NEWTON
by Peter Ackroyd
Chatto, £12.99; 176pp

ANYBODY WHO HAS attempted scientific research recognises those rare but happy moments when the light goes on and all suddenly seems clear. Yet you could spend a lifetime reading the literature and never see this eureka moment acknowledged or described.

It remains the private part of a public discourse, lost between the lines of a mathematical proof or buried in the cold embrace of scientific prose. Admitting to inspiration is letting the side down.

In his series of letters, Ian Stewart points out that, unfortunately, the feeling is just the same if you are wrong. The moment of illumination, vivid and utterly persuasive as it may seem, needs the reality check of empirical evidence or a formal proof before it is fit for public view.

Henri Poincaré was rare among mathematicians in trying to understand this process. He said that it had three stages. The first, preparation, involved intense thought, saturating the brain with every possible detail.

The second, which he called “incubation followed by illumination”, needed time and the intervention of the subconscious brain. The final stage was verification, confirming by logical procedures that the answer was right. Poincaré felt at times that he was “present at his own unconscious work”.

Much the same process was employed by Isaac Newton, and is described by Peter Ackroyd in a new life of the first great scientist. “I keep the subject constantly in mind before me and wait ’til the first dawnings open slowly, by little and little, into a full and clear light,” Newton said.

There was a pattern in his way of working. He would concentrate intensely for weeks or months; then abandon the work for a while. When he came back, he would make another great leap forward. As Ackroyd puts it: “He learned how to ‘husband’ his mind, as it were, to allow it to lie fallow before it became fruitful once more.”

Ackroyd’s short biography has many virtues, not the least of which is to remind us what an odd person Newton was. Remembered as a scientist who “mathematised the cosmos”, he spent as many hours in biblical studies and in alchemy as he did in science proper. He made no real distinction between his areas of interest, all of which engaged the intense focus of a mind with extraordinary powers of concentration. When he died, he left 850 pages of unpublished biblical studies behind him.

As the mould for scientific thought, Newton had serious defects. He hated publication, putting it off as long as he could for fear of argument or contradiction. Once he had satisfied himself that he knew the answer, that was enough; perhaps he also enjoyed the sense of power that comes from knowledge shared with nobody else. This is a profoudly anti-scientific attitude, today found only among the green-ink brigade who believe that they have disproved Einstein but will not disclose the evidence for fear that somebody will steal it.

Ackroyd is not out to prove anything, or to make new disclosures about Newton’s life; his is not a biography with a message, and is all the better for it. Written in splendidly elastic prose, each sentence a springboard for the next, it provides a concise, fair and highly readable biography of a singular genius.

Stewart is also a fine writer, even if the Americanised English of his book occasionally grates. Mathematics is plural, so math (singular) lacks logic as well as familiarity to an English ear. One might as well say that Newton specialised in Physic, Static and Dynamic.

Written as a series of letters to a young mathematician, Stewart offers interesting essays on many aspects of the mathematical life, from how to pick a supervisor to what constitutes a proof. His imaginary correspondent, Meg, is female, which sounds like a slice of political correctness until he reveals that these days as many women as men take degrees in mathematics.

The book’s greatest value is its insight into what it is to be a mathematician. Stewart is not of the modern persuasion that suggests we can all be good at anything we choose, if sufficiently motivated and trained, so he does not pretend that everybody can become a mathematician. Most courses of study offer benefits even for the relatively stupid, but mathematics chooses its practitioners more often than they choose it.

Without boasting or false modesty, Stewart gives a few clues. A gifted young mathematician, he was also lucky in his teachers. One directed him to Cambridge.

“No one drifts into being a mathematician” he writes. “On the contrary, it’s a pursuit from which even the talented are easily turned away.”

For those without that necessary talent, the beauty of maths can be glimpsed only intermittently, like a landscape seen from a train through a gap in the houses. Stewart presents plenty of such glimpses in a book that gets better as it goes along.

For example, did you know that if you want to wrap a number of tennis balls in plastic film, using as little as possible, the best arrangement is a sausage? That is, if you have 56 balls or fewer. If you have 57 or more, a better arrangement is clumping them together like potatoes in a sack. (We’re talking in three dimensions here but, being maths, somebody has also proved it in 42 dimensions.) “This is bizarre,” he comments. “I love it.” His enthusiasm is infectious.

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