Recent years have seen a booming interest in tracing genealogy, stoked by the television programme Who Do You Think You Are? and facilitated by websites such as Ancestry.com and RootsWeb.com. Parallel to this has been an apparently playful and increasingly popular interest in tracing one's "academic genealogy", whereby your "father" is your dissertation supervisor, your grandfather is your supervisor's supervisor, and so on. Googling the phrase yields page upon page of name strings, often running back centuries.

An academic genealogy isn't the same as an intellectual history. Intellectual history seeks to trace the influence that one thinker has on another by examining, for example, what books were in her library, what lectures he attended and whom she mentioned in letters. An academic genealogy dispenses with all this in favour of a simple mentor-mentee relationship. In terms of the analogy with genetic inheritance, intellectual history tries to trace the influence of "nurture", whereas the academic genealogist is content to draw a straight line of paternal inheritance.

It is a task made easier by the provision of internet databases that allow academic genealogists to trace far enough back through the thicket of modern scholarship to wed themselves to one of the main branches tapering into the very origins of their discipline. Take Steven Sibener, a professor of chemistry at the University of Chicago. He won a competition hosted by the American Physical Society by tracing his academic genealogy in a slightly doglegged but nevertheless unbroken line to Renaissance Padua and the Italian scientist Niccolo Leoniceno (1428-1524). Luminaries en route included Friedrich August Kekule, the founder of organic chemistry, and Robert Bunsen, of Bunsen burner fame.

Yet impressive as that first seems, the shine quickly dulls. Given the successive nature of mentoring, and the exponential growth in mentees, the chances of convergence on some or other famous figure are really quite high. These bottlenecks are a consequence of common descent: a large proportion of psychologists, for example, find themselves back with Wilhelm Wundt (1832-1920). But when you consider that Wundt more or less invented psychology as we know it, that is much less surprising. Not for nothing is Wundt known as "the father of experimental psychology". For the same institutional reasons, all trails eventually terminate with the inception of the modern universities - stopping at 13th-century Oxford, or Renaissance Italy. More difficult, you suspect, would be generating an academic lineage that did not include someone famous. Nonetheless, those who manage it seem to source a peculiar prestige from claiming Gauss or Goethe as one of their "ancestors".

³ÉÈËVRÊÓƵ

That this pride and prestige is not entirely warranted seems obvious. What's more puzzling is why so many manifestly intelligent people (they have all, by definition, earned PhDs) seem to behave as if it were otherwise.

Academic genealogies are especially popular with mathematicians. Why this should be the case isn't immediately clear. The obvious answer is that the mathematicians have at their disposal the vast Mathematics Genealogy Project (MGP) - an online database containing (as of April 2010, but growing all the time) 141,000 "ancestral" mathematicians. But this only prompts a deeper question: why did mathematicians spend so much time compiling such a database?

³ÉÈËVRÊÓƵ

The MGP was set up in the mid-1990s by Harry B. Coonce, a mathematician then at Minnesota State University-Mankato and subsequently North Dakota State University, where his successor, Mitchel T. Keller, now maintains the database. Coonce started the MGP almost as a retirement project; he has described it as a "labour of love". In the project's early days, progress was slow: Coonce initially sent out letters to institutions and scoured periodicals and obituaries, building up the database name by name. But the task became easier as the work gathered momentum and internet use expanded. Today, the project is largely self-perpetuating as new PhDs add their names to the database.

Keller doesn't see mathematics as a special case. He thinks the discipline's market lead in academic genealogy is a "historical accident" - had Coonce been a geographer, we might be talking instead of the "GGP". But there are a number of features peculiar to mathematics that have worked in Coonce's favour.

For a start, mathematics is a relatively small field. Not only does it recruit internally, attracting very few "outsiders", but, as J. David Velleman, a philosopher at New York University, points out, it also has an unusual degree of historical stability: "Mathematicians are part of an intellectual tradition that has retained its identity over centuries." For this reason, he doubts "whether any philosophical genealogy project will be interesting in the way that the mathematical project is".

Arguably, what's interesting about the other disciplines are exactly these multiple histories. The immutability of mathematics yields a very "direct" lineage: it's mathematicians all the way down. This is in contrast to most other departments, where the backgrounds of any two scholars often take very different paths - a literature professor may have a physicist "grandparent", a chemist a theologian - and it's in the branching and intertwining disciplinary histories that we can glimpse the emergence of what have become the autonomous fields of enquiry we recognise today.

Velleman's reservations notwithstanding, philosophy is one of mathematics' few rivals for disciplinary longevity, and not incidentally it boasts the MGP's only serious contender - the Philosophy Family Tree, which has more than 11,000 entries.

Randall Collins did some of this work in his enormously ambitious The Sociology of Philosophies: A Global History of Intellectual Change. But his focus on the "sociology" of philosophy - including mentor-mentee relationships - led to criticisms that formal relationships were elevated at the expense of content. Peter Munz, for example, took issue with how Collins lumped radically opposed philosophers into the same network: "If it does not matter what they are saying and why they differ, why trace the networks of who knew whom?" Munz's complaint, and it's one that applies with especial force to academic genealogy, is that this sort of formalism is content insensitive: it creates a pattern for the sake of it, an order without meaning.

It is tempting to see mathematicians as being intrinsically attracted to exactly this sort of activity - tracing genealogy by filial precursors is a way of collapsing the tangle of intellectual history into a linear numerical sequence. For the mathematical mindset, what is passed from mentor to mentee matters much less than the fact that a satisfying connection can be established according to the rules. The rules here have been set as who-supervised-whom, but it's possible to imagine many other ways to trace a lineage.

Indeed, mathematicians already have one. Their fondness for numerical connections has resulted in the concept of "Erdos numbers". Paul Erdos, a Hungarian number theorist, would generate theorems and proofs with such extraordinary frequency that he was unable to properly treat them all. He became increasingly reliant on collaborators to complete his astonishing 1,475 papers - more than any other mathematician before or since. Such was the honour of being an Erdos collaborator that even collaborating with someone who had collaborated with Erdos came to acquire a prestige. Thus, the Erdos number was created to record the "collaborative distance" from Erdos. Those who worked with him directly (more than 500) have Erdos number 1; those who have collaborated with Erdos number 1 authors have Erdos number 2 and so on. Erdos died in 1996, so the future will see low Erdos numbers becoming increasingly scarce.

³ÉÈËVRÊÓƵ

³ÉÈËVRÊÓƵ

The prestige attached to a low Erdos number has some good foundation. Erdos would co-author only with mathematicians who could keep pace, so there's a transitive qualification at work here. If you are good enough to collaborate with someone who collaborated with Erdos, then you have a sound claim that at least some of your peers think highly of you.

Something similar happens with academic lineages. Assuming that a student will seek the best supervisor he or she can acquire, and that a supervisor will accept only the most promising applicants, a loose market system will emerge that pairs the better mentors with the better students.

But given that it registers potential rather than actual achievement, the prestige attached to an academic genealogy is much less substantial. Meanwhile, as with the Erdos number, the mechanics of exponential growth mean that there is a severe diminution in whatever prestige is available with each successive step - having three or four obscure "stepping stones" on your way to the famous name leaves you a member of a group so inclusive that it would be difficult to hold a PhD and not be part of it. Mathematicians, especially, must be aware of this.

The other glaring point is that a glittering academic genealogy is no guarantee of academic prowess. Even as a proxy, it's a poor indicator. What's being passed here isn't achievement or actual prestige, but something more like a family name. Of course, the fact that people do believe that family names carry qualities through dynastic generations is one of the reasons why, in spite of the absurdity, we still thrill to find ourselves "related" to someone famous - genetically or academically.

There are many more useful ways to map influence. Bradford Paley of Columbia University compiled a "map of science" by entering details of more than 800,000 papers and charting bibliographic cross-referencing. A similar but less ambitious project is Jonathan Plucker's "History of influence in the development of intelligence theory and testing", which takes the form of a multi-branching spider diagram. There are no "stepping stones": to be a node in this nexus, you need to have been a significant contributor.

In noting how high that admission threshold is, some of the appeal of the academic genealogy becomes clearer: what is seductive about a paternal lineage is the ease with which an individual can insert himself into an august tradition.

Scientists are rather fond of repeating with a studied humility Newton's remark that his achievements were possible only because he was standing on the shoulders of giants. "Studied" because it's a rather disingenuous humility, one that directly aligns the speaker with the giants of the past and instigates a lineage through which Newton, Kelvin, Rutherford, Einstein and Bohr become - according to the "shoulders" metaphor - a "supporting cast". A successor, after all, is almost an equal.

It is a reminder that if there is something dishonest about not acknowledging influences, there is also the inverse of that problem: the retroactive alignment. The tactical acquisition of precursors. Here, then, is a more persuasive motive for the hundreds of graduates adding their names to the genealogies. By joining in, they stake a claim for a share of the inheritance, a slice of the intellectual legacy.

That sort of "inheritance" has much in common with the far more familiar, but not obviously more legitimate, practice of acquiring prestige through institutional affiliation. What else are venerable universities proving when they list their alumni? What does a researcher beginning a project at the University of Cambridge in 2010 really inherit from Newton or Maxwell? Every student and faculty member with any direct association with those illustrious forebears has long since been replaced. What torch is passed? Among both ancestors and descendants, there will be great scholars and there will be duds. Little or nothing is really carried forward - as anyone who discovers a murderer in the ancestry will be quick to point out.

The more you look, the less the genealogies seem like they are even trying to map influence or record the spread of ideas. Instead, we can see that the lineages play a primarily social role. Collins called such practices "intellectual rituals". But they are not especially "intellectual". Like any initiation rite, they strengthen group cohesion through the public declaration of community membership. When the new mathematics PhDs add their names to the MGP, they are announcing their arrival.

³ÉÈËVRÊÓƵ

These genealogies have little to do with inheritance, and everything to do with solidarity - less about what you "really" are, and more about what you want to inherit. And in that respect at least, the analogy with genetic family trees is legitimate and it is strong.

?