How can we explain the thermal phenomenon by a fractal meta-surface? This has
been puzzling scientists and engineers for at least ten years, and so far no
answer has been found. Now, modern mathematics offers a completely new
window to physically understand the magical phenomenon that lies far beyond
the Fourier law for heat conduction. A fractal-fractional modification of
the Fourier law is elucidated, and its extremely high thermal conductivity
is mathematically revealed. This article shows that thermal science is the
key to nanotechnology.