PRL has just published this paper (preprint here), with associated press release here. The press release explains that the authors have discovered how to use string theory to provide “an easier way to extract pi from calculations involved in deciphering processes like the quantum scattering of high-energy particles.”

The press release has led to stories here, here and here, as well as commentary from Sabine Hossenfelder.

As for applications of this, the press release refers to Positron Emission Tomography, while one of the stories linked above gives the more modest explanation of what this is good for:

The series found by IISc researchers combines specific parameters in such a way that scientists can rapidly arrive at the value of pi, which can then be incorporated in calculations, like those involved in deciphering scattering of high-energy particles, the release said.

**Update**: This just gets more and more idiotic as the press stories multiply. India Today now has Indian physicists untangle new pi series that could change maths forever. It would be helpful if the people who issued this press release had some sense of shame and had it withdrawn.

“The series found by IISc researchers combines specific parameters in such a way that scientists can rapidly arrive at the value of pi, which can then be incorporated in calculations”.

Is this serious? A new series for pi is interesting, especially if it converges significantly faster than any other series already known for pi. But, the comment above is ridiculous.

PHL,

There’s no claim this converges faster than any other known series. I suspect these series are not something really new, they are not being published in a math journal where relevant experts would have looked at such a claim.

I think it does not converge faster than the Chudnovsky algorithm.

To get 10 decimals of pi:

– Chudnovsky series: 1 term

– Series from the string theory paper: roughly 10 terms

That’s painful.

The precise claim made in the preprint (p. 9) is that the new series converges faster than the Madhava series for pi. Nowhere in the paper has it been claimed that it converges faster than all known algorithms.

https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

From one of the stories:

“He added that there have been many derivations of formulae over time. The formula the team has found is close to what was found by Indian mathematician Sangamagrama Madhava, which was written in the 15th century, in a poetic language.”

So what exactly that team discovered? (Apart from a 15-century poem). What they broke through?

It seems the calculation of \pi is just something they fed to the press story to attract the public’s attention to this work, and many statements written by the press seem quite silly. Would anyone from the field mind commenting on the significance of the paper (and why it’s accepted by PRL – presumably not because they managed to calculate \pi)

clueless_postdoc,

An excellent question, I was wondering the same. Seems mystifying why this was accepted by PRL, ignoring the pi nonsense.

Another question about PRL. They encourage people to issue press releases when a paper is published, but do they ever do anything when authors issue press releases misrepresenting what PRL published?

The press coverage is cringeworthy, but ridiculing the work without looking at isn’t terribly informative. The authors seem to have series for zeta(2) and pi that contain a free complex parameter. In other words, within the radius of convergence the values of the series are independent of the parameter. When the parameter is specialized to a particular value, each series reduces to a classical form: in the case of zeta(2) taking the parameter to zero gives the series of the Basel problem; for pi taking the parameter to infinity gives the Madhava series (a specialization of the series expansion of the arctan function). The classical series are extremely slow to converge. For other values of the parameter convergence can be vastly faster, but still, apparently, very slow relative to the state of the art. Whatever the significance of these series may be, it’s probably not going to be in numerical analysis.

I find it very hard to tell with these kinds of things whether the result is new, but it very well could be. Every person listed in the paper’s acknowledgments section appears to be a physicist, so it’s not clear whether the authors reached out to any mathematicians prior to publishing.

Will Orrick,

I did read the paper, and it’s ridiculous. The fact that they have written down a series for zeta(2) depending on a complex parameter is not in itself anything interesting. There’s zero evidence this series is any kind of advance in analytic number theory (much less one that “could change maths forever”), since there’s zero evidence that they bothered to consult with anyone who knows anything about analytic number theory.

India at the moment is hyper-nationalistic, so such exaggerated news coverages aren’t uncommon (in fact they are extremely common). So this coverage by Indian media is mostly a stance towards exaggerating Indian contributions to science (in the sense that the scientists are Hindus working at an Indian university rather than a foreign one.)

This is not to say that there aren’t other legitimate contributions by Indians to the Sciences, but India Today is well know to be biased twards the hypernationalism mentioned above.

They say that they can deduce the identity for zeta(2), but they don’t show how they did it. They also say that for lambda=0 the expression becomes the usual series for zeta(2), but it seems undefined for lambda=0.

I don’t see what the problem with this is. It doesn’t appear to me that they are claiming that this finding will revolutionize anything. If you think that it belongs to a hallway chat rather than an online publication, then I agree. But perhaps the same goes for this mockery of their work?

Good followup on mathoverflow

https://mathoverflow.net/questions/473931/possible-new-series-for-pi

and mathstackexchange

https://math.stackexchange.com/questions/4937730/is-the-new-series-for-a-big-or-even-medium-deal

I was the one who posted on MathOverflow, asking if the series is new. It’s a little soon to say for sure, but Jesús Guillera is one of the people I would think would recognize the series if it were known, and he didn’t recognize it. I agree with Will Orrick’s sentiment. There’s no reason to react either positively or negatively to the hype; one should just ignore that, and evaluate the mathematical result on its own merits. The formula is not particularly suited for computation, but it could be interesting for other reasons that remain to be discovered.

By the way, “analytic number theory” is probably not quite the right keyword for this type of thing. “Transcendental number theory” is closer, but the experts who are most likely to recognize such a formula are those with an interest in experimental mathematics, high-precision computation, and infinite series. Or possibly special functions.

Concerned Indian mathematician, is there reason to think there’s a particular ‘Hindutva’ angle behind this and that it’s not just the usual failing of the scientific press? I know Hindutva has successfully pushed many ahistorical narratives on math and science history into schools and popular thought, but in general I thought contemporary research is very under-emphasized by the Hindutva movement/current Indian government.

All,

I’ve deleted most of the incoming comments that want to argue about the current situation in India, probably should have deleted anything referring to this at all, will do so in the future.

Some discussion here as well –

https://youtu.be/rGd7Db52w1Q?si=rs7kP1WuHSMt40FU

The YouTube channel Numberphile has just posted an interview with Sinha and Saha.

https://www.youtube.com/watch?v=2lvTjEZ-bbw

In light of some of the discussion here, it’s worth pointing out that starting at 8:35, they mention that they consulted various mathematicians prior to publication, including Terence Tao.

Timothy Chow,

What they actually say is that they consulted one mathematician, a friend of theirs (he supposedly consulted others, including Terry Tao), and he hadn’t seen the formula. Also evidently they put a question on math stack exchange (after the paper had been submitted for publication) which no one responded to, see

https://math.stackexchange.com/questions/4876995/parametric-representation-of-the-euler-beta-function-zeta-functions-and-pi

They also admit that a lot of the press coverage was nonsense, but take no responsibility at all for the misleading press release that was issued in their name and the nonsense that was in it (they say the press release was the idea of their dean, not theirs).

Peter, what exactly in the press release itself (as opposed to subsequent stories that were written based on the press release) do you consider to be nonsense? I see you mention PET, but PET is mentioned only as an example of an application of some theoretical ideas by Dirac that he did not expect to have applications. There is no claim that their own work has practical applications, to PET or anything else; quite the opposite. I don’t see anything in the press release (at least regarding pi) that I consider to be “nonsense,” and I feel confident that Sinha and Saha stand behind it (in contrast to your claim that they “take no responsibility at all” for it). Also you made a comment that you suspect that the series is not new, but the evidence so far (from MathOverflow) seems to be that it is new. Finally, you said that there’s “zero evidence” that they consulted with anyone, which may have been true at the time you made the comment, but we now know that they did consult with at least one person who then consulted with others.

Timothy Chow,

About what is nonsense, I addressed that already in the posting:

1. “an easier way to extract pi from calculations involved in deciphering processes like the quantum scattering of high-energy particles.”

Besides being confusing, the “easier way to extract pi” claim is simply nonsense intended to mislead the reader.

2. Bringing positron emission tomography into it is complete nonsense, again, intended to mislead.

Another example:

3. “The series that Sinha and Saha have stumbled upon combines specific parameters in such a way that scientists can rapidly arrive at the value of pi, which can then be incorporated in calculations, like those involved in deciphering scattering of high-energy particles.”

This is complete nonsense: the signficance of a a new series for pi is that you can calculate pi more quickly which helps your scattering amplitude calculations???? Whoever wrote it had no understanding of what they were writing. It reappears in lots of the press stories.

As for whether the series is “new”, I can take any known series for pi, do a random transformation of variables and get a “new” series for pi. The question is whether it’s “new” in an interesting way. I’m guessing also that the question of whether the series is interesting is more relevant for the series they write down for the zeta function, where the reason for interest in such a series is clearer (very unclear why a series for pi is interesting, other than the technical reason of faster convergence, which isn’t a reason here).

The “zero evidence” they consulted anyone statement was accurate. Now a more accurate statement would be that they only consulted one person (Apoorva Khare), who had no expertise on such series expansions. Note that they thanked a lot of people in the acknowledgements, not including Khare. I’m guessing they only asked him about this after the paper was submitted (like the question on stack exchange).

I don’t know what evidence you have that these two “stand behind” the press release. In the video here’s their explanation of how it happened

“When the paper got published we sent it to our divisional chairman and director, both of whom are mathematicians. Both of them had good things to say, especially our divisional chairman. He said that we should actually make a press release focusing on pi so that’s how this story centered around pi originated. I don’t think it would have actually occurred to either of us to actually try to sell to the lay person that “look, we found a new formula for pi”.”

He’s very explicitly saying “this kind of publicity seeking is not something I would do, I did it because my divisional chairman told me to”. There’s also a lot of discussion about how much of the press coverage was misinformation. The obvious question of why that happened isn’t addressed in the interview. The obvious answer is that the press coverage was misinformation because the press release was misinformation.

Peter,

It seems obvious to me that Sinha and Saha stand behind their press release, because in the interview they had ample opportunity to disavow or repudiate it, but they didn’t. (It seems you agree with me that they didn’t repudiate the press release, since their non-repudiation is one of your complaints.) True, the press release wasn’t their idea in the first place, and they had mixed feelings about the reaction, but they never retracted anything they said, or said they wish they hadn’t done it. But I won’t continue to debate the point; if we really care, we could contact Sinha and Saha directly and ask them whether they stand behind their press release.

The things you call “nonsense” seem to me to be par for the course when it comes to science journalism. Perhaps I’m just more tolerant than most scientists on this score. In the long run, I find that the hyper-critical attitude toward science journalism that is so common in the scientific community amounts to shooting ourselves in the foot. For example, I disagree that “bringing positron emission tomography into it is complete nonsense.” It’s no more nonsense than saying, in response to whether a new theorem in number theory has practical applications, that there are currently no known applications, but that G. H. Hardy once boasted that number theory has no applications and yet much number theory has found applications in cryptography. Bringing up G. H. Hardy and cryptography is cliched, but it’s not nonsense.

As for the series for pi itself, I take the attitude that much of mathematics amounts to the search for hidden structure. Any new identity involving a fundamental constant is potentially the tip of some iceberg, a small hint that some large undiscovered structure lies hidden beneath the surface. Chasing down such hints doesn’t always work out, of course, but it’s a pretty good heuristic. As an analogy, my Ph.D. thesis advisor Richard Stanley once wrote a survey paper on log-concave and unimodal sequences in algebra, combinatorics, and geometry. I used to be puzzled why people would invest so much effort into studying, and trying to prove, unimodality. What’s so interesting about a unimodal sequence? It was only later that I understood that unimodality is usually interesting not so much for its own sake, but because it is so often a sign of interesting structure that lies hidden beneath the surface. Stanley doesn’t make this “iceberg” claim explicitly in his paper, but if you read his survey with this thought in mind, then the examples he discusses provide ample evidence for icebergs.

Returning to identities for pi, there are boatloads of identities for pi that have been discovered empirically, and I think one would have to be a diehard skeptic not to believe that there must be some underlying theory that explains why these identities exist. In many cases, the identities are either unproved or the only known proof is a “mechanical” proof using the WZ method. These identities may not be so interesting for their own sake, but they are begging for an explanation (note that “explanation” and “proof” are not synonymous). A big reason why Ramanujan has had such an enduring legacy is that so many of his discoveries (including formulas involving pi) have pointed the way to previously unsuspected mathematical structures.

The Sinha-Saha identity was surprising to several of the experts who saw it on MathOverflow. I therefore take it as a working assumption that there is an iceberg, until someone shows otherwise.