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Take calculus. This mathematical theory for describing and determining how things change over time is one of the most important and useful advances in human history. It is crucial to engineering—without it, we couldn't accurately build bridges or rockets—and it is used in nearly every scientific discipline to help us better understand the world. Many aspects of our lives today would not be possible without it.

So who takes the credit? The usual story is that Isaac Newton, an English mathematician, and Gottfried Wilhelm Leibniz, a German one, independently developed their own versions of calculus at around the same time in the seventeenth century. This much is true, but to know only this is akin to looking at Mercator's map—it is a distorted view. There is a far earlier claim to the ideas behind calculus.

In the fourteenth century, a school in Kerala, India, was a melting pot for mathematicians. Its founder, Madhava of Sangamagrama, was a brilliant mathematician, and among his achievements is describing a theory of calculus. He explored the key ideas that make calculus possible, which were then honed by successive mathematicians at the Kerala school. This theory was neither complete nor perfect, but that's always the case with something new. Many of the first light bulbs burned out too quickly and the glass turned black because of flaws in their design, but Thomas Edison is still recognized for his role in that nineteenth-century invention. It's time we recognized Madhava too.

Ideas are at the forefront of any history of mathematics, but they cannot be separated from the people who had them. To truly represent the origins of mathematics we must look at the origins of mathematicians too. Some of those featured in this book were not just impressive mathematicians but also broke down barriers to help make mathematics a more inclusive and global subject. In this book, we give greater prominence to these forgotten mathematicians and explain how they fit into the traditional story, as well as correcting mistruths and misrepresentations about them. Important people that didn't fit the accepted idea of a mathematician were not just oppressed during their lifetimes but have faced a continued attack from historians and commentators since.

Take Sophie Kowalevski, who was born in Moscow in 1850, just before the Crimean War. During her life, she was constantly discouraged and forbidden from pursuing mathematics. Her father refused her access to a proper education, believing that having a daughter who was a learned woman would bring shame upon him. Views like this were common at the time. Despite this, she pursued mathematics and produced work that was easily good enough to earn a doctorate. Yet because of her gender many universities wouldn't let her take the exam to obtain one.

Through immense determination, Kowalevski eventually managed to earn a position at Stockholm University, becoming the world's first female mathematics professor. Even then, her professorship was unpaid—she had to personally collect money from her students in order to survive. Some people were unhappy that she had even attained such a position. The famed playwright August Strindberg described the concept of a female professor as a "pernicious and unpleasant phenomenon."

After her death, Kowalevski's legacy was distorted by some biographers who too often relied on gender stereotypes to tell her story rather than the facts of her life. She was an extraordinary mathematician yet was presented as a sort of femme fatale who relied on her looks and charm to make progress, despite there being little evidence for this. It's time to put an end to the tainting of stories like Kowalevski's.

We believe that this retelling of the story of mathematics is important, but we hope that it will be more than that. Mathematics has been filled with fascinating characters for millennia. It is a subject in pursuit of truth, of eye-opening ways of thinking and theorems to blow your mind. It is not a passionless pursuit but a creative one. As Kowalevski once said, "It is a science which requires a great amount of imagination." The history of mathematics is an unmissable saga of the highest caliber.

No single book can right every wrong or tell a truly complete history, but in the same way that a new map can change how we view the world, a new history can do the same. In ours, we tell the story of mathematics as it really is—beautifully chaotic and collaborative. Mathematics today is an awe-inspiring amalgamation of concepts from all over the world pioneered by a group of mathematical boundary-smashers, people who ignored the limitations society placed on them because of their race, gender and nationality. Mathematics is a subject with a rich and diverse history. It is time to tell it.