ToC is a systematic approach to solving problems. Computation can occur more quickly when people use predefined machines, such as programs or algorithms. Complex computation problems take longer to solve than simplistic computation problems, even for those very adept at computation.
Computations are methods of processing information. Those who seek to study computations try to understand which problems are solvable and not solvable. In addition, theorists consider which problems can be solved but require enormous amounts of time, such as millions of years of computational time. By understanding which problems cannot be solved feasibly, researchers can avoid using these methods and can instead find alternative ways. Discoveries made through computational research help people identify problems that can be solved also help people develop tools that help them solve these problems.
Scientists focused on the ToC also focus on the computations carried out by biological systems. For example, theorists have studied the type of computations that neurons collectively carry out in the brain. They also ponder philosophical questions, such as "What is the nature of infinity?" Theorists try to figure whether people can distinguish random numbers from random-looking numbers created through deterministic means and whether people really need true randomness.
While sometimes branching out, ToC mostly focuses on what computers can do. Researchers ask questions such as whether there are computers inherently more powerful than other computers and whether there are limits on what computers can do. Theorists explore the limitations of quantum computers. Quantum computers are computers that use quantum phenomena like entanglement and superposition. Entanglement is when really small materials like electrons and photons interact.
One the most difficult problems in the ToC is the problem of peak versus NP. This involves the question of whether a computer can recognize a solution, yet cannot find the solutions without trying a very large number of possibilities. Theorists who can solve this problem will be able to apply it to a large variety of applications. Computational theories often end up having direct applications in the real world. For example, research conducted by Ron Rivest, Adi Shamir and Len Aldeman in 1976 led to knowledge that helped the creation of electronic commerce sites, such as eBay and Amazon.