Not that you can escape the maths. Our protagonists are Spain’s finest mathematicians, whose paths ultimately cross when they receive an invitation to attend an exclusive gathering organised by the elusive ‘Fermat’. The introduction of this unusual premise is handled well, and though the characters are fairly formulaic they’re framed sufficiently irreverently in opening to forgive them that and enjoy the fun. Of particular note is the rock star like adulation heaped on “Galois”, which appears to be particularly well deserved given that he has solved Goldbach’s conjecture. “Hilbert” also stands out, if only because he must surely spend his summers working as a professional Sir Laurence Olivier lookalike on cruise ships.

If it isn’t apparent by these early stages that you’ll need a large pinch of salt to get through the rest of the film, it will be when the boffins converge on Fermat’s Room. What then ensues is a series of mathematical ‘enigmas’ sent into the locked room via a mobile phone by the mysterious “Fermat”, with delayed or incorrect answers leading to the room contracting in on itself. This very quickly beds down into an utterly conventional murder (or, rather, maths) mystery rather than the kind of RAND Corporation training exercise you’d think such a scheme might entail. It also means that it will feel familiar to anyone who has watched an episode of Columbo. In fact, if you’ve seen the Mind Over Mayhem episode you’ll practically feel at home. It’s a shame really, as this fails to utilise what could have been a fairly unconventional and engaging plot device.

It also means that the characters suddenly seem utterly out of place, as though they’re the only ones who turned up to the party in fancy dress. You get a sense that even Piedrahita and Sopeña got bored of the maths, as the ‘enigmas’ recede into the background to make way for a run-of-the-mill whodunit. However, the failure to properly anchor the characters to plot removes any real sense of revelation and each new discovery tends to lessen rather heighten the suspense. Be sure to watch out for “Pascal” brake pedal story for a prime, and superbly hilarious, example.

Having said that, Fermat’s Room never outstays its welcome. Aside from the disconnect that emerges between the characters and the plot, the cast is sufficiently enjoyable and skilled, and present what they’re given with a earnestness that cannot fail but endear. In particular, the emergence of “Pascal” in the second half of the film provides a likeable cynic of a companion. As a self-declared “practical” mathematician he is as baffled as the viewer by overall scenario, and through him perhaps Piedrahita and Sopeña were signalling that we shouldn’t take it too seriously. Go into it expecting a well-executed mathematical pantomime, and you’ll not be too disappointed.

At the heart of this nosedive is 1996′s The Stendhal Syndrome, which remains probably his most divisive film. It’s certainly his most frustrating, a rag-tag mess of a film that contains that at times feels like it’s up there with his best work and at others feels plodding, inept and workmanlike.

Let’s start with the good stuff. The setup is an absolute killer. Argento’s daughter Asia stars as Italian cop Anna Manni, who suffers a rare (real-life) affliction called Stendhal Syndrome which causes her to become overwhelmed by works of art. Her pursuit of Alfredo Grossi, a serial rapist and murderer (played The Pianist’s Thomas Kretschmann), leads her to the Uffizi Gallery in Florence where she falls into a trance and collapses, leaving her in Grossi’s clutches. The opening twenty minutes is absolutely first rate; Argento’s oppressive direction of the Uffizi sequence effectively and economically conveys the impact of Anna’s unusual condition, and the dreamlike shots of her falling in and out of the various paintings are up there with his best visual gimmicks. Anna’s subsequent, traumatised attempts to both overcome her ordeal and rid herself of her affliction through painting are also well handled and visually striking.

Unfortunately Argento seems to lose interest in the Stendhal Syndrome itself less than an hour into the film – which is baffling, seeing as it is by far and away the most fascinating element. By the halfway point Anna is cured, Grossi is killed and the film seems to turn into a possession film, with Anna’s tormentor continuing to haunt her seemingly from beyond the grave. The ‘twist’ conclusion is blindingly obvious – I won’t spoil it here, but Anna’s sudden decision to wear a blonde wig and the unsubtle HIV test scene signpost it so far in advance that if you don’t work it out yourself you’re probably watching the wrong movie. The second half of the film is not only thunderingly inept, it’s thoroughly boring as well – the whole film clocks in at 118 minutes, which is really half an hour too long, especially given that Argento’s can’t sustain the initial premise for the full length of the film.

The lost potential of the setup is also reflected in Argento’s handling of Grossi himself. The director’s trademark is his suspenseful use of concealed, motif-based killers, yet Grossi’s identity is never in doubt and we see him raping and maiming his victims from the start. Not only is this uncharacteristically unsubtle and route-one for Argento (particularly unpleasant when his own daughter is playing the victim!) but it’s also a hugely missed opportunity; there’s surely much mileage in the idea of an art-obsessed psychopath exploiting a Stendhal Syndrome sufferer, but aside from a passing attempt to mirror Grossi’s smearing of his victims’ blood with Anna’s painting of herself to rid herself of her condition, he ignores this potentially profitable angle, to the film’s detriment.

Asia Argento herself has come in for some criticism over the years, but her performance is fairly serviceable, and she’s particularly effective in both the Syndrome scenes and as the terrified victim. She’s far less engaging in the second half, but given how the script unsubtly calls for her to become an enigmatic mad woman for no real reason until the end, there’s probably not much more she could have done with the material. She is, however, miscast; aged 20 at the time of filming, she looks even younger, which makes the police department’s decision to send her – solo – to another city in pursuit of a serial rapist and murderer even less believable. An older actress with greater presence might have been able to paper over some of the inconsistencies in the script, but instead she leaves the film’s flaws open for all to see.

Technically, the film ranges from good to unremarkable. The much-criticised use of CGI (it was apparently the first Italian film to do so) is indeed wretched, but is thankfully only restricted to a couple of brief shots. Argento continues his move into more naturalistic (i.e. boring) colours and composition, but some of his angles are interesting, particularly in the aforementioned Uffizi sequence, Marie’s murder in the gallery and the bizarre evocation of Alice in Wonderland as a blonde Anna runs around her apartment in a blue dress at the end (this may have been unintentional). Ennio Morricone’s score is pretty good too, wrapped around a looping motif that sounds by turns sinister and comforting depending on the context.

Argento has since claimed that The Stendhal Syndrome has an anti-censorship message, and that it was designed as a riposte to his critics: just as many of his films were cut because of the corrupting influence of their images, so Anna is overwhelmed by pictures on a wall. By a weird coincidence, in the same year Wes Craven, a director who early films were frequently cut to bits by censors, released Scream, a metatextual horror in which the killer has been depraved by horror films. But whereas this self-reflection is evident throughout Scream, it’s nowhere to be found here, and one suspects Argento made this up post-facto. The most maddening aspect of The Stendhal Syndrome is not that it’s simply bad, but that in patches it’s really good. But for the first time, Argento, once the king of leitmotif horror, can’t retain a handle on the fascinating ideas and images he sets up at the start of the film, and once he steps away from the art theme he never once offers anything interesting or developed to replace it, instead offering half-baked twists and tedious procedural drama. Sadly, The Stendhal Syndrome marks a turning point for Argento; after the halfway point he’d never make another good film again. A partially interesting failure, the film stands as both as his last gasp of greatness and the start of the terminal mediocrity that was to follow.

In many ways, the film shares traits with David Fincher’s Zodiac, released four later. Both follow serial murders that remain unresolved to this day, and this immediately creates a challenge: how do you present a rounded narrative when the story you are telling remains fundamentally unfinished? Both Bong and Fincher tackle this by making the details of the killings secondary to the effects of the investigations on those involved. Memories of Murder tells the story of rural detective Park Doo-man, who is forced to work with Seoul detective Seo Tae-yoon in solving the murders of local woman who are found raped and murdered near a field on rainy nights.

What impressed me most about The Host was its humanity, and this is even more true of Memories of Murder. Culture-clash detective stories are nothing new, but Bong’s dazzling characterisation really brings to life the awkward partnership of Park and Seo. Most impressive is the way he uses humour in unlikely circumstances to bring an extra layer of empathy to the characters; there’s nothing particularly funny about either the killings themselves or the brutal ways in which Park and his colleagues try to pin them on a string of “best fit” local weirdos (which will feel particularly resonant for UK viewers following recent acquittal of Barry George), but the exasperated desperation of the police is bravely played partly for laughs, as they scrabble around without leads, resources or procedure. In particular, the opening sequence at the scene of the crime is hilarious, as Park attempts to co-ordinate the investigation amidst chaos that borders on slapstick. Bong’s use of comedy strikes just the right tone; it’s irreverent without ever feeling tasteless or gratuitous, and humanises a cast of characters that might otherwise be simply inept or even thuggish.

Amidst the laughs, though, is a very trenchant look at the effect an unresolved crime can have on those tasked with delivering justice. Park and Seo are both changed across the course of the film by their involvement with the case and with each other. Park’s development is the more positive of the two, learning to respect the thorough practices and deductive techniques of his more urbane partner; an epilogue, set more than a decade later, shows him to be older and wiser in a nice modulation of Song Kang-Ho’s outstanding performance. Seo, on the other hand, reverts to brutality when his urban instincts fail to solve the crime; the sequence where he beats a promising but inconclusive suspect by a railway tunnel is particularly chilling. But what pervades the film most is a sense of isolation, that these are two men who have nowhere else to turn in order to stop the murderer from killing again. As with The Host, there’s an implicit criticism of the South Korean government here, made clear in the scene where Park and Seo appeal for backup only to be told that everyone’s busy suppressing a demonstration. And although the magnitude of the murders is clear, Bong remains tight in his focus, giving little indication of how the rest of the country is responding (Seoul feels like it might as well be on another continent) and thereby increasing the burden placed on the two detectives.

Unlike Fincher, Bong presents suspects but never points the finger or presents his own theories as to who the real killer is; as a result, the movie offers less closure to the viewer than Zodiac. The ending is understated but completely devastating, bringing Park full circle (literally) and leaving him a changed man, in some ways bettered but in other ways scarred by his involvement. By dint of its subject matter the film offers more questions than it answers, but such is Bong’s skill that it feels both complete and infuriatingly open in equal measure. Memories of Murder is an incredible film that lingers in the mind long after the credits have finished, a confident and assured statement from a directing talent on the rise.