Sixteen engineering and maths problems, ranked three ways. Five come out on top.
Room left under the physics or maths limit, what blocks progress now, and expected value by 2060. The five picks are in blue; robots and learning from little data together make the first.
B: the gap is measured against a benchmark (humans, or other countries’ costs), not a law of physics. ?: an open question, or no known ceiling. Value is order-of-magnitude, so neighbouring ranks are ties.
Each chart shows the number that binds today, with its limit or the best benchmark.
The best robot policy of 2025 finished only 12.4 % of household chores in new, randomised layouts. Unsupervised use needs 99 %+, and hands and rare edge cases are most of the gap.
Why first: a robot that reliably learns new physical tasks turns AI into labour in factories, care and homes, the biggest prize on the list. Failure rates need to fall about 90×.
A solar farm takes about seven months to build. In 2025 the median US project waited 61 months to connect, and only 13 % of requested capacity ever gets built. South Africa had a record 335 days of load-shedding in 2023.
Why second: cheap clean generation already exists, so connection speed sets how fast every other energy fix lands. The fix is mostly process and hardware supply, not new physics.
A logic gate still burns about 3×10⁴–3×10⁵ times the Landauer minimum, while data centres head from 485 TWh (2025) to about 950 TWh (2030). Every joule saved here shortens the power queue.
Why third: the largest proven headroom on the list. It ranks below the first two because AI build-out today waits more on grid connections and memory chips than on efficiency.
US construction output per worker was about 40 % lower in 2020 than in 1970. New York’s next subway costs about $2.5 billion per km, ten times the world average.
Why fourth: construction cost multiplies the price of grids, chip fabs and housing. Much of the gap is permits and procurement, so engineering can close only part of it.
Industrial heat is almost a fifth of world energy, and steel alone emits 7–8 % of greenhouse gases; the world average is 1.92 t CO₂ per tonne. Hydrogen-made steel works in pilots but costs about $225/t more in China at $5/kg hydrogen.
Why fifth: the chemistry already works, so what is missing is cheap clean electricity and hydrogen. Proving software correct is a near tie for this place.