"Who are the strongest European competitors on software ideas? Who is the best doctor to cure insomnia in a nearby hospital? Where can I attend an interesting conference in my field close to a sunny beach? This information is available on the Web, but no software system can accept such queries nor compute the answer. We hereby propose search computing as the new multi-disciplinary science which will provide the abstractions, foundations, methods, and tools required to answer these and many similar questions. The emerging paradigm of service computing has so far been neutral to the presence of search services, which are equal ""inter pares"". This proposal brings about a simple yet revolutionary idea: service computing evolves into search computing, a new paradigm where ranking is the dominant factor for composing services. While state-of-art search systems answer generic or domain-specific queries, search computing enables answering questions via a constellation of dynamically selected, cooperating search services. The idea is simple, yet pervasive. New foundational theories are needed, rooted into formal disciplines such as mathematics, statistics, and optimization theory. New language and description paradigms are required for expressing queries and for discovering services. New interfaces and protocols help capturing ranking preferences and enabling their refinement. Semantic domain knowledge helps enriching terminological knowledge about objects being searched. Ranking is always relative to individuals and context, thus the study of personal and social behaviour is also essential. Economical and legal implications of search computing must be understood and mastered. In summary, search computing is a multi-disciplinary effort which requires adding to sound software principles contributions from other sciences such as mathematics, operations research, psychology, sociology, knowledge representation, human-computer interfaces, economical and legal sciences."