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Mathematics has long been the bane of many schoolchildren. But some form of mathematics is crucial for any civilization to achieve technological maturity. This has certainly been the case here on Earth, and will likely be the case for any intelligent aliens hoping to understand the cosmos and reach beyond their own planet.

It is true that the history and development of the abstract concept of number and the precise nature of mathematics here on our planet has been a long and torturous affair. Yet over the centuries there have been many examples of convergent intellectual thinking on many of the fundamental problems of mathematics, as a new forthcoming book explains.

The Secret Life of Numbers: A Hidden History of the Unsung Pioneers of Mathematics provides a surprisingly insightful account of how humanity used numbers in ways that helped us develop calendars and methods of crop rotation. And it also gave us the opportunity to prove that our own piece of land is actually a sphere, and just one of numerous planets that traverse the night sky.

The book’s co-authors, mathematics historian Kate Kitagawa and science journalist Timothy Revell, explain how important mathematics is to understanding our planet, astronomy, and the rocketry that first took us away from Earth.

“Although mathematics is often portrayed as a unity consisting of clear, logical sequences of ideas, proofs, and theorems, its history is rarely so straightforward,” the authors write.

They point out that the first traces of human mathematical activities appeared about 20,000 years ago in the form of scratched notches in animal bones.

Algebra grows up

Twenty thousand years later, “hardly a day goes by without a headline containing the word ‘algorithm,’ which shows how dominant they have become in our everyday lives,” the authors write. But an algorithm is just a list of instructions that can be used to solve a problem or perform a task; even a cooking recipe is a type of algorithm, the authors note.

And what about calculus?

The mathematical study of continuous change, known as calculus, has brought us to where we are today and is one of the most useful advances in human history. Calculus is vital to engineering; building bridges, measuring curves, and building and launching rockets.

Although the development of infinitesimal calculus is usually 17^th In 14th-century Europe, there is evidence that a particular form of calculus was used in a school in the Indian coastal enclave of Kerala in the 14th century. Kerala had become a melting pot for mathematicians, the authors note.

But as the authors point out, the common belief is that the English mathematician Isaac Newton and the German mathematician Gottfried Wilhelm Leibniz each arrived at infinitesimal calculus independently of each other – about three centuries after the school in Kerala.

Like many mathematicians of his time, Newton was interested in using mathematical theories to understand both our planet and our solar system. To that end, Newton had come to believe that the Earth could not be a perfect sphere, the authors note. The Earth’s rotation on its axis would cause a stronger outward force at the equators than at the poles, meaning the Earth would swell there, they write. However, Newton believed that this would make the Earth an oblate (or flattened) spheroid rather than a sphere, they note.

Two scientific missions

To answer this question, the French Academy of Sciences sent two scientific missions, one to South America and one to northern Finland, to take measurements that would help determine the true shape of the Earth.

The idea was to measure the speed of a pendulum clock at different locations, the authors write. The stronger the gravity, the faster the clock should tick, they write. And by measuring the stars from each location, the teams could use mathematics to figure out whether or not the Earth is a perfect sphere, they write.

When the data from both missions were finally reported back and analyzed, it was clear that Newton was right: the Earth is an oblate spheroid.

Fast forward to the 1950s

The Cold War between the Soviet Union and the USA drove the space race, rocketry and mathematics to new heights.

In the USA, the African-American mathematician Katherine Johnson helped with the crucial calculations that ensured the success of the first NASA astronauts Alan Shepard and John Glenn’s suborbital and orbital flights.

Johnson also calculated the path that would take the astronauts to the moon. “We told them how fast they would fly, and by the time they got there, the moon would be there,” the authors quote her as saying.

The conclusion?

The secret life of numbers covers a lot of well-trodden ground, but most importantly provides context on many little-known mathematicians, too many to name here. The book is very detailed and comprehensive, and offers a novel look at how both non-Western cultures and women played key roles in the development of the discipline.

And what about ET’s use of calculators?

No matter how habitable a distant Earth 2.0 might be, the aliens living there would need some kind of codified method of problem-solving to understand the cosmos and develop a spacefaring civilization.