The positronic brain is the advanced artificial neural network that powers androids such as Data, first made to work successfully by Dr. Noonien Soong.
Scientists had pursued the idea of a positronic brain for generations without success. Noonien Soong achieved what others could not, building working positronic brains for Lore and later for Data, giving them a capacity for learning and reasoning comparable to or exceeding that of humans.
Data's brain was the subject of intense interest in Starfleet. In 2365 the cyberneticist Bruce Maddox sought to disassemble Data to study it, prompting a hearing that ruled Data was not Starfleet's property. When Data later built his own daughter Lal, her positronic matrix failed after an emotional surge, showing how difficult the technology was to master.
The B-4 android, an earlier and less sophisticated Soong prototype, also carried a positronic brain, and Data downloaded his memories into it before his death in 2379. Research into positronic technology continued, eventually contributing to the creation of Soji and Dahj and the synths of Coppelius.