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Physics, chemistry and mathematics in news

Physics, chemistry and mathematics as they reach the news: measurement and legal time, lasers and the physics of materials, chemistry, and famous problems in mathematics. Prelims has asked about the four fundamental forces and the Higgs boson.

Foundation note: The Large Hadron Collider and the Standard Model

OpenAI's Navier–Stokes claim

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Prelims and Mains

OpenAI's claim is a proposed answer to the Navier–Stokes problem, one of the Clay Mathematics Institute's prize problems: whether a smooth flow must stay smooth for ever. 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.
  • 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.
  • 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.

  • Navier–Stokes existence and smoothness

    Open, and the subject of OpenAI's claim

  • Poincaré conjecture

    Resolved by Grigori Perelman, who declined the prize

  • P versus NP

    Open

  • Riemann hypothesis

    Open

  • Yang–Mills existence and mass gap

    Open

  • Hodge conjecture

    Open

  • Birch and Swinnerton-Dyer conjecture

    Open

Seven problems named by the Clay Mathematics Institute, each carrying a million dollar prize. Status as reported in The Indian Express, 13 September 2026.

What changed

  1. 13 Sep 2026

    • OpenAI said its artificial intelligence agents had cracked the problem.
    • 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 mechanically, but the claimed proof is neither independently verified nor accepted.

    The Indian Express, 13 Sep 2026: OpenAI's Navier-Stokes claim: what the problem asks, and why mathematicians are uneasy (opens in a new tab)

Correct the Map resolution

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Prelims and Mains

Correct the Map is a non binding resolution of the United Nations General Assembly that names the Equal Earth projection as more accurate than Mercator's.

  • A globe cannot be laid flat without something being stretched, so a map projection keeps one property at the cost of the others.
  • The right choice depends on what the map is for.
From a globe to a flat Mercator mapTwo equal circles on a globe, at the equator and at 60 degrees north, become unequal on the Mercator map: the northern one is drawn twice as wide and four times the area.Two equal circles on the globelaid flat60°S30°S0°30°N60°NOn Mercator: 4 times the area at 60°

Every flat map distorts at least one of these

AreaHow large a landmass is relative to others

ShapeThe true outline of a country

DistanceThe actual space between two points

DirectionThe correct compass bearing between places

Circles drawn to Mercator's scale. Properties as defined in The Indian Express explainers, 5 and 9 September 2026.
Mercator (conformal)
  • Keeps angles and local shapes
  • Rhumb lines are straight, so it suits navigation
  • Inflates areas more towards the poles
  • Greenland looks as big as Africa, which is 14 times larger
Equal Earth (equal-area)
  • Keeps relative areas of continents true
  • Shapes stretch near the poles
  • Suits thematic maps of population, climate and resources
Winkel Tripel (compromise)
  • Keeps no property exact
  • Spreads error across area, distance and direction
From The Indian Express explainers, 5 and 9 September 2026

What changed

  1. 5 Sep 2026

    • The United Nations General Assembly adopted the non binding Correct the Map resolution, 164 to 1, with the United States alone against.
    • It names the 2018 Equal Earth projection as more accurate than Mercator's of 1569.
    • The case made was that the projection a map uses shapes how important a region looks, a matter of soft power.
    • India voted for it but said the resolution authenticates no map.
    • It said its territory, including Jammu and Kashmir and Ladakh, must be shown as in India's official map.

    The Indian Express, 5 Sep 2026: UN adopts Equal Earth map: Why no flat map can accurately show the globe (opens in a new tab) · 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)

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