One of the abiding pleasures of the history of art is its “whodunnit” aspect. It sometimes appears as if hardly a month goes by without some dramatic discovery, and seemingly it is an unwritten rule that the greater the artist, the less readily the scholarly community accepts the newcomer into the fold. Of course, if the work in question lives in a museum, then the change of name makes no difference to its value. If it is the still much-debated Leonardo Salvator Mundi, then it makes $450 million-worth of differences; I am proud to report that the record bribe I have thus far turned down for an attribution is £1 million.

The kinds of works of art discussed here (which should be readily findable via Google Images) will all be Old Masters. In the main, the older the work, the harder it is to be sure what it is. No doubt forgeries of contemporary pieces are rife, but it is certainly a huge advantage to be able to ask a living artist if he or she was responsible for a given work. In the case of a Botticelli or a Michelangelo, they are no longer in a position to help us out. Since the area I know best is the Italian Renaissance, my examples will be drawn from that period. Many of my case studies will relate to discoveries or proposals I have put forward, not for egomaniacal reasons, but rather because in such instances I am able to speak authoritatively about the thought processes involved.

Attribution revolves around authorship, originality, and authenticity, and I will attempt to explain not only how they may at least sometimes be established, but also why authorship is by far the trickiest of the three. By a nice coincidence, it is also the one that has the most dramatic consequences in the big bad world where the ivory tower bumps up against the dollar sign.

The two ways of attempting to approach these related problems are through more or less secure proofs, above all scientific and documentary, and through the judgment of the eye. It is not hard to understand why the former seem more reassuring. A story I was told by an old friend may serve as a cautionary tale regarding the limits of connoisseurship. One day my friend went into the office of the then Director of the V&A, the formidable Sir John Pope-Hennessy (invariably known as the Pope), and found him holding a small bronze in his hand. “This”, Pope-Hennessy explained, “is Benvenuto Cellini’s modello for the head of Medusa in his statue of Perseus in Florence.”

He went on to reveal that he had just acquired it for the museum and boasted about how little he had paid for it, at which my friend said, “But that’s highway robbery” or words to that effect. Pope-Hennessy was clearly delighted, and riposted, “Yes, indeed. But, then again, it is only a Benvenuto Cellini because I say it is.” As it happens, nobody subsequently appears to have disagreed with this particular instance of papal infallibility, but self-evidently such ex cathedra pronouncements fall far short of Karl Popper’s criterion of falsifiability and are all too rife in the murky world of attributions. What is more, it hugely suits the market — win or lose — to designate a single individual as the world expert on a particular artist.

In the context of old art, various scientific and technical tools to establish the approximate age of artifacts have been developed. Two relate to radiocarbon dating of ivories and dendrochronology for wood. Both methods are generally reliable in determining when the elephant — or walrus or narwhal — died or when the tree in question lived. In consequence, such tests are as a rule all but foolproof in determining the age of the raw materials, which admittedly is not quite the same thing as the date of their transformation into works of art.

The term “originality” is arguably less straightforward, but is normally understood to refer to prime originals and to distinguish them both from all but contemporary copies and from later ones. Here, too, scientific investigation can prove to be of immense value. Both x-ray analysis and infra-red reflectography have the potential to reveal what is underneath the surface of paintings and, above all, changes of mind both subtle and radical. There may be all sorts of other kinds of reasons for believing Jan van Eyck’s Arnolfini Wedding to be an original, but the remarkable network of modifications revealed by infra-red reflectography represent a species of proof. The same goes for Raphael’s Madonna of the Pinks, likewise in the National Gallery, where the changes of mind are altogether less radical, but where, once again, infra-red reflectography discloses the fact that one of the toes of the Christ Child’s right foot was originally underdrawn in a different place.

In the field of drawings, features such as what are known as Klebkorrekturen, where additional bits of paper are stuck onto sheets to effect a change of mind, are pretty overpowering indications of originality. A good example, because it occurs on a meticulously detailed sheet, is found on a drawing by Mantegna I discovered in Munich, a final study for his engraving of the Risen Christ between Saint Andrew and Longinus, where the head of Christ has been cut out and reinserted at a slightly different angle. It had previously been regarded as a copy after the print.

Strictly speaking, none of these approaches is of any real use in establishing authorship, as opposed to originality and authenticity. The reason is very simple: even the most lonerish artists have almost invariably been surrounded by apprentices, pupils, and hangers-on who ape their style, and will have used exactly the same raw materials as their masters. Moreover, there are any number of examples of works which are uncomplicatedly agreed — sometimes on the basis of documents, sometimes on the basis of the judgment of the eye — to be by more than one hand. A contract and other documents indicate that the National Gallery version of the Virgin of the Rocks (the other one is in the Louvre) and its two flanking Angels were done in conjunction with a Milanese artist called Ambrogio de Predis, and much ink has been spilled not only over which of them did what, but also to suggest that still other hands were involved. Elsewhere, close attention to detail and a sense of quality makes it hard to doubt that in a Portrait of Camilla Gonzaga and Her Three Sons by Parmigianino in the Prado, one of the boys is by another — and palpably inferior — hand.

Identifying an artist’s hand is not so very different from recognising a friend’s voice on the phone, a piece of music when you switch on the radio, even — for the great experts who can bring it off — not just the château but also the vintage of a fine wine. It is also usually both instant and entirely instinctive. Conversely, all the technical data in the world can only ever determine an approximate date, not what separates Rembrandt and Vermeer from — as it were — Kevin Rembrandt and Barry Vermeer. This is also the problem with the now basically discredited approach pioneered by Giovanni Morelli (1816-91), who argued that individual artists unconsciously depict minor physiognomic details such as earlobes in a unique way, since his method has no way of discriminating between an original and a faithful copy.

Having referred to documents, it seems logical to proceed next to discuss the extent of their value. The first thing to observe is that remarkably few works of art of any antiquity have what might be described as the double advantage of a documented beginning and an uninterrupted subsequent history up to the present day. Among those that do are a number of frescoes, which as a rule — although even then there are occasional exceptions — have not moved about. A straightforward case in point is Michelangelo’s Sistine Chapel ceiling, where we have evidence of an agreement in 1508 between Michelangelo and Cardinal Francesco Alidosi on behalf of Pope Julius II, various records of payments, and a known completion date of 1512.

When it comes to the other main public staple of Italian Renaissance art, namely altarpieces in churches, the number of paintings for which we are in possession of both a contract and a continuous history is very significantly fewer, but there are of course some. However, even the artist’s signature is not an unimpeachable proof of authorship, given the degree to which artists collaborated. Indeed, some works were explicitly team efforts: they may even have double signatures, but these do not reveal precisely who did what. In the very particular case of Titian’s last altarpiece of the Pietà in the Accademia in Venice, the inscription states “that which Titian left unfinished was reverently completed by Palma [Giovane]”. Similarly, single sheets of paper can be drawn on by more than one artist: a Michelangelo drawing in the Ashmolean in Oxford reveals the clumsy efforts of a pupil to copy the master, with one of the profile heads being by each of them and only three of the 11 eyes being by Michelangelo.

The vast majority of smaller-scale religious paintings, not to mention mythologies and portraits, are incomparably harder to trace back to any evidences of their creation. By no means all of them were formally commissioned, since artists produced work off the peg — so to speak — as well as made to measure. Even those that were commissioned — as portraits almost invariably were — were also less likely to have been designed for very specific locations within the home. All these types of works also tend to be less discussed at the time, and to move around more over the centuries, and they are therefore in even greater need of being attributed.

It is more rewarding to find a hitherto unrecognised work by a favourite artist than to demonstrate why something is not by someone, but giving something the thumbs down can on occasion be more uncomplicatedly definitive. Some years ago, as I was walking round an exhibition in Bologna devoted to a local artist called Amico Aspertini, I was incredibly struck by a hitherto unpublished picture from a private collection that seemed to me blatantly not to be by him. Something about the composition instantly rang a bell, and I pretty swiftly — but in that case not immediately — realised that it was based on elements of a painting by Pieter Bruegel the Elder in the Courtauld Gallery. In view of the fact that Aspertini died in 1552, and Bruegel’s painting is dated 1565, the idea that it might be by the former consequently went up in smoke. When my observation was published, I am reliably informed that — understandably enough — I became public enemy number one with the owner of the work, a well-known and now deceased Italian crooner.

Turning to drawings, the number that are absolutely definitely by particular artists is microscopic.

Renaissance contracts not infrequently make reference to drawings by the relevant artists being physically attached to them, but these have almost invariably gone their separate ways over the centuries. An exception is an unimpeachable contract drawing by Francesco Vanni in Worcester, Massachusetts, which is connected with his altarpiece of Saint Ansanus Baptising the People of Siena.

It has an autograph declaration written by the artist countersigned by an ecclesiastical official on its reverse that refers to the contract.

In the case of a drawing by Raphael in Lille, there is an autograph note on the reverse addressed to an associate of his called Domenico Alfani, who subsequently executed an altarpiece based upon this very sheet. It is worth noting in passing that this is as good a case as one could wish for of the authorship of a preliminary drawing not being any sort of guarantee that a related painting is by the same hand. More generally, however, the fact that a drawing relates to a known painting can be a good indication of who did it, especially if either a rare subject is involved or the pose of an individual figure matches up almost perfectly.

With Renaissance sculpture, and in particular bronze sculpture, by the time of L’Antico, operating in Mantua around 1500, not to mention Giambologna in the second half of the 16th century, statuettes were as often as not planned to be multiples, and there is certainly no guarantee that the first cast is the best. Intriguingly, there is solid evidence in the form of a letter to his patron Ottavio Farnese, Duke of Parma, that Giambologna — whose judgment is not to be sneezed at — preferred his bronzes not to be polished up — “chased” is the technical term — within an inch of their lives.

All the technical data in the world can only ever determine an approximate date, not what separates Rembrandt and Vermeer from – as it were – Kevin Rembrandt and Barry Vermeer.

The piece he is writing about is a two-figure Rape of a Sabine group in Naples, which is indeed very different in its degree of finish from another version in Vienna. Conversely, there are models of Giambologna bronzes, cast by Antonio Susini and bearing the latter’s initials, which are supremely refined and for which there was evidently a taste.

Moreover, even the finest visual memories are going to be challenged by the task of comparing a cast in one collection with its counterparts elsewhere, not least because photography is a distinctly imperfect guide to the actual appearance of a work of art, and a fortiori one in three dimensions. In the 1978- 79 Giambologna exhibition, a concerted effort was made to assemble a group of casts of various pieces. Charles Avery, one of the organisers of the show, subsequently expressed the disarming opinion that “even the direct juxtaposition of different examples of the same model failed to provide simple and satisfactory conclusions, except in a very few cases”.

Being able to compare an original with a copy is also as a rule immensely helpful, and there are many instances of works hitherto believed to be originals being demoted thanks to the reappearance of the real thing. In my Correggio monograph of 1997, I assumed the version of his celebrated Mary Magdalen that vanished from Dresden in 1945 must have been autograph, but earlier this year I published what I am sure is the rediscovered original, and the Dresden picture all of a sudden seems a blatant copy.

In somewhat the same fashion, being able to connect a preparatory drawing and a painting for which it is a study is often incredibly helpful: in the mid-1990s I identified a Parmigianino portrait of a Knight of Malta in the gallery in Hanover from far across the room before I could see it close to, for the simple reason that I knew his related first idea on paper and immediately recognised both the sitter’s features and the Maltese cross on his chest. The same process can also work the other way round, and lead one back from a finished painting to a preliminary drawing.

Mention of the perils of relying on photography to make judgments about all these matters should also be balanced by a mild corrective. In an ideal world, the original is obviously what one prefers to study, but it is a gross exaggeration to claim — as some people do — that nothing else will do. In a world where every year I receive literally hundreds of unsolicited email requests for opinions, accompanied by jpegs, it would be almost unbearably exhausting not to reply before seeing the original. In any event, the truth is that works that are right as rain or absolute stinkers are not all that hard to spot — only the middle ground is less straightforward. It is also worth pointing out that in some cases — and notably with works destroyed in the Second World War, the Correggio perhaps being the exception that proves the rule — a decent photograph is all one has to go on at this point, but it is usually perfectly adequate, as in the case of Caravaggio’s Saint Matthew, formerly in Berlin.

There remains the thorny issue of the monetary value of attributions, and indeed of advising collectors whether they should buy particular works. Long, long ago, it was pretty standard for experts to be paid for their opinions: Bernard Berenson notoriously had a clandestine arrangement with Joseph Duveen, based upon getting a percentage of the sale price, but also advised collectors, on occasion encouraging them to make acquisitions in which he had a financial stake.

When my opinion was published, I am reliably informed that I became public enemy number one with the owner of the work, a well-known and now deceased Italian crooner

Pronouncing by writing on the backs of photographs was another favourite approach, which did at least mean that a letter authenticating one Madonna could not be repurposed to sell a completely different one. Nowadays making a killing is definitely frowned upon, but that does not mean nobody does it. Some people adopt a less venal approach, and simply ask for an unchanging flat fee and/or travel expenses.

I refuse even the latter and either wait until I am in the right place or require the work of art to be brought to London for inspection. The reason for such caution is straightforward: sometimes one feels poised on a knife-edge between saying yes and saying no, and it is pretty obvious which way one would incline if looking on the bright side would cause one’s bank balance to bulge. After all, the prospect of the professional glory of making a mega-discovery is often more than enough to make people suspend their disbelief, even when money is not involved. A donation to a good cause is a completely different matter, and I now tell people who want to show their gratitude that they might like to support the university department in which I teach. I never specify how much they should give.

It is unsurprising that giving works the thumbs-up can make one distinctly popular and understandable that turning things down sometimes obliges one to suffer the rage and fury of grumpy owners or dealers. Much the most amusing reaction I have ever experienced consisted of an anonymous typed letter, which was accompanied by a roll of loo paper whose outside is adorned with images of £20 notes stylishly modified so as to replace the Queen’s head with that of the Mona Lisa. The letter reads as follows:

Distinguished and Emeritus Dr. David Ekserdjian,/This is what you can do with your “opinion” on Leonardo …/Wipe your “ASS” with it!!/Regards,/An Admirer …

It is one of my most cherished possessions.