Many technologically and societally important mathematical problems are essentially intractable for traditional, serial computers. Therefore, a significant need exists for parallel computing approaches that would be able to solve such problems faster than current serial computers. This project will develop and benchmark a novel paradigm for future parallel computing approaches, based on biological entities. Specifically, we will encode mathematical problems into networks consisting of nano- or microsized channels and nodes, and will use self-propelled biological agents to explore these networks and find the solution to the encoded mathematical problems. Due to the very large number of agents, the problem is solved in a highly parallel manner. A number of different types of micro- and nanoscale biological agents will be used, including innate objects (protein filaments propelled by molecular motors) and living systems (bacteria and fungi). The novelty of this approach lies in the use of self-propelled agents (avoiding scalability issues associated with the use of external driving forces), as well as in the combination of human intelligence (in the target-oriented design of networks) with the parallelism enabled by large numbers of biological agents. Key aims of the project will be the benchmarking against existing computational approaches, and the identification of application areas where this novel paradigm may lead to transformative applications. Benefits to society will include the ability to solve hitherto intractable problems, and the development of a sustainable and energy-efficient computing approach that is radically different from current ICT technology.