Physics, chemistry and mathematics in news

Prelims and Mains

The Navier–Stokes equations are Newton's second law written for a fluid, balancing pressure, viscosity and the fluid's own momentum. The difficulty sits in the term where the flow carries itself along, which is not proportional to velocity and lets small swirls feed large ones. Whether a smooth flow must stay smooth for ever is the question nobody has answered, and an artificial intelligence company now says it has.

• Turbulence is where the equations resist analysis, which is why engineers solve them by computer rather than exactly.
• A singularity would mean the equations stop describing a real fluid at that instant, marking the limit of the model rather than of the fluid.
• Smoothness for all time would show the model is self consistent, and methods built to prove such a thing usually outlast the result.
• OpenAI said that 10,000 of its artificial intelligence (AI) agents had cracked the problem in about 88 hours.
• Its paper builds a fluid whose velocity becomes infinite at a point in finite time while the flow's energy stays bounded, so it claims blow-up rather than smoothness.
• The proof was formalised in Lean, which checks each step of an argument mechanically.
• Formal checking shows that a proof is correct, not how the model reached it.
• The claimed 100 page proof is still neither independently verified nor accepted.
• Fields Medal winners warned that using mathematical problems as a benchmark pulls the subject away from understanding.
• The Clay Mathematics Institute's own rules require a result to appear in a refereed journal and to stand unchallenged for two years before a prize is considered.
• OpenAI cannot rule out that de-identified data from researchers using its products improved its models, which raises the question of epistemic ownership.

Prelims and Mains

A globe cannot be laid flat without something being stretched, so a map projection keeps one property at the cost of the others and the right choice depends on what the map is for. Which property the world's default map keeps has now become a question for diplomats.

• The United Nations General Assembly adopted the Correct the Map resolution, which is not binding, naming the 2018 Equal Earth projection as more accurate than Mercator's of 1569.
• It passed 164 to 1, with the United States alone against.
• India voted for it but said the resolution authenticates no map, and that its territory, including Jammu and Kashmir and Ladakh, must be shown as in India's official map.
• The case made was that the projection a map uses shapes how important a region looks, which is a matter of image and soft power.

Background reading: The Indian Express, 6 Sep 2026: India backs UN world map resolution, draws firm line on Jammu and Kashmir and Ladakh (opens in a new tab)

Prelims and Mains

A clock is only as good as what it is checked against, and traceability is the unbroken chain of comparisons that ties one to the national standard. Until these rules, nothing in law said which chain an Indian system had to be on. The rules are made under the Legal Metrology Act, 2009, and put Indian Standard Time on a legal footing for the first time.

• Time dependent systems in government and in critical sectors must take Indian Standard Time from a traceable, authorised source and be able to show that traceability.
• The rules take effect 180 days after publication, and serve the stated vision of One Nation, One Time.
• The CSIR-National Physical Laboratory (CSIR-NPL), India's National Metrology Institute, generates the national time scale with its atomic clocks and supplies traceability to it.
• The Legal Metrology Department regulates and enforces, as it already does for shop weights and petrol pump gauges.
• NavIC, the satellite navigation system the Indian Space Research Organisation (ISRO) built after the Global Positioning System (GPS) was denied to India during the Kargil War, takes its own time reference from CSIR-NPL.
• Many systems took time indirectly from GPS or from a telecom provider, sources that can differ by seconds or even minutes.
• Guidelines of 2023 from the Indian Computer Emergency Response Team (CERT-In) already asked government systems to synchronise with NPL and NIC, because tracing a cyber incident needs trustworthy time stamps.

Background reading: PIB, 2 Sep 2026: Legal Metrology (Indian Standard Time) Rules, 2026 Notified: Major Step Towards "One Nation, One Time" (opens in a new tab)