Algorithmic Differentiation (AD) is a family of computational techniques for the efficient computation of derivatives. Despite being an active area of investigation in computer science for almost 50 years, mysteriously, its potential in other areas of natural and applied sciences has remained largely untapped until very recently.

In this colloquium, I will discuss how the power of Adjoint Algorithmic Differentiation (AAD) has been recently rediscovered in Financial Engineering where it has opened a new important chapter in risk management, by making possible the calculation of the risk borne by large portfolios of securities accurately, in real time and with limited computational costs, ultimately boosting profitability through better risk management practices.

The same simple ideas can be used in any scientific application that can benefit from the efficient and accurate computation of a large number of sensitivities. In particular, I will show how AAD opened the way to full ab-initio quantum Monte Carlo simulations of electronic and molecular properties, pushing the boundaries of what can be investigated with the state-of-the-art methods of computational Physics.