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What is important about graphene is the new physics it has delivered.

Essentially, every technology you have ever heard of, where electrons move from here to there, has the potential to be revolutionized by the availability of molecular wires made up of carbon. Organic chemists will start building devices. Molecular electronics could become reality.

Carbon nanotubes are amazing because they're really good electrical conductors, yet they are only a few atoms in diameter. You can make transistors out of them in the same way you can with silicon. At Berkeley, we made the narrowest device anybody had ever made. It was basically a single molecule.

Carbon is probably a bit harder to wrap since it's procedural.

I would say there are three important things about graphene. It's two-dimensional, which is the best possible number for studying fundamental physics. The second thing is the quality of graphene, which stems from its extremely strong carbon-carbon bonds. And finally, the system is also metallic.

The hierarchy of relations, from the molecular structure of carbon to the equilibrium of the species and ecological whole, will perhaps be the leading idea of the future.

It is important that carbon storage is carefully regulated, that the process is transparent to the public, and that there is a clear accounting of what happened to the CO2. This is particularly true of underground storage, where there is always a small chance that pressurized CO2 could escape.

A carbon nanotube is just a graphene sheet that's rolled up seamlessly, and this happens in nature; carbon nanotubes are found in mineral deposits around the planet.

Carbon-carbon bond formation reactions are important processes in chemistry because they provide key steps in building complex, bio-active molecules developed as medicines and agrochemicals.

A cap on carbon is important because it sets a specific goal for reducing carbon emissions 80% by 2050.