The AdS/CFT spectral problem, i.e. computation of conformal dimensions in planar N=4 SYM, was a hot topic during the last decade, with more than thousand publications devoted to it. Though it was formally solved by TBA and more recently simplified by FiNLIE, the solution was never formulated in a clear and lucid style.
In this talk I will present our new advancement which unveil the whole beauty of the AdS/CFT spectrum: it is described by a "quantum spectral curve" -- matrix Riemann-Hilbert equations on a few Q-functions. A given state in the spectrum is encoded into an asymptotics at infinity and into a solution of the exact Bethe equations which, in the spirit of functional Bethe Ansatz, are nothing but the regularity conditions on the Q-functions.
During the talk I will also demonstrate the efficiency of the new approach by computing the Konishi anomalous dimension up to 8 loops in real time using a single CPU.
