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

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 mathematician Paul Erdős (March 26, 1913–September 20, 1996), the protagonist of The Boy Who Loved Math (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.

BP

The Illustrated Story of Persian Polymath Ibn Sina and How He Shaped the Course of Medicine

How a voraciously curious little boy became one of the world’s greatest healers.

Humanity’s millennia-old quest to understand the human body is strewn with medical history milestones, but few individual figures merit as much credit as Persian prodigy-turned-polymath Ibn Sina (980–1037), commonly known in the West as Avicenna — one of the most influential thinkers in our civilization’s unfolding story. He authored 450 known works spanning physics, philosophy, astronomy, mathematics, logic, poetry, and medicine, including the seminal encyclopedia The Canon of Medicine, which forever changed our understanding of the human body and its inner workings. This masterwork of science and philosophy — or metaphysics, as it was then called — remained in use as a centerpiece of medieval medical education until six hundred years after Ibn Sina’s death.

As a lover of children’s books that celebrate the life-stories of influential and inspiring luminaries — including those of Jane Goodall, Henri Matisse, Pablo Neruda, Henri Rousseau, Julia Child, Albert Einstein, and Maria Merian — I was delighted to come upon The Amazing Discoveries of Ibn Sina (public library) by Lebanese writer Fatima Sharafeddine and Iran-based Iraqi illustrator Intelaq Mohammed Ali, a fine addition to these favorite children’s books celebrating science.

In stunning illustrations reminiscent of ancient Islamic manuscript paintings, this lyrical first-person biography traces Ibn Sina’s life from his childhood as a voracious reader to his numerous scientific discoveries to his lifelong project of advancing the art of healing.

A universal celebration of curiosity and the unrelenting pursuit of knowledge, the story is doubly delightful for adding a sorely needed touch of diversity to the homogenous landscape of both science history and contemporary children’s books — here are two Middle Eastern women, telling the story of a pioneering scientist from the Islamic Golden Age.

The Amazing Discoveries of Ibn Sina comes from Canadian indie powerhouse Groundwood Books, who have also given us such treasures as a wordless illustrated celebration of the art of noticing, a tender love letter to winter, and a heartening celebration of gender diversity.

Illustrations courtesy of Groundwood Books; photographs my own.

BP

What Mathematics Reveals About the Secret of Lasting Relationships and the Myth of Compromise

Why 37% is the magic number, what alien civilizations have to do with your soul mate, and how to master the “negativity threshold” ideal for Happily Ever After.

In his sublime definition of love, playwright Tom Stoppard painted the grand achievement of our emotional lives as “knowledge of each other, not of the flesh but through the flesh, knowledge of self, the real him, the real her, in extremis, the mask slipped from the face.” But only in fairy tales and Hollywood movies does the mask slip off to reveal a perfect other. So how do we learn to discern between a love that is imperfect, as all meaningful real relationships are, and one that is insufficient, the price of which is repeated disappointment and inevitable heartbreak? Making this distinction is one of the greatest and most difficult arts of the human experience — and, it turns out, it can be greatly enhanced with a little bit of science.

That’s what mathematician Hannah Fry suggests in The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation (public library) — a slim but potent volume from TED Books, featuring gorgeous illustrations by German artist Christine Rösch. From the odds of finding your soul mate to how game theory reveals the best strategy for picking up a stranger in a bar to the equation that explains the conversation patterns of lasting relationships, Fry combines a humanist’s sensitivity to this universal longing with a scientist’s rigor to shed light, with neither sap nor cynicism, on the complex dynamics of romance and the besotting beauty of math itself.

She writes in the introduction:

Mathematics is ultimately the study of patterns — predicting phenomena from the weather to the growth of cities, revealing everything from the laws of the universe to the behavior of subatomic particles… Love — [like] most of life — is full of patterns: from the number of sexual partners we have in our lifetime to how we choose who to message on an internet dating website. These patterns twist and turn and warp and evolve just as love does, and are all patterns which mathematics is uniquely placed to describe.

[…]

Mathematics is the language of nature. It is the foundation stone upon which every major scientific and technological achievement of the modern era has been built. It is alive, and it is thriving.

In the first chapter, Fry explores the mathematical odds of finding your ideal mate — with far more heartening results than more jaundiced estimations have yielded. She points to a famous 2010 paper by mathematician and longtime singleton Peter Backus, who calculated that there are more intelligent extraterrestrial civilizations than eligible women for him on earth. Backus enlisted a formula known as the Drake equation — named after its creator, Frank Drake — which breaks down the question of how many possible alien civilizations there are into sub-estimates based on components like the average rate of star formation in our galaxy, the number of those stars with orbiting planets, the fraction of those planets capable of supporting life, and so forth. Fry explains:

Drake exploited a trick well known to scientists of breaking down the estimation by making lots of little educated guesses rather than one big one. The result of this trick is an estimate likely to be surprisingly close to the true answer, because the errors in each calculation tend to balance each other out along the way.

Scientists’ current estimate is that our galaxy contains around 10,000 intelligent alien civilizations — something we owe in large part to astronomer Jill Tarter’s decades-long dedication. Returning to Backus’s calculation, which yielded 26 eligible women on all of Earth, Fry notes that “being able to estimate quantities that you have no hope of verifying is an important skill for any scientist” — a technique known as a Fermi estimation, which is used in everything from job interviews to quantum mechanics — but suggests that his criteria might have been unreasonably stringent. (Backus based his formula, for instance, on the assumption that he’d find only 10% of the women he meets agreeable and only 5% attractive.)

In fact, this “price of admission” problem is also at the heart of a chapter probing the question of how you know your partner is “The One.” Fry writes:

As any mathematically minded person will tell you, it’s a fine balance between having the patience to wait for the right person and the foresight to cash in before all the good ones are taken.

Indeed, some such mathematically minded people have applied an area of mathematics known as “optimal stopping theory” to derive an actual equation that tells you precisely how many potential mates to reject before finding the perfect partner and helps you discern when it’s time to actually stop your looking and settle down with that person (P):

Fry explains:

It tells you that if you are destined to date ten people in your lifetime, you have the highest probability of finding The One when you reject your first four lovers (where you’d find them 39.87 percent of the time). If you are destined to date twenty people, you should reject the first eight (where Mister or Miz Right would be waiting for you 38.42 percent of the time). And, if you are destined to date an infinite number of partners, you should reject the first 37 percent, giving you just over a one in three chance of success.

[…]

Say you start dating when you are fifteen years old and would ideally like to settle down by the time you’re forty. In the first 37 percent of your dating window (until just after your twenty-fourth birthday), you should reject everyone; use this time to get a feel for the market and a realistic expectation of what you can expect in a life partner. Once this rejection phase has passed, pick the next person who comes along who is better than everyone who you have met before. Following this strategy will definitely give you the best possible chance of finding the number one partner on your imaginary list.

This formula, it turns out, is a cross-purpose antidote to FOMO, applicable to various situations when you need to know when to stop looking for a better option:

Have three months to find somewhere to live? Reject everything in the first month and then pick the next house that comes along that is your favorite so far. Hiring an assistant? Reject the first 37 percent of candidates and then give the job to the next one who you prefer above all others. In fact, the search for an assistant is the most famous formulation of this theory, and the method is often known as the “secretary problem.”

But the most interesting and pause-giving chapter is the final one, which brings modern lucidity to the fairy-tale myth that “happily ever after” ensues unabated after you’ve identified “The One,” stopped your search, and settled down him or her. Most of us don’t need a scientist to tell us that “happily ever after” is not a destination or a final outcome but a journey and an active process in any healthy relationship. Fry, however, offers some enormously heartening and assuring empirical findings, based on a fascinating collaboration between mathematicians and psychologists, confirming this life-tested and often hard-earned intuitive understanding.

Fry examines what psychologists studying longtime couples have found about the key to successful relationships:

Every relationship will have conflict, but most psychologists now agree that the way couples argue can differ substantially, and can work as a useful predictor of longer-term happiness within a couple.

In relationships where both partners consider themselves as happy, bad behavior is dismissed as unusual: “He’s under a lot of stress at the moment,” or “No wonder she’s grumpy, she hasn’t had a lot of sleep lately.” Couples in this enviable state will have a deep-seated positive view of their partner, which is only reinforced by any positive behavior: “These flowers are lovely. He’s always so nice to me,” or “She’s just such a nice person, no wonder she did that.”

In negative relationships, however, the situation is reversed. Bad behavior is considered the norm: “He’s always like that,” or “Yet again. She’s just showing how selfish she is.” Instead, it’s the positive behavior that is considered unusual: “He’s only showing off because he got a pay raise at work. It won’t last,” or “Typical. She’s doing this because she wants something.

She cites the work of psychologist John Gottman, who studies why marriages succeed or fail. He spent decades observing how couples interact, coding and measuring everything from their skin conductivity to their facial expressions, and eventually developed the Specific Affect Coding System — a method of scoring how positive or negative the exchanges are. But it wasn’t until Gottman met mathematician James Murray and integrated his mathematical models into the system that he began to crack the code of why these toxic negativity spirals develop. (Curiously, these equations have also been used to understand what happens between two countries during war — a fact on which Fry remarks that “an arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.”)

Fry presents the elegant formulae the researchers developed for explaining these patterns of human behavior. (Although the symbols stand for “wife” and “husband,” Fry notes that Murray’s models don’t factor in any stereotypes and are thus equally applicable to relationships across all orientations and gender identities.)

She breaks down the equations:

The left-hand side of the equation is simply how positive or negative the wife will be in the next thing that she says. Her reaction will depend on her mood in general (w), her mood when she’s with her husband (rwWt), and, crucially, the influence that her husband’s actions will have on her (IHM). The Ht in parentheses at the end of the equation is mathematical shorthand for saying that this influence depends on what the husband has just done.

The equations for the husband follow the same pattern: h, rHHt, and IHM are his mood when he’s on his own, his mood when he’s with his wife, and the influence his wife has on his next reaction, respectively.

The researchers then plotted the effects the two partners have on each other — empirical evidence for Leo Buscaglia’s timelessly beautiful notion that love is a “dynamic interaction”:

In this version of the graph, the dotted line indicates that the husband is having a positive impact on his wife. If it dips below zero, the wife is more likely to be negative in her next turn in the conversation.

What all of this translates into is actually strikingly similar to Lewis Carroll’s advice on resolving conflict in correspondence. “If your friend makes a severe remark, either leave it unnoticed, or make your reply distinctly less severe,” Carroll counseled, adding “and if he makes a friendly remark, tending towards ‘making up’ the little difference that has arisen between you, let your reply be distinctly more friendly.” Carroll was a man of great psychological prescience in many ways, and this particular insight is paralleled by Gottman and Murray’s findings, which Fry summarizes elegantly:

Imagine that the husband does something that is a little bit positive: He could agree with her last point, or inject a little humor into their conversation. This action will have a small positive impact on the wife and make her more likely to respond with something positive, too… [But] if the husband is a little bit negative — like interrupting her while she is speaking — he will have a fixed and negative impact on his partner. It’s worth noting that the magnitude of this negative influence is bigger than the equivalent positive jump if he’s just a tiny bit positive. Gottman and his team deliberately built in this asymmetry after observing it in couples in their study.

And here is the crucial finding — T- is the point known as a negativity threshold, at which the husband’s negative effect becomes so great that it renders the wife unwilling to diffuse the situation with positivity and she instead responds with more negativity. This is how the negativity spirals are set off. But the most revelatory part is what this suggests about the myth of compromise.

As Fry points out, it makes sense to suppose that the best strategy is to aim for a high negativity threshold — “a relationship where you give your partner room to be themselves and only bring up an issue if it becomes a really big deal.” And yet the researchers found the opposite was true:

The most successful relationships are the ones with a really low negativity threshold. In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such a case, couples don’t bottle up their feelings, and little things don’t end up being blown completely out of proportion.

She adds the important caveat that a healthy relationship isn’t merely one in which both partners are comfortable complaining but also one in which the language of those complaints doesn’t cast the complainer as a victim of the other person’s behavior.

In the remainder of The Mathematics of Love, Fry goes on to explore everything from the falsehoods behind the standard ideals of beauty to the science of why continually risking rejection is a sounder strategy for success in love (as in life) than waiting for a guaranteed outcome before trying, illustrating how math’s power to abstract reality invites greater understanding of our most concrete human complexities and our deepest yearnings.

Complement it with a fascinating look at what troves of online dating data reveal about being extraordinary, Dan Savage on the myth of “The One,” and Adrienne Rich on how relationships define our truths.

BP

The Man Who Turned Paper into Pixels: How Mathematician and Black Jack Wizard Claude Shannon Ignited the Information Age

How the most important man you never heard of laid the groundwork for the digital world.

The so-called Information Age we live in, like all major leaps in human achievement, isn’t a self-contained bubble that coalesced out of nothingness in a flash of genius but the cumulative product of incremental innovation stretching back centuries. It builds upon the work of multiple inventors, scientists, and thinkers, including Lady Ada Lovelace, celebrated as the world’s first computer programmer, Alan Turing, considered the godfather of modern computing, Paul Otlet, who built a proto-internet in the early twentieth century, and Vannevar Bush, who envisioned the web in 1945.

Among them was the American mathematician, engineer, and cryptographer Claude Shannon (April 30, 1916–February 24, 2001), who laid the foundation for the Information Age. According to British filmmaker Adam Westbrook — who gave us those fantastic video essays on the long game of creativity — Shannon is “the most important man you’ve probably never heard of” and his work impacted the modern world as profoundly as Einstein’s did. In this short film inspired by James Gleick’s remarkable The Information: A History, A Theory, A Flood (public library) — one of the very best, most illuminating and stimulating books I’ve ever read — Westbrook traces Shannon’s story and his enduring legacy, which permeates our everyday lives more powerfully than we dare imagine.

A Renoir and a receipt — they’re completely different… You couldn’t possibly think of them in the same way — or could you?

For a deeper dive, do treat yourself to Gleick’s The Information, then complement with the story of The Antikythera Mechanism, the world’s first analog computer circa 150 B.C., and The Mundaneum, an analog version of the world wide web from the early twentieth century.

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