“A beautiful mind” is the title of the critically acclaimed, unauthorised biography of the mathematician John Nash, who famously made great contributions to mathematics, in particular in game theory, while battling paranoid schizophrenia for decades and spending long periods of time in psychiatric hospitals.

John Nash is a classic example often used in popular culture to illustrate the hypothesised link between mathematics and madness, or at least between mathematics and mental disorders.

Kurt Gödel is one of the most important mathematicians in the history of the field of mathematical logic. By the age of 25, he had already authored and proved the incompleteness theorem that made him a celebrity.

Throughout his life, however, Gödel suffered many periods of mental instability. When he was awarded the National Medal of Science, he refused to travel to the White House to the award ceremony, fearful that he might contract an illness. He had an obsessive fear of being poisoned and thus would only eat food prepared by his wife, Adele.

When she was hospitalised for 6 months in 1977, he simply stopped eating and starved himself to death. His wife died three years later and was buried beside him.

Grigori Perelman is a Russian mathematician, who solved a century-old mathematical problem in 2002 known as the Poincaré conjecture (about the characteristics of spheres), which most mathematicians thought was unsolvable.

By the time he defeated the Poincaré conjecture, after seven years of concentrated and total dedication to the problem, he decided to quit his job and the world of mathematics while still in his 30's. He then stopped talking to people all together and became a recluse living with his mother in a small apartment in Saint-Petersburg. In 2006, he became the first (and only person so far) to turn down the Fields Medal, the top award in mathematics, and in 2010, he declined the Millennium Prize worth $1 million.

He has been referred to as “the cleverest and craziest person on the planet”.

John Nash, Kurt Gödel and Grigori Perelman are few of several examples of “beautiful minds” who could solve the most complex mathematical problems but whose lives and those of their inner circle were greatly shattered by their eccentric personalities and troubled behaviours. To this list, one could equally add the likes of Isaac Newton, Alexander Grothendieck, Georg Cantor, Yutaka Taniyama or Paul Erdos, the latter being the subject of a highly recommended biography entitled “the man who loved only numbers”.

Do these examples point towards a general pattern linking the practice of mathematics to personality and behavioural disorders?

John Nash himself blamed his mental problems on mathematics, when he said:

“I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.”

— JOHN NASH

After all, to be able to search and find solutions to complex mathematical problems requires a certain degree of obsession, as the great mathematician David Hilbert stated:

“Wir müssen wissen. Wir werden wissen. (We must know. We will know).”

— DAVID HILBERT

While there has been very little research on the connection between mathematics and mental illness, the existing evidence, though scarce, provides some interesting insights.

A large study performed in Belgium answers part of our question.

The authors analysed a group of 3,659 PhD students from sciences (the category to which mathematics belong), biomedical sciences, applied sciences, humanities, and social sciences, and found that there were no significant differences in the prevalence of mental illness between these disciplines.

However, they also noticed that research students were at higher risk of mental illness than highly educated individuals, highly educated employees, and high-education students. This study indicates that it is the inherent nature of research, which is demanding for the mind, which seems to impact the person’s mental state, for all disciplines and not only for mathematics or sciences.

Interestingly, the study also highlighted that it is the contextual factors, including work-family interface, job demands, and team decision-making culture, that ultimately make the difference when it comes to the occurrence of mental health problems such as depression and anxiety.

Therefore, we will not reduce mental illness by switching research fields or by discouraging the practice of mathematics as some high-risk discipline for the mind, but by improving the conditions in which all research (in mathematics as well as in other fields) is carried out.

Another study went one step forward and suggested there are potential mental health benefits in practicing mathematics. Undertaken at Duke University, the research found that engaging the brain in mental exercises involving mathematics is associated with better emotional health.

For this, 186 participants underwent a type of brain scanning called functional imaging, while solving mathematical problems from memory, and then completed tests for assessing their mental health status and emotional coping strategies. The results showed that the participants had a higher ability to adapt their thoughts in relation to emotionally difficult situations when they activated specific regions of the brain while performing mental mathematic exercises.

Matthew Scult, the main author of the study, says:

“Our work provides the first direct evidence that the ability to regulate emotions like fear and anger reflects the brain’s ability to make numerical calculations in real time.”

— MATTHEW SCULT

For a long time, popular culture and mass media have concentrated their storytelling on the extremes of the distribution: stereotypical mathematicians who were romanticised because they were beautiful but also unhealthy minds.

Nearly every movie that touched on the subject of mathematics in cinema (A beautiful Mind, Pi, Good Will Hunting, Enigma, Proof, and others) ended up portraying the eccentric mathematics genius who is ultimately driven to insanity.

But we should not forget the vast and silent majority of mathematicians, for whom mathematics is a form of mental gymnastics that enhances their emotional resilience.

They live their passion for mathematics while leading normal and balanced lives, far from the cameras of Hollywood, as beautiful and healthy minds.

NOTE FROM THE EDITORS: We want to say a huge thank you to Karim Lekadir for writing this very interesting blog for us. Karim Lekadir is a researcher at the Department of Mathematics and Informatics at the University of Barcelona. It is wonderful to have a blog which combines mathematics and mental health. Thank you again Karim!