Cantor, Gauss, Riemann, Euler. Hilbert.
Poincaré. Noether. Hypatia. Klein, Minkowski,
Turing, von Neumann. Cauchy, Lie, Dedekind,
Brouwer. Boole. Peano. Hamilton, Laplace, Lagrange.
If you’re unfamiliar with the names and contributions of the theoretical mathematicians in the modern era, then you may find Cormac McCarthy’s latest novel Stella Maris a challenging read. It doesn’t have to be, even if you’re one of those people who find it exasperating that 2 is the only even prime number, constituting a set of itself; or that the appearance and pattern of prime numbers aren’t predictable, though the set of primes appears to be infinite; or that some infinities are denser than others, meaning there are more real than natural numbers – even though there are infinite sets of both.
Set in 1972 in Black Falls, Wisconsin, the novel opens as Alicia Western, twenty-year-old mathematics prodigy, admits herself to a psychiatric hospital after receiving a diagnosis of paranoid schizophrenia. Told entirely from the transcripts of Alicia’s therapy sessions with resident psychiatrist Dr. Cohen, Alicia’s story unfolds as a series of evolutions revealing the extent to which her genius is manifestly frightening. Not only is she hypermnesic, gifted with photographic recall, but she also experiences numbers and letters in color, a condition called synesthesia. At one point in their exchange, Dr. Cohen quizzes Alicia about the perceived elegance of equations:
Are the equations themselves beautiful?
Not if you don’t know what they mean.
Is E=mc2 a thing of beauty?
You should see it in color.
Alicia has spent three years majoring in mathematics at Princeton and a year as a doctoral candidate at the University of Chicago. Drawn to math for its presumptive promise of predictability, she instead discovers to her disappointment that operations of advanced mathematics are anything but stable and that the elite coterie of theoretical mathematicians orbiting in the highest realms of abstraction often have a tenuous hold on reality. To illustrate her point, she relates to Cohen the longish narrative of David Hilbert and Kurt Gödel. Hilbert, a German mathematician considered one of the greats of the late nineteenth and early twentieth centuries, spent four decades trying to discover an axiom uniting all branches of mathematics. Fellow German Kurt Gödel upended Hilbert’s formulations in a paper read in Venice in 1931 now popularly called the Incompleteness Theorem. Gödel’s work is best understood in the context of paradox:
Consider the sentence:
“This statement is false.” Is that true? If so, that would make
the statement false. But if it’s false, then the statement is true.
This sentence creates an unsolvable paradox; if it’s not true and
it’s not false, then what is it?
Where mathematics is concerned, Alicia admits she’s at the end of her tether “because you can’t mathematize mathematics.” In other words, Gödel’s theorem means there can be no mathematical theory of everything, no unification of what’s provable and what’s true. Mathematics exists outside operations of the human mind. The inadequacies of math sadden Alicia, as heard in the following exchange about the insufficiency of numbers that don’t add up:
You’re skeptical about mathematics?
You feel disappointed in the discipline in some way?
I’m not sure how you can be skeptical about the entire subject.
But it has disappointed you.
That would be one way to put it.
How would it do that?
Well. In this case it was led by a group of evil and aberrant and
wholly malicious partial differential equations who had conspired
to usurp their own reality from the questionable circuitry of its
creator’s brain not unlike the rebellion which Milton describes
and to fly their colors as an independent nation unaccountable to God
or man alike. Something like that.
Alicia makes a convincing case for an indissoluble connection between math and madness, describing the last days of her hero Kurt Gödel:
He wouldn’t eat. Thought the food was poisoned. When he died
he weighed about seventy pounds. Oppenheimer [nuclear physicist
and ‘father of the atomic bomb’] was head of IAS [Institute for Advanced Study]
at the time and he would go over to see him in the hospital. One day
the doctor came in. He didn’t know who Gödel was – just some nutty
professor from the university – and Oppenheimer told him to take care
of Gödel because he was the greatest logician since Aristotle. And the
doctor nodded and began to edge toward the door and Oppenheimer
realized that he was thinking: Good God, now there’s two of them.
McCarthy’s novels have a way of circling back to East Tennessee, in this case to provide Alicia’s backstory. As part of his therapeutic initiative, Dr. Cohen asks about her upbringing. Alicia discloses she was born in Los Alamos, New Mexico, but spent her childhood in Wartburg, Tennessee, close to Oak Ridge, where her physicist father had worked for Robert Oppenheimer in developing the atomic bomb.
He’d also married a local girl, a beauty contestant and later Alicia’s mother, who’d taken pains to conceal her Jewishness. Dr. Cohen asks Alicia what being Jewish is like for her. She replies that “Jews represent two percent of the population and eighty percent of mathematicians. If those numbers were even a little more skewed we’d be talking about a separate species.”
If Jews are copiously represented in mathematics, women are not, despite tallying significant achievements. Alicia takes for granted she will be an outlier in the hyper-cerebral atmosphere of the University of Chicago. With a few exceptions, Alicia is snubbed by colleagues in the traditionally male-dominated field. Being diagnosed as mentally ill augments the complexities she experiences as a mathematician and a woman. She acknowledges the problematic status of smart women opposing the status quo in every age:
Women enjoy a different history of madness. From witchcraft
to hysteria we’re just bad news. We know that women were
condemned as witches because they were mentally unstable but
no one has considered the numbers – even few as they might be –
of women who were stoned to death for being bright. That I havent
wound up chained to a cellar wall or burned at the stake is not
a testament to our ascending civility but to our ascending skepticism.
If we still believed in witches we’d still be burning them. Hooknosed
crones strapped into the electric chair. No one has ever seemed to
comment that the stereotypical witch is meant to appear Jewish.
I guess the skepticism is okay. If you can stomach what goes with it.
I’m happy to be treated well but I know that it’s an uncertain business.
When this world which reason has created is carried off at last
it will take reason with it. And it will be a long time coming back.
Perhaps the most interesting detail Alicia reveals is her father’s imperviousness to the terrors he and his coterie of scientists unleash on the world. Their lack of imagination regarding the consequences for future generations is troubling. Dr. Cohen asks if Alicia’s father ever lost sleep for his participation in the Manhattan Project:
My father didnt sleep before the bomb and he didnt sleep after. I think
most of the scientists didnt give that much thought to what was going
to happen. They were just having a good time. They all said the same
thing about the Manhattan Project. That they’d never had so much fun
in their lives. But anyone who doesnt understand that the Manhattan Project
is one of the most significant events in human history hasnt been paying
attention. It’s up there with fire and language.
McCarthy’s Stella Maris has an ending but not a conclusion, though Alicia hints at one that never materializes when Dr. Cohen indicates their therapy session is over:
I think our time is up.
I know. Hold my hand.
Hold your hand?
Yes. I want you to.
All right. Why?
Because that’s what people do when they’re waiting for the end of something.
Readers shouldn’t expect much of a plot either. There are no high moments we’ve come to expect from narrative. McCarthy isn’t the only author to write a plotless novel. James Joyce and his Finnegans Wake come readily to mind. In some ways, Stella Maris is as frustrating as Joyce’s sprawling stream-of-consciousness experiment. Like Joyce, too, McCarthy eschews such niceties as punctuation. However, his hardcore readers won’t be deterred by the novelist’s eccentricities as it’s been sixteen years since his novel The Road was released. That’s been a long dry spell for his readership.
McCarthy’s Stella Maris delivers particularly with the characterization of Alicia Western who is steadfastly unforgettable, by turns fragile and frightening. McCarthy has successfully deconstructed the rarefied world of advanced mathematics. Those keeping up with him know the author has spent years at the Santa Fe Institute, a think tank billing itself as a place asking “big questions.” As the only writer in residence at the institute, McCarthy has been the decades-long beneficiary of conversations with mathematicians and physicists over a long span of time. We can only speculate about his colleagues’ influence, but McCarthy’s Stella Maris illuminates the life of the higher mind with shimmering intelligence and flashes of brilliance uniquely the author’s own.
**Featured Image: Pawel Szvmanski, Unsplash