The Sciences

Infinite in All Directions: Titanic Storms, IIT-JEE Toppers, Riemann Hypothesis

The hot news this week from the mathematical physics world is that the noted mathematician Michael Atiyah claimed to have solved the Riemann hypothesis, one of the most difficult unsolved problems known.

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Hypothetical Homepage

You can’t have all news items on the homepage all the time even though they might each deserve that place, nor can a single publication cover all the notable news in the world on a given day. But if given the chance, these are the stories I would have liked to showcase on my hypothetical homepage September 28 morning:

Regulators accuse Tesla’s Elon Musk of securities fraud – “The SEC statement said that, according to Mr Musk, he calculated the $420 price per share based on a 20% premium over that day’s closing share price because he thought 20% was a ‘standard premium’ when taking companies private transactions. This calculation resulted in a price of $419, and Mr Musk stated that he rounded the price up to $420 because he had recently learned about the number’s significance in marijuana culture and thought his girlfriend, the Canadian indie singer Grimes, ‘would find it funny, which admittedly is not a great reason to pick a price’.” Is this guy for real?

Half of all killer whales doomed to die from pollution – “Although the poisonous chemicals, PCBs, have been banned for decades, they are still leaking into the seas. They become concentrated up the food chain; as a result, killer whales, the top predators, are the most contaminated animals on the planet. Worse, their fat-rich milk passes on very high doses to their newborn calves. PCB concentrations found in killer whales can be 100 times safe levels and severely damage reproductive organs, cause cancer and damage the immune system.”

Why this weird little frog should care about Brett Kavanaugh – If one particular case is re-heard with Kavanaugh or another conservative judge in the SCOTUS, the definition of ‘habitat’ as is pertinent to the US Endangered Species Act 1973 could change to the detriment of the endangered dusky gopher frog. Specifically, if Kavanaugh is confirmed by the Senate by 10 am on Monday, then he will get a vote on a case that seeks to redefine the word ‘habitat’, and likely swing the court’s verdict in favour of a definition that limits it to include only those areas where an animal already resides and not all of the areas required to protect the animal, even if they aren’t currently inhabited.

* Titan just keeps getting more awesome – A reanalysis of data from the Cassini probe (which ‘died’ this month last year) suggests that Saturn’s moon Titan has storms over its surface. Paul Gilster writes: “We have a world that is active not only in its hydrocarbon cycle and its geology, but also in what we can call its ‘dust cycle.’ The only moon in the Solar System with a dense atmosphere and surface liquid offers yet another analogy with Earth, a similarity that highlights the complexity of this frigid, hydrocarbon-rich world.”


Science is frequently understood as an enterprise engaged in the unearthing of new facts, or verification of older, supposed facts, through methods that strive to eliminate biases. Missing in this picture is the key role of interpretation itself: science lies in its facts but also in how those facts are interpreted together in various contexts. In turn, this requires us to view science as a knowledge-building enterprise for all of society, beyond just for a group of specialists.

Capitalism is the answer to why growth can’t be green – “Many policymakers have [been] pushing for what has come to be called “green growth.” All we need to do, they argue, is invest in more efficient technology and introduce the right incentives, and we’ll be able to keep growing while simultaneously reducing our impact on the natural world, which is already at an unsustainable level. It sounds like an elegant solution to an otherwise catastrophic problem. There’s just one hitch: New evidence suggests that green growth isn’t the panacea everyone has been hoping for. In fact, it isn’t even possible. … the promise of green growth turns out to have been based more on wishful thinking than on evidence. In the years since the Rio conference, three major empirical studies have arrived at the same rather troubling conclusion: Even under the best conditions, absolute decoupling of GDP from resource use is not possible on a global scale.”

* A snapshot of IIT–JEE all India one rankers (1979–2018) – “A snapshot of IIT–JEE all India one rankers of the last 40 years shows that 15 of them obtained bachelor’s degree from IIT Bombay, 13 from IIT Kanpur, four each from IIT Delhi and IIT Madras, and four migrated to the US to pursue under-graduation. In most cases, they chose computer science (32), followed by physics (4), electrical (3) and robotics (1). It may be relevant to note that a majority of them moved to USA for higher studies and obtained MS/PhD from the world’s top rated institutions. Curiously, if a bright Indian student wants to study for a doctorate at a top rated university in any field of science and technology, she is forced to study overseas. Not surprisingly, majority of the toppers, who complete their MS/PhD from a foreign university, remain overseas, either in a university/institution or corporate sectors.”

* Shanti Swarup Bhatnagar Prizes – The S.S. Bhatnagar Prizes “are awarded annually” on September 26 “for notable and outstanding research, applied or fundamental”. As India’s most exalted awards for scientific work, the Bhatnagar Prizes need to be celebrated. Although each prize carries a purse of Rs 5 lakh, it’s even more important to render the prize as a marker of all-round excellence. And the way to do this is to make the prize a reflection of those contemporary social and moral values that make the world a better place. The Millennium Plaque of Honour awarded by the Indian Science Congress is an illustration of how not to do this: the 2017 prize was given to Appa Rao Podile (and Avula Damodaram, the VC of the university hosting the congress), and somehow it doesn’t seem that desirable anymore. The Bhatnagar Prizes may not be doing well on this count and this needs to be mended. For example, the prizes last year and the year before were all given to men. The prizes this year include only one woman. In at least one instance, the prize has also been given to someone conducting questionable research combining genomics and ayurveda.


Piecing together stories published at disparate times and places but which have a theme or two in common.

The hot news this week from the mathematical physics world is that the noted mathematician Michael Atiyah claimed to have solved the Riemann hypothesis, one of the most difficult unsolved problems known and whose resolution carries a $1 million prize. The problem is that Atiyah’s solution, while remarkable for its brevity, may not hold water.

The Riemann hypothesis is concerned with the Riemann zeta function, which – in very broad terms – provides a way to predict the position of prime numbers on the number line. Computers have been able to find prime numbers with scores of digits and mathematicians have been able to find in hindsight that, yes, the zeta function predicts they exist. However, what mathematicians don’t know (and this is the Riemann hypothesis) is whether the function can predict prime numbers ad infinitum or if it will break at some particularly large value. And solving the Riemann hypothesis problem means proving that the zeta function can indeed predict the position of all prime numbers on the number line.

When I first heard Atiyah’s claim, I was at a loss for how to react. Most claimed solutions for the Riemann hypothesis are usually dismissed quickly because they contain leaps of logic not backed by sufficient mathematical rigour. At the same time, Atiyah isn’t just anybody. He won the Fields Medal in 1966 and the Abel Prize in 2004, and has been associated with some famous solutions for problems in algebraic topology. So as a quick way out, I hopped over to Shtetl Optimized, the famous quantum computing blog written by Scott Aaronson. And there, at the end of a long post about the weirdness of quantum theory, was this line: “As of Sept. 25, 2018, it is the official editorial stance of Shtetl-Optimized that the Riemann Hypothesis and the abc conjecture both remain open problems.” Aha!

Some of you will remember that three physicists made a major announcement last year about finding a potential way to solve the Riemann hypothesis because they had unearthed an eerie similarity between the Riemann zeta function, central to the hypothesis, and an equation found in quantum mechanics. While they’re yet to post an update, the physicists’ thesis was compelling and wasn’t dismissed by the wider mathematical community, raising hope that it could lead to a solution.

Atiyah’s solution also concerns itself with a famously physical concept: the fine-structure constant, denoted as α (alpha). The value of this constant determines the strength with which charged particles like electrons interact with the electromagnetic field. It has the value of about 1/137. If it were higher, the electromagnetic force would be stronger and all atoms would be smaller, apart from numerous other cascading effects. Atiyah’s resolution of the Riemann hypothesis is pegged to a new derivation for the value of α, and this where he runs into trouble.

Sean Carroll, a theoretical physicist Caltech, called the derivation “misguided”.  Madhusudhan Raman, a postdoc at the Tata Institute of Fundamental Research, said that while he isn’t qualified to comment on the correctness on the Riemann hypothesis proof, he – like Carroll – had some problems with the physics of it.

His full explanation is as follows (paraphrased): It is tempting to think of α as a fixed number, like π (pi), but it is not. While the value of π does not change, the value of α does because it is related to the energy at which it is being measured. At higher energies, such as inside the Large Hadron Collider, the value of α will be higher. So α is not a number as much as a function that says its value is X at energy Y. However, Atiyah appears to have worked with the assumption that α is a single, fixed number like π. This isn’t true and therefore his derivation is suspect.

Sabine Hossenfelder, a research fellow at the Frankfurt Institute for Advanced Studies, also had the same issues with Atiyah’s effort. Carroll went a step further and said that if he had to be very charitable, then the derivation could pass muster but not without also discussing various issues in physics associated with α. However, he wrote, “Not a whit of this appears in Atiyah’s paper.”

At the same time – and unlike in numerous previous instances – these physicists and others besides continue to have great respect for Atiyah and his work, and why not? Though he is 89, as one comment observed on Carroll’s blog, “It’s brave to fight to the last, and, who knows, with his distinguished record and doubtless vast erudition, maybe there’s some truth or useful insights in these latest papers, even if [it’s] not quite what he claims.”

So also, the Riemann hypothesis endures unresolved. I’ve written an article-sized biography of Georg Bernhard Riemann, the German mathematician who formulated the zeta function and the conjecture, here and a more detailed – yet understandable, I hope – explanation of the zeta function here.


Sciencey things people are trying to do that are out of the ordinary in some way.

* Studying octopodes with ecstasy – (I’m struggling to find the source of this statement I read a while ago on an essay about octopodes; just bear in mind that I’m not the originator:) The octopus could only have been created if evolution, after having created humans, reset itself back to zero and started all over again – that’s how different these tentacled creatures are from us. However, scientists recently found one similarity, and they had to take an unconventional route to do so: they dosed an octopus with ecstasy (MDMA). NY Times: “They … found that humans and octopuses share parts of an ancient messaging system involved in social behaviours, one enhanced by the presence of MDMA in both animals. These shared lineages may have been conserved to reduce fear and enable social behaviours.”

* More octopus fun:


Some interesting articles from around the web.

* Everything you know about obesity is wrong – “More Americans live with “extreme obesity“ than with breast cancer, Parkinson’s, Alzheimer’s and HIV put together. And the medical community’s primary response to this shift has been to blame fat people for being fat. Obesity, we are told, is a personal failing that strains our health care system, shrinks our GDP and saps our military strength. It is also an excuse to bully fat people in one sentence and then inform them in the next that you are doing it for their own good. That’s why the fear of becoming fat, or staying that way, drives Americans to spend more on dieting every year than we spend on video games or movies. Forty-five percent of adults say they’re preoccupied with their weight some or all of the time—an 11-point rise since 1990. Nearly half of 3- to 6- year old girls say they worry about being fat.”

* As gutkha stands banned, use of dohra rises in Uttar Pradesh – “Oncologists have red-flagged a smokeless tobacco product prevalent in parts of eastern Uttar Pradesh as a possible carcinogen. The product – called dohra – is a mixture of areca nut (supari), catechu (kattha), edible lime, peppermint, cardamom and flavouring agents. It is mainly consumed in parts of eastern Uttar Pradesh and its use is growing as people perceive it to be safer than gutkha which stands banned in the state, a new study has observed.

* We shouldn’t use animal behaviour to explain our own – “I’m interested in the potential folly of using animal behaviour in trying to explain human behaviour. It’s part of my ongoing battles with evolutionary psychology, a field frequently beset by just-so stories masquerading as science. The most prominent in the current phalanx of these ideologues is Jordan Peterson, who asserts that male-dominated hierarchies in lobsters are evidence to support the existence of male hierarchies in human societies. Odd that he didn’t choose giraffes, for whom most sexual encounters are male-male with penetration. Or hyenas, who live in a matriarchy, established by licking each other’s clitorises, which, by the way, are almost the same size and shape as the penis. Or dolphins, which sometimes perform mass infanticide. Or the famously adorable sea otters, who sometimes drown females and use their carcasses to copulate with.”

Why a society publisher is moving towards read and publish models – “China has emerged as a dominant research nation and now publishes more research articles than any other country in the world. Like many other countries, China is experimenting with OA, however, for a variety of reasons Chinese authors appear to favour pure Gold OA journals rather than the hybrid route. India is growing its scientific base and infrastructure, but its journey with OA has only just started and the perception of OA in India has been heavily dented by predatory publishers. It is therefore viewed with much suspicion within parts of the research community, as well as by government and funding agencies. Ultimately the global uptake of Read & Publish will depend on the political, policy, and market force drivers at play, the pricing structure that is negotiated, and how this compares with the current spend the customer has with the publisher. … [The basic premise of] Read & Publish models … is that the buying (and negotiation) power of the university/consortia is leveraged to allow a transition from a subscription payment toward an OA author-pays model, using the hybrid journals that are well-recognised and popular with authors – although less so with funders – as a mechanism to increase the speed of this transition.”