Deep are the eigenvectors that Google uses to classify its links, and deep are the things upon which rich people choose to spend their money. Deep is String theory and Riemann's Zeta function.
Not deep are communism, progressivism, Islam, discrete mathematics, Loop Quantum Gravity, and prime numbers.
Deeply thinks the mighty Lumo and deeply does he write:
Deep ideas are those that are unique among conceivable similar statements at comparable levels of complexity and that are able to cover a large set of particular examples (models, phenomena, metaphenomena) and explain a large number of patterns using a small number of independent assumptions and parameters, especially if the deep ideas are inevitable. Whether or not a given idea is unique among ideas that a priori look analogous, may often require hours or years of calculations. These calculations are crucial because we must choose our deep ideas not only according to the impression they make in the first 3 minutes, but also according to their ability to offer us true insights in the long term.