Today, some scientists will tell you that the Price equation is empty. It is like a footballer who, when asked how their team will win the next match, says they will score more goals than the other team. By trying to explain the game at its most fundamental level, say the critics, the equation explains and predicts nothing about why certain traits should increase or decrease fitness.

In her own quest to crack its meaning, Farnworth went to ask three evolutionary biologists who think there is more to it than that. One told her it was “quite simple, really”. Another jumped up and started scribbling diagrams and equations on the whiteboard in his office. The third said, “None of us understands it really; it resonates in context.” For its supporters, the Price equation is the closest thing biology has to E=mc2. It is a fundamental expression of natural selection that can be used to clarify concepts, separate different components of selection, and compare more specific mathematical models of evolution.

As for Hamilton, he was delighted with it from the moment he saw it. The Price equation was not, as Price had hinted to him, a new derivation or correction of his ideas. Instead, it was “a strange new formalism that was applicable to every kind of natural selection”. Its strangeness came precisely because Price was not a biologist – instead of starting from the work of their scientific forebears, he had worked everything out for himself from first principles.

“In doing so,” wrote Hamilton, “he had found himself on a new road and amid startling landscapes.”

In June 1970, just a few months after Hamilton had written to say how “enchanted” he was with the equation, Price had a profound religious experience (he refused to tell his friend the details, sensing that Hamilton would be as unbelieving of such things as Price himself would have been until that point). Depressed, apparently by his role in confirming that altruism had selfish origins – though it is just as likely that he had stopped taking his thyroxine pills again – he had become obsessed with coincidences in his life, not least the sheer improbability that he, who hadn’t known “a covariance from a coconut”, should have discovered that equation. All at once, despite a lifetime of hardline atheism, he became convinced that a higher power had been at work.

The nearest church was All Souls, just above Regent Street in central London. He walked in and started praying. By the time he walked out again, he had given himself to Jesus.

At first, he brought the full weight of his intellect to bear on the Bible – he concluded that Easter week had taken 12 days, not eight, and was determined to persuade others of this truth, writing arguments as rigorous and detailed as his scientific research. Typical Price: start from first principles, take nobody else’s word for it, test it obsessively and try to find your own way to the truth.

© Jasu Hu

Then, at the end of 1972, he had a second conversion. He had already decided to trust in Jesus completely. He’d stopped taking his thyroxine pills and by now his insurance money was starting to run out – but if Jesus wanted to save him, Jesus would find a way. Around Christmas, he collapsed, close to death. A neighbour found him and he was rushed to hospital where the doctors saved his life. For Price, this was a sign that Jesus did want him to live, but also to change his ways and stop worrying about the length of Holy Week. He told Hamilton he had “sort of ‘encountered’ Jesus”. He had had a vision, in other words, and heard Jesus whisper, “Give to everyone who asks of you.”

Not everyone approved. A friend advised him against trying to “out-God God”, while even the vicar at All Souls said giving money to down-and-outs was “seldom more than an easy way out for ourselves”. But Price carried on giving away his worldly possessions whatever the consequences. He would even give away the big aluminium cross he wore round his neck if someone asked for it. Giving had become a compulsion, an addiction.

Farnworth turned to Isabel Valli at the Institute of Psychiatry, King’s College London, to analyse Price’s letters for clues to his mental state during this period. The meticulous detail in his letters suggested they were reliable accounts of events, but to Valli they were like a psychiatric interview. She got an insight into the way his thought processes were changing while he was in London. Linearity gradually gave way to circular thinking; he would go off on tangents, spiralling ever further away from what he was trying to say. There was a logic to it, but one that became harder for anyone else to follow.

Price was probably experiencing psychotic delusions, paranoia and hallucinations beyond his visions of Jesus, not to mention depression exacerbated by thyroid hormone deficiency. According to Valli, it is human nature when trying to make sense of delusions to construct explanations based on things already significant in our lives; for Price, those things were religion and altruism (and also marriage – he proposed to several women around this time, including suggesting to Julia that they get remarried; like the others, she declined).

It’s not that his altruism was a symptom of mental illness, nor that his equation turned him into an altruist; it was just another part of his increasingly disordered life that he was trying to incorporate into a consistent worldview.

For him, the most rational explanation available was that he had been chosen by God to discover the Price equation and to become an extreme altruist. He was happy to tell people about it, too – if he is remembered at all, one of the first things people tell you about him is that he ran through the corridors of University College London shouting that he had “a hotline to Jesus”. In some ways his life had become extremely complicated, but it was also much more simple to be willing to give up anything and everything and put all his faith in Jesus.