The unprecedented power of the brain suggests that it may process information quantum-mechanically. Since quantum processing is already achieved in superconducting quantum computers, it may imply that superconductivity is the basis of quantum computation in the brain too. Superconductivity could also be responsible for long-term memory. Following these ideas, the paper reviews the progress in the search for superconductors with high critical temperature and tries to answer the question about the superconductivity in brain. It focuses on recent electrical measurements of brain slices, in which graphene was used as a room-temperature quantum mediator, and argues that these measurements could be interpreted as providing evidence of superconductivity in the neural network of mammalian brains. The estimated critical temperature of superconducting network in the brain is rather high, 2022 ± 157 K. A similar critical temperature was predicted in the Little’s model for one-dimensional organic chains linked to certain molecular complexes. A reasonable suggestion is that superconductivity develops in microtubules inside the neurons of the brain.