The Oscar-winning movie "The Beautiful Mind" shows the mathematical prodigy John Nash having many imaginary conversations with people. It was not until he realised that the little girl with whom he had been talking with never grew up, even though years had passed since their first encounter, did he finally admit to be schizophrenic. Schizophrenia is a life long brain disorder where patients usually reside in a "non-existent" alternative reality, similarly to John Nash. According to reports from the World Health Organisation, seven in a thousand adults are afflicted by this disorder. Overall, schizophrenia affects about 24 million people worldwide.

Studies and pathological reports on the cause of schizophrenic disorders suggest that there is disruption of information processing in two main regions of the brain: the thalamus and the cortex. Thalamus acts a "router" or a "middleman" in transporting signals such as light, sound or touch to specific regions of the cortex. The cortex then processes these signals and helps perform cognitive functions like memory, attention, awareness and consciousness, to name a few. As there is a problem in communication between the thalamus and the cortex in schizophrenia, it has become essential to study and understand how these brain areas interact.

As with any brain disease, in schizophrenia it is critical to obtain the correct diagnosis as a first step for treatment. Although it is extremely difficult to detect schizophrenia using physical exams, recent advances in diagnostic screening tests have made it possible to use EEG (electroencephalography) scans, which produce records of brain activity. However, since EEG is a non-invasive procedure, it is difficult to gain access to deeply localized brain areas like the thalamus, for instance. To understand why schizophrenia occurs, it is therefore necessary to find an alternative technique to detect activity disruption between the thalamus and cortex.

Scientists from the University of Cologne have now used mathematics to dissect the wiring between different brain regions. They speculated that if the underlying cause for schizophrenia lies in the EEG data obtained from patients, then maths is the key to unlock it.

Anke Brockhaus-Dumke and colleagues created a system of equations that describe the wiring between thalamus and cortex and calculate the information flow between them, just like an engineer calculates the amount of electricity flowing through an electrical circuit. They used data gathered in screening tests, and as expected, the EEG measurements of schizophrenic patients showed differences in brain activity when compared to healthy subjects.

Solving their equation under different conditions resulted in EEG patterns mimicking the actual measurements. Using these equations, the group discovered that in a healthy person, the messages between the thalamus and cortex travelled at the same time. On the other hand, when they didn't, the brain activity resembled that of an individual with schizophrenia.

That brings us to the idea of "synchrony" or "timing of events". Back in the 1970s, a very exciting natural phenomenon was reported to have occurred in the Far East. A large group of fireflies was seen flashing at the same time as a firework display going on, rather than in typical individual random spurts. This created a rhythmic event named "synchrony". Similarly, based on the findings of Brockhaus-Dumke's team, synchronised communication between the thalamus and cortex is what sets healthy individuals apart from schizophrenic patients.

So how does this math model help schizophrenic patients? The model is powerful as it helps interpreting EEG data so that we can predict the probability of a person having schizophrenia based on current EEG patterns. While this is an exciting start, a lot more work needs to be done. These findings pave the way for potential future collaborations between mathematics and medicine, to improve schizophrenia early detection and measure treatment effectiveness.