term is not just a heart, but a heart sitting on an underline. Note also that two intersecting circles is not the only shape that encloses three separate regions. (A box divided into thirds by vertical lines, three circles in a row, three triangles, etc. could also be the next term in the sequence.) Since your characterization leaves so much free choice and does nothing to explain the mysterious underline beneath the heart, it is not a very satisfying answer.
Contributed by
Peter Matthews
I agree on all points. I only adduced it to make the same point that as you say, the book does, that ‘valid' is one thing — I think that my answer is that — but ‘satisfying' is quite another — and I agree, my answer is not. So this particular type of puzzle has more to do with psychology than mathematics.

