To celebrate Bruno Kahn's 63rd birthday

Motives and quadratic forms interact in fruitful ways: motives have successfully been used to understand and compute invariants of quadratic forms, while conversely, quadratic forms play a surprisingly deep and structural role in the motivic stable homotopy category of schemes. Moreover, over arithmetic bases, motives can be used to extract information of number theoretical nature from quadratic forms or other algebraic or geometric objects.