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 It would be helpful if the people who issued this press release had some sense of shame and had it withdrawn.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.