When I was in high school I took the ACT, a college aptitude exam used as an admissions criterion by most American universities. My score was in the lowest third of all students. That was painful enough but, adding insult to injury, the ACT score report informed me that, based on my score, my expected probability of succeeding at my hometown college, the University of Utah, was around 15%. As I remember it, my chance of success at my dream school of Harvard University was less than 3%.

I felt pretty hopeless about my future. After all, these stark percentages were endowed with the sober authority of mathematics. Before I took the exam, I had thought that one day I might become a scientist or neurologist, but no – what a silly fantasy that was.

Standardised tests of aptitude, talent and intelligence have become more widespread than ever. Key Stage tests, GCSEs and A levels size up whether someone has what it takes to succeed in school, university or work. Though we might feel intuitively that something is wrong with using our results on a single day of testing to measure our potential, we reluctantly endure it because exams have the imprimatur of objective fact. After all, testing has been endorsed by more than a century’s worth of psychologists and psychometricians. But what if the mathematics serving for aptitude tests was profoundly flawed?

It is, and we know this because of a burgeoning new interdisciplinary science. “The science of the individual” is revolutionising the methods of many fields including medicine, biology, neuroscience, genetics and the social sciences. For example, oncologists have switched their emphasis from standardised treatments to personalised ones that target individual cancers. Neuroscientists have begun to abandon their reliance on measuring how individual brains deviate from average brain maps. Nutritionists are moving from universal dietary recommendations to personal diets.

Two principles explain why it is never permissible to use a single test result to judge someone’s potential. The jaggedness principle holds that all mental qualities we care about – intelligence, character, talent, performance – are multi-dimensional. Whenever we try to reduce the true complexity of someone’s abilities into a simple number, we lose everything important about the individual.

Secondly, the context principle asserts that performance always depends on the interaction of a specific individual and situation; it is meaningless to evaluate any performance without reference to the particular environment in which the individual performs. Multiple-choice tests will not evaluate someone’s ability to drive a car on the road.

Decisions made from a single test result are questionable or even meaningless. This is not an article of faith, but a mathematical fact. It is a conclusion of 21st-century mathematics, rather than outmoded 19th-century statistics. That’s why major companies such as Google and Deloitte have abandoned them.

Nevertheless, far too many schools, universities and businesses continue to apply obsolete tests. This prevents the institutions from getting a clear portrait of individual talent. It compels students to accept a false notion of their own promise.

Even though I was crushed by my own embarrassing exam result and spent years feeling inferior, eventually I decided there was more to me than a percentile. I pursued my dreams of a science career – and today I teach at Harvard.

The End of Average by Todd Rose with Ogi Ogaso is published by Allen Lane at £20. To order a copy for £16, go to bookshop.theguardian.com