Mathematics has long been the bane of many students. But some form of mathematics is vital for any civilization to reach technological maturity. It was certainly true here on earth and will likely be true of any intelligent alien who has any hope of understanding the world and moving beyond their own planet.

It is true that the history and evolution of the abstract concept of numbers and the exact nature of mathematics here on our own planet has been a long and agonizing affair. But over the centuries, there have been many examples of convergent intellectual thinking about many of the basic problems of mathematics, as a forthcoming new book explains.

*The Secret Lives of Numbers: A Hidden History of Math’s Unsung Trailblazers *serves up a surprisingly enlightening account of how humanity harnessed numbers in a way that helped us invent calendars and methods of crop rotation. And it also provided us with the means to prove that our own piece of the terra-firma is indeed a sphere and only one of the many planets that traverse the night sky.

The book’s co-authors, historian of mathematics Kate Kitagawa and science journalist Timothy Revell, provide a framework for how mathematics is important to understanding our planet, astronomy and the rocket that first launched us from the world .

“Although mathematics is often presented as consisting of neat, logical sequences of ideas, proofs, and theorems, its history is rarely that simple,” the authors write.

The first traces of human mathematical activity began to appear about 20,000 years ago, in the form of scratched counting marks on animal bones, they note.

## Algebra is coming of age

Twenty thousand years later, “Hardly a day goes by without a news headline featuring the word ‘algorithm,’ showing how ever-dominant they have become in our daily lives,” the authors write. But an algorithm is simply a list of instructions that can be used to solve a problem or perform a task. Even a recipe is an algorithm of sorts, the authors note.

As for calculus?

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

Although the development of calculus is usually attributed to 17^{u} century in Europe, there is evidence that a form of calculus was used in a school in the coastal enclave of Kerala in the 14th century in India. Kerala had become a melting pot for mathematicians, the authors note.

But, the authors point out, the usual story is that English mathematician Isaac Newton and German mathematician Gottfried Wilhelm Leibniz arrived at calculus independently—some three centuries after the school in Kerala.

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

## Two scientific missions

To settle the matter, the French Academy of Sciences sent two scientific expeditions, 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 that they would measure the speed of a pendulum clock at different locations, the authors note. The stronger the gravity, the faster the clock must tick, they write. And by counting stars from each different location, the teams could use the math to figure out whether Earth was a perfect sphere or not, they write.

When the data from both missions were finally reported and analyzed, it proved conclusively 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 pushed the space race, rocketry and mathematics to a new fever pitch.

In the US, African-American mathematician Kathryn Johnson helped make the critical calculations that ensured NASA’s first astronauts, Alan Shepard and John Glenn, would be successful in their suborbital and orbital flights.

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

## The bottom line?

*The secret lives of numbers* it covers a lot of trodden ground, but more importantly it provides the context for many little-known mathematicians who are too numerous to mention here. Richly detailed and comprehensive in scope, the book offers a fresh perspective on how both non-Western cultures and women have been instrumental in the development of the industry.

As for ET using calculators?

No matter how habitable some distant Earth 2.0 might be, the aliens living there would need some kind of coded problem-solving method to make sense of the world and become a space-faring civilization.