The Mercurial Mathematician

COMMENT BOOKS & ARTS DITH PRAN/THE NEW YORK TIMES REDUX/EYEVINE TIMES YORK NEW PRAN/THE DITH

John Conway, seen in his office at Princeton University in New Jersey, has contributed to group theory, geometry, surreal numbers and combinatorial game theory.

MATHEMATICS including Robert Curtis and Simon Norton. Conway is also famous for his ‘Monstrous Moonshine Conjecture’ with Norton, a bridg- ing of two disparate fields — finite-group and The mercurial complex-function theory — that was proved by Conway’s student Richard Borcherds in 1992 (although not to Conway’s satisfaction). Conway made contributions to geometry, mathematician including work on sphere-packing, polytopes and knot theory; for surreal numbers, the largest possible extension of the real num- Michael Harris relishes a biography of the playful, ber line, which he constructed in the form complicated group theorist John Horton Conway. of a game; and (with Simon Kochen) for the 2006 Free Will Theorem, which purports to prove that if humans have free will, then f you want to read about what John he’s an asshole,” she writes. In Conway, Rob- so do elementary particles. There is also Conway has done and why his peers erts has found a personality neither tragic nor Conway the combinatorial game theorist, shower him with superlatives — “most austere, like so many biographized mathema- often introduced — Icreative”, “best combinatorialist”, “one of the ticians. He is loquacious, joyous and most of too often for his taste most eminent mathematicians of the century” all, playful: as he said more than 30 years ago, — as “best known for — there are a number of popularizations. The “if you or your readers saw what I actually did, his invention of the marks he has left on mathematics are diverse they’d be disgusted. They’d say, ‘Good money ‘Game of Life’”. This and profound, but some of their depth can be is being paid out to support these people’.” landmark in the his- grasped given curiosity and patience. What does he do? My work tends to the tory of cellular autom- You should, however, read Siobhan abstract, so I know Conway mainly as a ata (and in Martin Roberts’s Genius at Play if you want to know central player in the successful classifica- Gardner’s Scientific what it feels like to be with Conway, and tion of finite simple groups, the elementary American ‘Mathemati- glimpse what it must feel like to be him. Rob- structures of symmetry. The ATLAS of Finite Genius At Play: cal Games’) column is The Curious Mind erts breathes more life into the stories of a liv- Groups (Clarendon, 1985) was a 12-year col- of John Horton notoriously addictive. ing mathematician than I thought possible. lective enterprise that aimed to record all the Conway Conway’s most “He’s high-maintenance, he’s generous. He’s groups’ “interesting properties”; run under SIOBHAN ROBERTS memorable contribu- emotional, he’s impassive. He’s a sweetheart, Conway’s guidance, it involved colleagues Bloomsbury: 2015. tions have the appeal

406 | NATURE | VOL 523 | 23 JULY 2015 © 2015 Macmillan Publishers Limited. All rights reserved BOOKS & ARTS COMMENT of a good puzzle, even when not directly SCIENCE FICTION inspired by games. Roberts’s “kalei- doscope of inquiry” is a marvel for its virtuoso juggling of narrative speeds, reminiscences, implausible digressions Star-flight dreaming and long passages of precise, comprehen- sible mathematics. She packs it all into a Gregory Benford probes Kim Stanley Robinson’s tidy chronology framed by the story of a politics-drenched tale of interstellar travel. road movie starring Conway; she plays his amanuensis, occasional driver and “back channel” through which the world com- uman star flight is a vast prospect — municates with this most mercurial and one many think impossible. To arrive untidy of mathematicians. in a single lifetime demands travel at “I’m confused at some times,” Conway Hspeeds approaching that of light, especially for says. “In fact … it’s a permanent state.” stars such as τ-Ceti, some 3.7 parsecs (12 light He was speaking of mathematics, but his years) away. ‘Generation ships’ containing casual attitude to the mundane details of large biospheres stable over centuries are the his personal history poses a challenge, only plausible method yet mooted. even for a biographer as accomplished as Aurora, by veteran science-fiction writer Roberts. Conway encapsulates his philos- Kim Stanley Robinson, hinges on such an

VICTOR HABBICK/VISUALS UNLIMITED/GETTY HABBICK/VISUALS VICTOR ophy of life (and work) as a “Vow”: “Thou expedition, setting out from Earth in the shalt stop worrying and feeling guilty; twenty-sixth century. In 2012, Robinson was thou shalt do whatever thou pleasest.” quoted in Scientific American as saying, “It’s a T h e r e a r e joke and a waste of time to think about star- “Thou shalt glimpses of the ships or inhabiting the galaxy. It’s a systemic stop worrying abyss. As Conway lie that science fiction tells the world that the and feeling attempts to explain galaxy is within our reach.” Aurora seems to An artist’s impression of a ‘generation ship’. guilty; thou the ATLAS to Rob- be a U-turn, involving unlikely plot devices. shalt do erts, he exclaims, The starship is like a car axle, with two large good matrix” for their reproduction. whatever thou “I know all the wheels turning for centrifugal gravity; the As plans and back-up plans go awry, Rob- theorems. But biomes along their rims support 24 Earthly inson skimps on characterization to focus pleasest.” there’s still some- life-zones that need constant tending. Arrival on the detail of ecosphere breakdown and thing that to me is (after two centuries) at Aurora, the Earth-like the human struggle against the iron laws of unknown, unknowable … It makes me moon of super-Earth Planet E, brings home island biogeography. Bacteria evolve swiftly, sad that I’ll probably never understand just how technologically and socially complex making “the whole ship sick”. The colonists’ it.” Roberts shows us his private abysses: such a venture might be. We certainly learn lifespans, bodies and IQs shrink. Factions three marriages and three divorces, with why ships’ captains are preferable to mob rule. form in the once placid 2,000-strong com- hints of numerous affairs; two heart Like Robinson’s mid-1990s Mars trilogy, munity, where humans had seen themselves attacks, two strokes and a suicide attempt. Aurora is a drama of political strife. Robin- as biome managers, farming and fixing their But Conway’s playfulness surfaces and son seems to prefer harnessing the scale and ship with assistance from a web of artificial resurfaces. He notes that surreal numbers exotic frame of space to stage reflections intelligences (AIs). The Robinson trope of “is the thing I’m proudest of … Because it on human nature, rather than grasping the fragmentation in near-utopian societies slides pokes fun at people who do things in com- great problem of science fiction: the alien. In towards tragedy: “Existential nausea comes plicated ways.” And in research guidance Aurora he meditates on the enormous diffi- from feeling trapped … that the future has to his students, he writes: “No no no no culties that a novel biosphere would present. only bad options.” As the discord turns deadly, no! You’re being far too reasonable.” The misgivings of physicist Paul Davies in the the AIs form a collective consciousness capa- To see this motley of Conways squeezed anthology Starship Century (Lucky Bat, 2013) ble of decision-making, following the humans into one outlandish personality is to want and of biologist E. O. Wilson in The Meaning with gimlet eyes and melancholy analysis. to join the chorus of his admirers. Roberts of Human Existence (Liveright, 2014) about Aurora finally becomes a tale of two voy- has masterfully untangled Conway’s com- living on exoplanets are explicated: the voy- ages, although I will not spoil the ending. plexities. His ways of being in the world, agers include sophisticated biologists, but Robinson offers, with fiction-as-footnote in Roberts’s telling, amount to a class of adjusting Earth life to even apparently simple thoroughness, an acute analysis of what adjectives yet to be invented, to join his worlds is hard, maybe impossible. interstellar exploration would entail. Living mathematical innovations. The apparently lifeless Aurora has Earth- for two centuries in a sealed environment In search of the best ways to talk about like levels of atmospheric oxygen. Robinson’s imposes tensions that become intolerable if numbers, groups, shapes and games, colonists implausibly believe that these could the dream of colonization dies. Roberts has rediscovered the power of have survived from its birth, forgetting about Immigrants to far lands seldom solicit talking about the people who dedicate rust (which makes Mars red) and the fact that the views of their children or grandchildren their lives to their study; and what an our oxygen comes from living organisms. first. Should interstellar colonies be differ- enjoyable discovery that is. ■ Ultimately, that error leads to the demise of ent? Apparently, Robinson thinks so. ■ their dreams. They discover that Aurora har- Michael Harris is a mathematician at bours nanometre-scale organisms they deem Gregory Benford is professor emeritus of Columbia University in New York City. a possible “interim Aurora physics and astronomy at the University His latest book is Mathematics Without step toward life”, and KIM STANLEY of California, Irvine, and the author of Apologies. disquietingly note that ROBINSON Timescape. e-mail: [email protected] humans “appear to be a Orbit: 2015. e-mail: [email protected]