The Boy Who Loved Math: The Illustrated Story of Eccentric Genius and Lovable Oddball Paul Erdos

How a prodigy of primes became the Magician from Budapest before he learned how to butter his own bread.

The great Hannah Arendt called mathematics the “science par excellence, wherein the mind appears to play only with itself.” Few minds have engaged in this glorious self-play more fruitfully than the protagonist of The Boy Who Loved Math: The Improbable Life of Paul Erdős (public library) by writer Deborah Heiligman and illustrator LeUyen Pham — a wonderful addition to the most intelligent and imaginative picture-book biographies of great artists and scientists, telling the story of the eccentric Hungarian genius who went on to become one of the most prolific and influential mathematicians of the twentieth century.

Tucked into Pham’s illustrations are a number of mathematical Easter eggs, such as the palindromic primes, dihedral primes, Leyland primes, and other prime varieties — a particular obsession for Erdős — she built into her Budapest cityscape.

Erdős was born in Budapest to Jewish parents who were both math teachers. His two sisters, ages three and five, died of scarlet fever the day of his birth and his father spent the first six years of little Paul’s life as a prisoner of war in Russia. It was his mother, Anna, who nurtured the young boy’s early love of math.

Even as a toddler — or an epsilon, a very small amount in math, as he would later come to call children — he was already doing complex calculations in his head.

One day, when he was 4, Paul asked a visitor when her birthday was. She told him.

What year were you born? he asked.
She told him.

What time?
She told him.

Paul thought for a moment.
Then he told her how many seconds she had been alive.

Paul liked that trick. He did it often.

But despite — or, rather, because of — his extreme intelligence, Paul didn’t do so well in school. His intellectual vigor paralleled his bodily restlessness — he simply couldn’t sit still in the classroom.

Paul told Mama he didn’t want to go to school anymore. Not for 1 more day, for 0 days. He wished he could take days away — negative school days! He pleaded with Mama to stay home.

Luckily, mama was a worrier. She worried about germs a lot. She worried Paul could catch dangerous germs from the children at school.

Anna finally relented and Paul was entrusted in the care of the stern Fraülein. She and his mother did everything for him — they cut his meat, buttered his bread, and dressed him. But while such attentive care gave the boy room to grow his genius — we do know, after all, that parental presence rather than praise is the key to a child’s achievement — it made for substantial social awkwardness later in life.

By the time time he was twenty, he was already a world-famous mathematician, known as The Magician from Budapest — but he still lived with his mom, who still did his laundry and cooked for him and buttered his bread.

Heiligman illustrates the magnitude of his everyday incapacity with an amusing anecdote:

When Paul was 21, some mathematicians invited him to go to England to work on his math.

[…]

They all went to dinner.

Everyone else talked and ate, but Paul stared at his bread. He stared at his butter. He didn’t know how to butter his bread.

Finally he took his knife, put some butter on it, and spread it on his bread. Phew. He did it! “It wasn’t so hard,” he said.

But the buttering of the bread was merely the trigger for a larger realization — young Paul saw that the traditional path of settling down in one place, with a wife and children, working at a nine-to-five job, wasn’t the right path for him, he who longed to do math for nineteen hours a day. Heiligman writes:

Here is what he did:

Paul would get on an airplane with two small suitcases filled with everything he owned — a few clothes and some math notebooks. He might have $20 in his pocket. Or less.

He flew from New York to Indiana and to Los Angeles. He flew across the world, from Toronto to Australia.

“I have no home,” he declared. “The world is my home.”

More than half a century before Airbnb, he began staying with mathematicians all over the world, who would take him into their homes and take care of him just like his mother had. He wasn’t the easiest of house guests — he would wake up at 4 in the morning to do math, and one time he caused a colorful kitchen explosion by stabbing a carton of tomato juice with a knife, having grown impatient with figuring out how to open it properly — but his friends around the world loved him dearly for his brilliant mind and generous collaborative spirit.

Indeed, for all his eccentricity — TIME famously called him “The Oddball’s Oddball” — Erdős was no lone genius. If Voltaire was the epicenter of the famous Republic of Letters, Erdős was the epicenter of a Republic of Numbers — over the course of his long life, he collaborated with more than 500 other mathematicians and greatly enjoyed his role as what Heiligman aptly terms a “math matchmaker,” introducing peers around the world to one another so they could cooperate in moving mathematics forward. These collaborations advanced the progress of computing and paved the way for modern search engines.

He became affectionately known as Uncle Paul and mathematicians came to talk of “Erdős numbers” to measure their collaborative distance from the beloved genius in degrees of separation — those who worked with him directly earned the number 1, those who worked with someone who had worked with him directly got 2, and so forth.

Paul said he never wanted to stop doing math. And he didn’t. To stop doing math, Paul said, was to die.

So Paul left this world while he was at a math meeting.

(His famous peer John Nash — who inspired the film A Beautiful Mind, was awarded the Nobel Prize, and bore the Erdős number 3 — wasn’t so lucky.)

Complement the warm and wonderful The Boy Who Loved Math with the illustrated life-stories of other celebrated minds, including Jane Goodall, Albert Einstein, Ibn Sina, and Maria Merian. For a grownup biography of Erdős, see the excellent The Man Who Loved Only Numbers.

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Gorgeous 19th-Century Illustrations of Owls and Ospreys

The science of the familiar “owl-face” and the art of its varied permutations.

In his glorious meditation on science and spirituality, Alan Lightman writes beautifully of finding transcendent experiences in our quotidian existence — experiences like his life-altering half-second encounter with two baby ospreys. Indeed, birds of prey like ospreys, owls, hawks, eagles, and falcons have long possessed the human imagination. A fixture of fables and fairy tales — in other words, a symbolic centerpiece of our civilizational proclivity for thinking with animals — they have continued to enchant storytellers and scientists alike.

Nowhere does the transcendent magnificence of this avian family come more fully alive than in the fourth volume the the six-volume masterwork The Royal Natural History (public library | public domain) by English naturalist, geologist, and writer Richard Lydekker, originally published in 1893.

The fifth chapter of the volume explores owls and ospreys, with engravings at once scientifically scrupulous and wonderfully expressive, emanating a warm celebration of the splendid biodiversity of our world.

Barn-owls

Snowy owl and Lapp owl

Ural owl

The beautiful art, of course, is but a complement to the scintillating science:

[The] characteristic “owl-face” is due, firstly, to the forward direction of the eyes; and, secondly, to a circular disc of radiating feathers, more or less distinctly developed round each eye, and which may be bounded by a ruff of closely-set feathers. In common with many diurnal birds of prey, the owls have a short, stout beak, of which the upper ridge is strongly curved, and the tip deflected in a perpendicular direction ; at its base is a cere, usually covered with stiff bristles concealing the nostrils. The feet are furnished with strong, curved, and sharp claws, and have the fourth toe reversible.

Short-eared owl

Scops owl and long-eared owl

Little owl

Hawk-owl

Tengmalm's owl and pigmy owl

Tawny owl

Eagle-owl

Indian fish-owl

Burrowing owl

Osprey and young

Complement Lydekker’s The Royal Natural History with this showcase of some of the rarest and most beautiful natural history illustrations of the past 500 years.

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The Art of Science Communication: William Zinsser on How to Write Well About Science

How to master the inverse pyramid of transmuting information into wisdom.

I have always considered writing a way of organizing reality — of organizing one’s own mind and, in recording that process, decluttering the reader’s understanding of some subtle or staggering aspect of the world.

Few writers have articulated the philosophies and practicalities behind this artful organization with more clarity and conviction than William Zinsser (October 7, 1922–May 12, 2015) in his 1976 classic On Writing Well: An Informal Guide to Writing Nonfiction (public library) — a masterwork partway, in both time and tenor, between E.B. White’s vintage bible The Elements of Style and psycholinguist Steven Pinker’s contemporary counterpart The Sense of Style.

William Zissner (Photograph: Damon Winter / The New York Times)

With the hindsight of three decades, Zinsser — who had written the book in the early 1970s with nothing but “a dangling lightbulb, an Underwood standard typewriter, a ream of yellow copy paper and a wire wastebasket” — reflects in the preface to the 30th anniversary edition:

Computers have replaced the typewriter, the delete key has replaced the wastebasket, and various other keys insert, move and rearrange whole chunks of text. But nothing has replaced the writer. He or she is still stuck with the same old job of saying something that other people will want to read.

But Zinsser points out that while the job of the writer may have gotten easier as the computer became “an everyday tool for people who had never thought of themselves as writers,” the task of the writer — that ability to say something which “other people will want to read” — has gotten, in many ways, harder:

Any invention that reduces the fear of writing is up there with air-conditioning and the lightbulb. But, as always, there’s a catch. Nobody told all the new computer writers that the essence of writing is rewriting. Just because they’re writing fluently doesn’t mean they’re writing well.

[…]

Two opposite things happened: good writers got better and bad writers got worse. Good writers welcomed the gift of being able to fuss endlessly with their sentences—pruning and revising and reshaping — without the drudgery of retyping. Bad writers became even more verbose because writing was suddenly so easy and their sentences looked so pretty on the screen. How could such beautiful sentences not be perfect?

'Paper Typewriter' by Jennifer Collier from 'Art Made from Books.' Click image for more.

Even in the decade since the 30th anniversary edition, the technological barriers of entry for writing and publishing nonfiction online have gotten exponentially lower and the stakes of good writing and journalism exponentially higher — nowhere more so than in science, where bad writing is not only unpleasurable for the reader but also potentially dangerous.

Indeed, one of the most enduring and urgently important sections of Zinsser’s classic deals with the art of writing about science — something that often befuddles both writers and scientists. The most solid common ground between them, Zinsser playfully suggests, is built upon a shared panic at the prospect of writing — with the expectation of writing well — about science. He addresses this often irrational trepidation:

Writing is not a special language owned by the English teacher. Writing is thinking on paper. Anyone who thinks clearly can write clearly, about anything at all. Science, demystified, is just another nonfiction subject. Writing, demystified, is just another way for scientists to transmit what they know.

[…]

Scientific and technical material can be made accessible to the layman. It’s just a matter of putting one sentence after another. The “after,” however, is crucial. Nowhere else must you work so hard to write sentences that form a linear sequence. This is no place for fanciful leaps or implied truths. Fact and deduction are the ruling family.

To illustrate the importance of this sequential storytelling, Zinsser cites a science assignment he often gives to his writing students — the seemingly simple exercise of describing how something works: “how a sewing machine does what it does, or how a pump operates, or why an apple falls down, or how the eye tells the brain what it sees.” Reflecting on how this assignment plants the seed for good science writing, Zinsser touches on the essential function of writing as a tool for organizing reality:

Describing how a process works is valuable for two reasons. It forces you to make sure you know how it works. Then it forces you to take the reader through the same sequence of ideas and deductions that made the process clear to you. I’ve found it to be a breakthrough for many students whose thinking was disorderly.

This principle of science writing, Zinsser points out, applies to all nonfiction writing, for it teaches the writer to lead the reader, step by step, from knowing nothing about a subject to understanding enough to grow enchanted with its broader significance.

Zinsser illustrates this approach by outlining an inverse Maslow-style pyramid of informational needs:

Imagine science writing as an upside-down pyramid. Start at the bottom with the one fact a reader must know before he can learn any more. The second sentence broadens what was stated first, making the pyramid wider, and the third sentence broadens the second, so that you can gradually move beyond fact into significance and speculation — how a new discovery alters what was known, what new avenues of research it might open, where the research might be applied. There’s no limit to how wide the pyramid can become, but your readers will understand the broad implications only if they start with one narrow fact.

But as someone who thinks a great deal about the challenge of transmuting information into wisdom, I find myself inclined to push Zinsser’s model a step further and consider the importance of cultivating a layer of wisdom above the layer of “significance and speculation.” The difference might be subtle, but it’s an important one: After all, when one reads the very finest science writing — be it Oliver Sacks writing about the mind or Diane Ackerman about the senses or Stephen Jay Gould about lepidoptery or Robin Wall Kimmerer about moss — one walks away informed about the significance of these scientific phenomena, certainly, but more than that, one walks away elevated and enriched and illuminated with a new appreciation of our “strange and shimmering world.”

On Writing Well remains absolutely indispensable, exploring such essential aspects of the craft as the key to sophisticated simplicity, the core transaction between the writer and the reader, the art of the interview, and the most fruitful attitude for the writer. Complement it with Cheryl Strayed on the importance of faith and humility in writing, Susan Sontag’s advice to aspiring writers, Virginia Woolf on writing and self-doubt, E.B. White on the two faces of discipline, and Ann Patchett on why self-forgiveness is the most important tool of writing, then revisit this ongoing archive of great writers’ advice on the craft.

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A Biologist-Turned-Buddhist and His Philosopher Father on the Nature of the Self and the True Measure of Personal Strength

“You first need to have an ego in order to be aware that it doesn’t exist.”

For the past few centuries, Western philosophy has maintained that human beings are driven by enlightened self-interest — a view predicated on the needs and desires of a solid self. Meanwhile, Eastern philosophies and spiritual traditions have long considered the self an illusion — a view with which modern science has recently begun to side.

These contradictory conceptions of the self as a centerpiece of identity and success, per the Western view, and as an illusion, per the Eastern one, are what French philosopher Jean-François Revel and his biologist-turned-Buddhist son, Matthieu Ricard, explore in their extraordinary conversation, published as The Monk and the Philosopher: A Father and Son Discuss the Meaning of Life (public library).

What makes the conversation particularly compelling is the unusual pairing of perspectives — it is not only an intergenerational dialogue between a father and a son who both possess enormous intellectual potency, but a dialogue between Western philosophy and Eastern spirituality with a strong emphasis on science. The scientific perspective, in fact, comes not from Revel but from Ricard, who gave up a promising career as a molecular biologist — he had worked with Nobel laureate Jacques Monod — to move to Nepal and study Tibetan Buddhism. Doubly significant is Ricard’s route to Buddhism: Raised in the strongly secular home of two prominent French intellectuals — his mother, Revel’s wife, was the painter Yahne Le Toumelin — he grew up with only an intellectual curiosity toward religion and turned to Buddhism not out of disappointment with Western faiths but out of what his father calls “a state of indifference to any religion, a kind of religious weightlessness.”

Matthieu Ricard (right) with his father, Jean-François Revel (Photograph: Raphaelle Demandre)

So in 1999, when Revel traveled to Ricard’s home in Kathmandu and the two sat down for this remarkable intellectual encounter, it was the philosophical rather than the religion dimensions of Buddhism that took center stage as the father and son contemplated such immutable human concerns as free will, the meaning of life, the value of scientific progress, and the pillars of the good life. As they speak, each addresses the other as much as he is confabulating with himself, which results in a masterpiece of the art of conversation at its most elevated and ennobling — an exchange of dynamic contemplation between and within minds, driven not by the self-righteous slinging of opinions but by a deep commitment to mutual understanding and to enriching the shared pool of wisdom.

One of the most pause-giving dimensions of the conversation deals with this notion of the self and its illusory nature. When Revel takes issue with the Buddhist concept of reincarnation, pointing out its mystical and scientifically ungrounded suppositions, Ricard emphasizes its metaphorical and philosophical importance over its literal interpretation. Embedded in that notion, he suggests, is the key to unmooring ourselves from the tyranny of the self in the here and now:

It’s important to understand that what’s called reincarnation in Buddhism has nothing to do with the transmigration of some “entity” or other… As long as one thinks in terms of entities rather than function and continuity, it’s impossible to understand the Buddhist concept of rebirth.

[…]

Since Buddhism denies the existence of any individual self that could be seen as a separate entity capable of transmigrating from one existence to another by passing from one body to another, one might well wonder what it could be that links those successive states of existence together… It’s seen as a continuum, a stream of consciousness that continues to flow without there being any fixed or autonomous entity running through it.

Illustration from 'The Magic Boat' by Tom Seidmann-Freud, Sigmund Freud's niece. Click image for more.

Ricard likens this concept to “a river without a boat descending along its course” and is careful to point out a common misconception: Although Buddhism denies the existence of the individual self, it doesn’t deny individual consciousness. He explains:

The fact that there’s no such discontinuous entity being transferred from one life to the next doesn’t mean that there can’t be a continuity of functioning. That the self has no true existence doesn’t prevent one particular stream of consciousness from having qualities that distinguish it from another stream. The fact that there’s no boat floating down the river doesn’t prevent the water from being full of mud, polluted by a paper factory, or clean and clear. The state of the river at any given moment is the result of its history. In the same way, an individual stream of consciousness is loaded with all the traces left on it by positive and negative thoughts, as well as by actions and words arising from those thoughts. What we’re trying to do by spiritual practice is to gradually purify the river. The ultimate state of complete clarity is what we call spiritual realization. All the negative emotions, all the obscurations that render the underlying wisdom invisible, have then been dissolved.

Echoing the great Zen teacher D.T. Suzuki’s assertion that “the ego-shell in which we live is the hardest thing to outgrow,” Ricard argues that this recognition of individual consciousness is central to the dissolution of the ego-shell:

It’s not a question of annihilating the self, which has never really existed, but simply of uncovering its imposture. Indeed, if the self did have any intrinsic existence we’d never be able to bring it from existence into nonexistence.

[…]

A nonexistent self can’t really be “abolished,” but its nonexistence can be recognized. What we want to abolish is the illusion, the mistake that has no inherent existence in the first place… whatever we judge to be disagreeable or harmful. But as soon as we recognize that the self has no true existence, all these attracting and repelling impulses will vanish… The self has neither beginning nor end, and therefore in the present it has no more existence than the mind attributes to it.

Ricard, who has since written about the secret of happiness, considers how our natural, everyday experience of the “I” mutates into the illusion of the self, from which all of our suffering stems:

There’s a natural feeling of self, of “I,” which makes you think “I’m cold, I’m hungry, I’m walking,” and so forth. By itself, that feeling is neutral. It doesn’t specifically lead to either happiness or suffering. But then comes the idea that the self is a kind of constant that lasts all your life, regardless of all the physical and mental changes you go through. You get attached to the idea of being a self, “myself,” a “person,” and of “my” body, “my” name, “my” mind, and so on. Buddhism accepts that there is a continuum of consciousness, but denies any existence of a solid, permanent, and autonomous self anywhere in that continuum. The essence of Buddhist practice is therefore to get rid of that illusion of a self which so falsifies our view of the world.

Illustration by Mimmo Paladino for a rare edition of James Joyce's Ulysses. Click image for more.

When his father probes how one is expected to effect positive change in the world without a sense of personal agency — another common critique by those who misunderstand the foundational philosophies of Buddhism — Ricard responds:

The wish to allay others’ suffering, which may inspire a whole lifetime’s work, is an admirable ambition. It’s important to distinguish between negative emotions, like desire, hatred, and pride, that solidify still further our self-centered outlook, and positive ones, like altruistic love, compassion, and faith, that allow us to free ourselves little by little from those negative and self-centered tendencies. Positive emotions don’t disturb our mind, they reinforce it and make it more stable and more courageous.

In a sentiment that calls to mind David Foster Wallace on the dark side of ambition, Ricard makes an important distinction between the two types of ambition:

Positive ambition — the pursuit of others’ well-being by all possible means, the fervent wish to transform oneself — is one of the cardinal virtues in Buddhism. In fact, Buddhists nurture one main ambition without any limits, that of removing the suffering of all living beings throughout the whole universe. That sort of ambition stops you succumbing to inertia and makes you strong-minded and determined. So the distinction between the positive and negative, selfless and self-centered sides of ambition is important. You could say that ambition is positive if its aim is to help others. That’s the simplest definition. Conversely, ambition is negative if achieving it is detrimental to others, and an emotion is negative if it destroys your own and others’ inner peace.

He illustrates this with a verse from the eight-century Buddhist sage Shantideva:

All the joy the world contains
Has come through wishing happiness for others.
All the misery the world contains
Has come through wanting pleasure for oneself.
Is there need for lengthy explanation?
Childish beings look out for themselves,
While Buddhas labor for the good of others:
See the difference that divides them!

With that great Eastern capacity for holding paradox and fusing contradictory concepts into a unity of wisdom, Ricard argues that shedding the ego-shell actually requires first fortifying our ego — more than that, he suggests, true altruism is the product not of selflessness but of a strong sense of self:

Buddhism’s goal of uncovering the “imposture of the ego,” this ego that seems so powerful and causes us so much trouble while having no existence in itself. Nevertheless, as a first step it’s important to stabilize this feeling of a self in order to distinguish all its characteristics. You could say, paradoxically, that you first need to have an ego in order to be aware that it doesn’t exist. Someone with an unstable, fragmented, amorphous personality has little chance of being able to identify that powerful feeling of “me,” as a prior step to recognizing that it doesn’t correspond to any real entity. So you need to start with a healthy and coherent self to be able to investigate it. You can shoot at a target, but not in fog.

[…]

But it’s important not to think that once the imposture of the ego is unmasked you find yourself in a state of inner nothingness, to the point that the destruction of the personality renders you incapable of acting or communicating. You don’t become an empty container. It’s quite the opposite. When you’re no longer the plaything of an illusory despot, like the shadows in Plato’s cave, your wisdom, love for others and compassion can be freely expressed. It’s a freedom from the limitations imposed by attachment to a self, not at all an anesthesia of the will. This “opening of the eyes of wisdom” increases your strength of mind, your diligence, and your capacity to take appropriate and altruistic action.

Revel contrasts this with the West’s “cult of the self” and our civilizational emphasis on “the strong personality” as a hallmark of success, questioning whether there can be a common ground between cultural and philosophical traditions so diametrically opposed in this regard. But Ricard, once again, meets the problem with semantic lucidity that melts away the apparent conflict:

If by personality you mean exacerbation of the ego, simply to have a strong personality seems to me, unfortunately, a highly dubious criterion of success. Hitler and Mao Tse-tung had very strong personalities.

Illustration by André François from 'Little Boy Brown' by Isobel Harris. Click image for more.

Echoing Bertrand Russell’s famous assertion that “construction and destruction alike satisfy the will to power, but construction is more difficult… and therefore gives more satisfaction to the person who can achieve it,” Ricard adds:

It’s important not to confuse strong individuality and strength of mind. The great teachers I’ve been able to meet had indomitable strength of mind. You could say they had very impressive personalities, and that they radiated a sort of natural strength that everyone who met them could perceive. But the big difference was that you couldn’t find the slightest trace of ego in them. I mean the kind of ego that inspires selfishness and self-centeredness. Their strength of mind came from knowledge, serenity, and inner freedom that were outwardly manifested as an unshakable certainty. They were worlds apart from Hitler, Mao Tse-tung and the like, whose powerful personalities arose from an unbridled desire to dominate, and from pride, greed, or hatred. In both cases, we’re faced with immense power, but in the first that power is a flow of constructive altruism, while in the second it’s negative and destructive.

The Monk and the Philosopher is a remarkable read in its totality, addressing with enormous depth and dimension such aspects of the human experience as happiness, suffering, education, ethics, and love. Complement it with D.T. Suzuki on how Zen can help us cultivate our character and Jack Kerouac’s Zen-inspired meditation on the self illusion and “the golden eternity,” then revisit Albert Einstein and the Indian philosopher Tagore’s historic conversation entwining Eastern and Western perspectives with great mutual curiosity and goodwill.

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