Math has changed a lot over the years. When most people think of math, they likely think of someone sitting quietly at a desk with a book or some paper. It’s an unmoving image. When we think of people who are good at math, we conjure up people who blaze through problems quickly and alone. They follow the rules in math and in life.

But this is a relatively recent picture of mathematics. Throughout history, math has been a place for rebels and weirdos, charismatic personalities and dramatic story-tellers. The modern image of a mathematician is totally disconnected from the people who developed of mathematics, who often worked on one problem for weeks, months, or even years, and reached out to other mathematicians constantly.Today we’ll meet a few people who drastically changed mathematics in their time, to see what lessons they can teach today’s math students.

# 1. Pythagoras (570-495 BC, Greece)

Most people who’ve taken 8^{th} grade math have heard of the Pythagorean Theorem. But did you know that Pythagoras was the leader of a secret society who was likely burned to death because of his mathematical beliefs? His followers believed in the purity of mathematical truth as the essence of nature and religion. The society enforced a vegetarian (but, oddly enough, bean-free) diet and allowed women to join. Pythagoras’ commitment to logic seems unexciting to us today, but was radical at the time. Other people felt that their religious beliefs were directly threatened by Pythagoras’ ideas. Legend has it that the members of the society were attacked and their homes were burned down; Pythagoras did not escape. Nowadays, math might seems like a safe and quiet discipline, but its roots are much more wild.

## Moral of the story

Math is weird. See if you can adopt a perspective of seeing it for what it is – a complex network of ideas that fit together in surprising ways – instead of some random rules some people are trying to make you learn.

Learn more about Pythagoras here.

# 2. Emmy Noether (1882-1935, Germany)

The vast majority of people who come to mind at the phrase “famous mathematician” are men. Is that because math ability is somehow dependent on gender? Consider Emmy Noether. Emmy was born to a mathematician and his wife and eventually became instrumental in developing fundamental ideas in abstract algebra. She spent the early years of her math career taking math classes without getting credit and teaching under false names and without pay, because women were not allowed in academics. It is likely that none of this would have happened at all if Emmy’s father weren’t a mathematician, meaning that she grew up surrounded by math books and professors. In fact, a surprising number of female mathematicians had unusual parental circumstances – if you’re interested, take a look at Hypatia of Alexandria and Ada Lovelace. Throughout much of history, men have been invited into the mathematics classroom, while women could only enter the discipline if they happened to be born in a family of mathematicians. These women who had access to math made just as important contributions as their male peers, even while having to fight or beg for people to just let them do math. Hypatia, Ada, and Emmy start to show us that it’s not your biology that makes you good at math – it’s your circumstances and ability to fight for your chance to learn.

## Moral of the story

Fight assumptions about who’s smart. Make sure you’re not subconsciously responding to ideas that your gender/ race/ religion/ hometown/ height/ hobbies mean you can’t be good at math.

Read about Emma Noether, Hypatia, and Ada Lovelace futher!

# 3. Andrew Wiles (1953-present, England)

Andrew Wiles himself is not a historical figure, but he’s part of a story that took place over almost 400 years. In 1637, Pierre de Fermat, an amateur mathematician, wrote a few sentences in the margin of one of his books claiming that he knew something to be true (a^n+b^n=c^n had no integer solutions besides 0 when n was greater than 2), and that he had a proof for it, but it didn’t fit in the margins. When other mathematicians discovered his claim, they thought it must be a simple proof, but they failed to complete it. Large cash prizes were posted and people all over the world took a stab at it. Over the centuries, progress was made, but nobody could find a final proof. It wasn’t until 1994 that Andrew Wiles finally figured finished the proof. He spent years devoting most of his working hour to figuring it out, even presenting some ideas that turned out to be flawed before he was finished. In math classes, many people assume that the faster someone works, the smarter they are. But the most interesting problems that require the deepest understanding of mathematics take time – sometimes several centuries!

## Moral of the story

Math takes a long time to do! If you’re trying to figure something out and it’s taking a while, that doesn’t mean you’re dumb -- that means your brain is learning something new and important.

Learn more about Andrew Wiles and Fermat’s Last Theorem here.

# 4. Sophie Germaine (1776-1831, France)

Sophie was another woman who was born to a philosopher father and who was not accepted into mathematical study because of her sex. She didn’t want to just hole up in her father’s library and let her ideas wither away, but she couldn’t go to classes or gatherings. She did the only thing she could: she wrote letters. She asked for lecture notes from the nearby school to be sent to her home and, using a male alias, mailed ideas back and forth with a professor. She furthered her ideas, on the boundaries of the mathematics of her time, both by spending time deep in thought and by exchanging notes with many other prominent mathematicians of the time. Without these exchanges, Sophie’s work would have been limited. She worked hard to find collaborators in order to have the best ideas that she could.

## Moral of the story

Asking for help is a sign of a quality mathematician. Talking about math is necessary to get better at it. How can you make sure that you’re talking more about math? Start by having conversations about your classwork and homework with your teachers, your tutor, and your classmates.

Learn more about Sophie Germain here!

Math is a wild, weird subject that pushes people’s brains to the limit. If your classwork gets dry or your homework feels impossible, try to remember what Pythagoras, Emmy, Andrew, and Sophie knew: math is crazy, it takes time to do, and you learn more when you work with other people.

Ready to work on your own mathematics problems, but need some guidance? Contact us for mathematics tutoring in Boston or New York, or online anywhere in the world!

Want to read more on mathematics as a subject? Check out some of our previous math blog posts below!