Mathematical Lives

His Lifestyle:

Erdős had no interest in possessions, comfort, or conventional life. He never married. He never owned a house. He traveled constantly with his single suitcase, living as a mathematical monk. His only goal: prove as many theorems as possible before he died.

He would arrive at a mathematician's door and announce: "My brain is open. Let's work." They'd collaborate intensely—sometimes for days without sleeping. Then Erdős would leave to visit the next collaborator.

His Work Ethic:

Erdős published around 1,500 papers—more than almost any mathematician in history. He collaborated with over 500 mathematicians (also a record). He worked until the day he died at 83, literally collapsing while attending a mathematics conference.

He fueled his marathon math sessions with coffee, caffeine pills, and amphetamines. When friends worried about his drug use, he quit for a month to prove he could—then complained: "You've set mathematics back a month!" and resumed.

His Unique Language:

Erdős spoke his own quirky language:

• "The Supreme Fascist" = God (Erdős was an atheist but joked that God kept the most elegant proofs in a book)
• "Epsilon" = small child
• "Bosses" = women
• "Slaves" = men
• "Captured" = married
• "Liberated" = divorced
• "Died" = stopped doing mathematics
• "Left" = actually died

The Erdős Number:

Because Erdős collaborated with so many mathematicians, academics created the "Erdős number":

• Erdős himself: Erdős number = 0
• Someone who wrote a paper with Erdős: Erdős number = 1 (about 500 people)
• Someone who wrote a paper with someone who wrote with Erdős: Erdős number = 2
• And so on...

Having a low Erdős number became a badge of honor in mathematics. It's a measure of how connected you are to the collaborative network of mathematics.

The Divine Inspiration:

Ramanujan was deeply religious. He claimed the Hindu goddess Namagiri appeared to him in dreams and revealed mathematical formulas. When he woke up, he would write them down—often without proofs, just the results.

Other mathematicians would spend years trying to prove that Ramanujan's formulas were correct. They almost always were. It was as if he could see mathematical truths directly, without needing to derive them step by step.

The Letter That Changed Everything:

In 1913, Ramanujan wrote a letter to G.H. Hardy, a famous mathematician at Cambridge University. The letter contained page after page of incredible theorems—formulas Hardy had never seen, many of which seemed impossible.

Hardy later said: "I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class."

Hardy invited Ramanujan to Cambridge. This created a dilemma: As a devout Hindu, Ramanujan wasn't supposed to cross the ocean. His mother prayed for guidance. She too had a dream—the goddess told her to let her son go.

The Cambridge Years:

Ramanujan traveled to England in 1914. The culture shock was immense. He was vegetarian in a country with almost no vegetarian food. The cold British weather affected his health. The racism and classism of early 1900s England isolated him.

But mathematically, he thrived. Working with Hardy, he published paper after paper. He developed formulas that are still being used and explored today—in number theory, in physics, even in string theory (discovered decades after his death).

The Taxicab Number:

A famous story: Hardy visited Ramanujan in the hospital. Making small talk, Hardy mentioned he'd arrived in taxi number 1729, which seemed "rather a dull number."

Ramanujan immediately replied: "No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways!"

(1729 = 1³ + 12³ = 9³ + 10³)

Even while sick in bed, Ramanujan saw deep properties of numbers instantly. His brain worked differently.

Tragic End:

Ramanujan's health deteriorated in England. He contracted tuberculosis. He returned to India in 1919 but died a year later, at age 32.

In his brief career, he produced nearly 4,000 theorems and formulas. Mathematicians are still working through his notebooks, still discovering that his "wild" formulas are actually correct and important.

The Analytical Engine:

In the 1830s, Charles Babbage designed (but never built) a mechanical computer called the Analytical Engine. It would use punch cards and gears to perform calculations—any calculation you could program into it.

When Ada Lovelace met Babbage at age 17, she became fascinated by the machine. She understood something Babbage himself hadn't fully grasped: This machine could do more than just math.

The First Algorithm:

In 1843, Ada translated an article about the Analytical Engine from French to English. But she didn't just translate—she added her own notes that were three times longer than the original article.

In these notes, she included what's now recognized as the first computer program ever written: step-by-step instructions for the Analytical Engine to calculate Bernoulli numbers.

This was the first algorithm designed to be processed by a machine—the first computer program, written before computers existed.

Her Vision:

What made Ada truly remarkable was her vision of what computers could become. She wrote:

In 1843, she imagined computers creating music! She saw that machines could manipulate symbols of any kind—not just numbers. This insight anticipated modern computers by a century.

Against the Odds:

As a woman in Victorian England, Ada faced constant barriers. Women weren't allowed to attend university. They weren't taken seriously in science. Ada had to hide her mathematical work from some family members who thought it "unfeminine."

She also battled serious health problems throughout her life, dying of uterine cancer at age 36—the same age her father died.

Lost and Found:

Ada's work was largely forgotten after her death. It wasn't until the 1950s—when electronic computers finally existed—that historians rediscovered her notes and realized: This woman had understood computer programming a century before anyone else.

Today, the U.S. Department of Defense's Ada programming language is named in her honor.

The Unlikely Beginning:

Maryam's first year of middle school was discouraging—the math teacher didn't believe girls could do mathematics. Maryam nearly lost interest entirely.

But the next year, she got a different teacher who encouraged her. Suddenly mathematics clicked. Within a year, she was competing in the International Mathematical Olympiad. She won gold medals two years in a row—scoring perfect scores both times.

Her Work (Simplified):

Mirzakhani specialized in geometry—specifically, the geometry of curved surfaces. Imagine surfaces like a doughnut (called a torus) or a pretzel. How many different ways can you draw a simple closed loop on these surfaces? What paths are possible? What patterns emerge?

Her work combined geometry, dynamical systems, and complex analysis in groundbreaking ways. She proved theorems about these curved spaces that mathematicians had struggled with for decades.

Her mathematics was so complex that even other professional mathematicians found it hard to understand. But it was beautiful, deep, and opened new directions for research.

The Fields Medal:

In 2014, Maryam became the first woman ever to win the Fields Medal—often called the "Nobel Prize of Mathematics." (The Fields Medal has been awarded since 1936. In 78 years, no woman had won it. Think about that.)

At the award ceremony, her young daughter wasn't impressed. She asked if being the first woman to win was a big deal. Maryam said yes. Her daughter replied: "But is that going to be on the news?"

Her Process:

Maryam's approach to mathematics was artistic. She would draw elaborate doodles and sketches on large sheets of paper, exploring ideas visually before formalizing them mathematically. Her daughter called it "painting" because the floor would be covered with sheets of paper filled with drawings.

She described mathematics as "like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

Tragic Loss:

In 2013, Maryam was diagnosed with breast cancer. She continued her mathematical work while battling the disease. The cancer metastasized. She died in 2017 at age 40.

The mathematical community was devastated. Here was someone at the peak of her creative powers, with so much more to contribute, taken away far too soon.

Game Theory Breakthrough:

At age 21, as a graduate student at Princeton, Nash wrote a 27-page doctoral dissertation that changed economics forever. He proved the existence of what's now called the "Nash Equilibrium"—a concept that explains how people make strategic decisions when their choices affect and are affected by others' choices.

This wasn't just abstract mathematics. Nash Equilibrium is used to understand:

• How companies compete
• How nations negotiate
• How evolutionary strategies develop
• How internet routing works

His dissertation became one of the most influential papers in 20th-century mathematics.

The Descent:

In 1959, at age 30, Nash began experiencing paranoid delusions. He believed he was receiving coded messages from extraterrestrials through The New York Times. He thought he was being recruited for a secret cryptographic role. He started seeing patterns and conspiracies everywhere.

He was diagnosed with paranoid schizophrenia. Over the next decades, he went in and out of psychiatric hospitals. He underwent insulin shock therapy. His brilliant career seemed over. His wife divorced him (though she later remarried him and supported him throughout).

The Ghost of Princeton:

During his illness, Nash would wander the halls of Princeton, writing cryptic mathematical formulas on blackboards. Students called him "The Phantom of Fine Hall." He believed he was a messianic figure. He renounced his American citizenship, declaring himself a citizen of the world.

Yet even in his delusions, the mathematical thinking remained. Colleagues noted that his "crazy" ideas often had kernels of mathematical insight buried within them.

The Recovery:

Remarkably, in the late 1980s, Nash's symptoms began to recede. He never fully explained why. He later said he consciously decided to reject delusional thinking—to intellectually recognize when thoughts were irrational and dismiss them.

It was like retraining his mind to think logically again, using mathematical discipline to overcome mental illness. By the 1990s, he was doing mathematics again, teaching, and interacting normally with colleagues.

Recognition and Tragedy:

In 1994, Nash won the Nobel Prize in Economics for his game theory work from 45 years earlier. He became a living legend—the mathematician who lost his mind and found it again.

In 2015, he and his wife were killed in a car accident in New Jersey. They were returning from Norway, where Nash had just received the Abel Prize (one of mathematics' highest honors). He was 86.