On Monday, Quanta magazine released an article on a man who transformed the way we do particle physics: Stefano Laporta. I’d tipped them off that Laporta would make a good story: someone who came up with the bread-and-butter algorithm that fuels all of our computations, then vanished from the field for ten years, returning at the end with an 1,100 digit masterpiece. There’s a resemblance to Searching for Sugar Man, fans and supporters baffled that their hero is living in obscurity.
If anything, I worry I under-sold the story. When Quanta interviewed me, it was clear they were looking for ties to well-known particle physics results: was Laporta’s work necessary for the Higgs boson discovery, or linked to the controversy over the magnetic moment of the muon? I was careful, perhaps too careful, in answering. The Higgs, to my understanding, didn’t require so much precision for its discovery. As for the muon, the controversial part is a kind of calculation that wouldn’t use Laporta’s methods, while the un-controversial part was found numerically by a group that doesn’t use his algorithm either.
With more time now, I can make a stronger case. I can trace Laporta’s impact, show who uses his work and for what.
In particle physics, we have a lovely database called INSPIRE that lists all our papers. Here is Laporta’s page, his work sorted by number of citations. When I look today, I find his most cited paper, the one that first presented his algorithm, at the top, with a delightfully apt 1,001 citations. Let’s listen to a few of those 1,001 tales, and see what they tell us.
Once again, we’ll sort by citations. The top paper, “Higgs boson production at hadron colliders in NNLO QCD“, is from 2002. It computes the chance that a particle collider like the LHC could produce a Higgs boson. It in turn has over a thousand citations, headlined by two from the ATLAS and CMS collaborations: “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC” and “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC“. Those are the papers that announced the discovery of the Higgs, each with more than twelve thousand citations. Later in the list, there are design reports: discussions of why the collider experiments are built a certain way. So while it’s true that the Higgs boson could be seen clearly from the data, Laporta’s work still had a crucial role: with his algorithm, we could reassure experimenters that they really found the Higgs (not something else), and even more importantly, help them design the experiment so that they could detect it.
The next paper tells a similar story. A different calculation, with almost as many citations, feeding again into planning and prediction for collider physics.
The next few touch on my own corner of the field. “New Relations for Gauge-Theory Amplitudes” triggered a major research topic in its own right, one with its own conference series. Meanwhile, “Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond” served as a foundation for my own career, among many others. None of this would have happened without Laporta’s algorithm.
After that, more applications: fundamental quantities for collider physics, pieces of math that are used again and again. In particular, they are referenced again and again by the Particle Data Group, who collect everything we know about particle physics.
Further down still, and we get to specific code: FIRE and Reduze, programs made by others to implement Laporta’s algorithm, each with many uses in its own right.
All that, just from one of Laporta’s papers.
His ten-year magnum opus is more recent, and has fewer citations: checking now, just 139. Still, there are stories to tell there too.
I mentioned earlier 1,100 digits, and this might confuse some of you. The most precise prediction in particle physics has ten digits of precision, the magnetic behavior of the electron. Laporta’s calculation didn’t change that, because what he calculated isn’t the only contribution: he calculated Feynman diagrams with four “loops”, which is its own approximation, one limited in precision by what might be contributed by more loops. The current result has Feynman diagrams with five loops as well (known to much less than 1,100 digits), but the diagrams with six or more are unknown, and can only be estimated. The result also depends on measurements, which themselves can’t reach 1,100 digits of precision.
So why would you want 1,100 digits, then? In a word, mathematics. The calculation involves exotic types of numbers called periods, more complicated cousins of numbers like pi. These numbers are related to each other, often in complicated and surprising ways, ways which are hard to verify without such extreme precision. An older result of Laporta’s inspired the physicist David Broadhurst and mathematician Anton Mellit to conjecture new relations between this type of numbers, relations that were only later proven using cutting-edge mathematics. The new result has inspired mathematicians too: Oliver Schnetz found hints of a kind of “numerical footprint”, special types of numbers tied to the physics of electrons. It’s a topic I’ve investigated myself, something I think could lead to much more efficient particle physics calculations.
In addition to being inspired by Laporta’s work, Broadhurst has advocated for it. He was the one who first brought my attention to Laporta’s story, with a moving description of welcoming him back to the community after his ten-year silence, writing a letter to help him get funding. I don’t have all the details of the situation, but the impression I get is that Laporta had virtually no academic support for those ten years: no salary, no students, having to ask friends elsewhere for access to computer clusters.
When I ask why someone with such an impact didn’t have a professorship, the answer I keep hearing is that he didn’t want to move away from his home town in Bologna. If you aren’t an academic, that won’t sound like much of an explanation: Bologna has a university after all, the oldest in the world. But that isn’t actually a guarantee of anything. Universities hire rarely, according to their own mysterious agenda. I remember another colleague whose wife worked for a big company. They offered her positions in several cities, including New York. They told her that, since New York has many universities, surely her husband could find a job at one of them? We all had a sad chuckle at that.
For almost any profession, a contribution like Laporta’s would let you live anywhere you wanted. That’s not true for academia, and it’s to our loss. By demanding that each scientist be able to pick up and move, we’re cutting talented people out of the field, filtering by traits that have nothing to do with our contributions to knowledge. I don’t know Laporta’s full story. But I do know that doing the work you love in the town you love isn’t some kind of unreasonable request. It’s a request academia should be better at fulfilling.