History books are filled with conflicts, royalty and events that changed the world. That’s all good and well but what about equations? It might seem that equations are only for math and physics nerds but in reality, there are some equations that changed our world forever. This may seem like a bold statement but have you considered what it would be like without Einstein’s theory of relativity or Newton’s law of gravity? Would we still have been able to contemplate space travel without them?

Now, imagine how many more important equations there have been thus far and the larger impact it has had on on our lives. In Pursuit of The Unknown contains 17 equations that have changed the world in some way. This book summary will discuss a few of the more well-known ones.

In this book summary, readers will discover:

- The Pythagorean Theorem
- The Theory of relativity
- Newton’s law
- Schrödinger’s equation
- Chaos Theory
- Normal Distribution

## Key lesson one: The Pythagorean Theorem

Who can ever forget learning the Theorem of Pythagoras whilst in school? It was one of the easier ones to remember in geometry, a^{2}+b^{2} = c^{2 }and was used to describe the relationship of the three sides of a right-angle triangle.

You might wonder what is the big deal with this simple equation but this theorem enabled triangulation which was crucial to accurate map production. When producing maps, the area of interest is covered in triangles which then allows mapmakers to measure the angles and distances between pieces of land. Nowadays, there are other technologically advanced tools that can measure these distances without the use of triangulation. But, triangulation is still used when trying to narrow down locations from satellite data.

In recent years, generalizations of the theorem have been used to measure the shape of the universe. As crazy as it sounds, the theorem was adapted to curved surfaces. The Earth is a sphere, and applying triangles to this sphere made it possible to measure the planet and its curvature. This is now being extrapolated to space to determine if the universe is curved or not. Pretty cool right?

## Key lesson two: Newton’s law

We all know the story. Isaac Newton was sitting under an apple tree when an apple fell from the tree and hit him in the head. This was where he got the inspiration for his law of gravitation. Whether the story is accurate remains a mystery but his law of gravitation changed the way we look at the universe.

It enabled and still enables accurate predictions regarding the movement of the solar system. The law does this by determining the force of attraction between two bodies with regards to their mass and the distance between them. Most importantly, the law states that gravitation acts universally. With this, the movements of the solar system could be predicted accurately. Thus, the movement of the moon could be predicted in relation to the sun and earth.

Not only did Newton’s law understand how movement occurs in space, but it also plays a role in space travel. NASA still uses the law of gravitation to work out the trajectory of a spacecraft and it played an integral part in determining routes from earth to the moon and other planets. Even the Apollo missions used Newton’s law to determine their routes by calculating the force that the earth and the moon would have on the spacecraft.

GPS technology, satellite communication and more recently, the Mars rover have all been possible as the law of gravitation allows us to calculate trajectories of these objects.

## Key lesson three: The Theory of relativity

Albert Einstein’s theory of special relativity changed the world of physics forever and inspired generations of physicists. It provided an understanding of the universe in terms of its origins and structure. Einstein’s theory contradicted earlier ones which said that time was independent of space and that the mass of an object did not change when moved. The theory also showed that the speed of light was constant and not relative to anything else. Einstein also put forward a new idea about gravity being a curvature of space-time. This managed to explain how black holes are created and how the universe expanded with the Big Bang.

The theory of relativity is applied daily whether we are conscious of it or not. Take the navigation system in cars. This technology works by using GPS which determines the car’s position using a network of satellites. This could not occur without accurately time signals because if the signals are not times properly, the car’s position would differ and the directions would not be correct. The theory of relativity accurately predicts the loss of time between the clocks on the satellite, those on the ground and the time difference caused by Earth’s gravity. This allows GPS technology to function properly and allow us to travel to our destination safely. If the theory of relativity were not taken into consideration, it would take just 10 minutes before we ended up on the wrong street.

## Key lesson four: Schrödinger’s equation

Most people have heard about Schrodinger’s cat but how many are familiar with Schrodingers equation? The experiment with the cat was actually just used by Schrodinger to describe the way people consider quantum mechanics at the time. Funnily enough, he came up with it whilst communicating with Einstein. Schrodinger’s equation, however, relates to quantum theory.

Schrodinger’s equation stated that all matter exists as a wave and not a particle. This allowed the development of quantum theory as we now know it. Quantum theory is an area of physics that deals with things that happen at the atomic and subatomic level. It is an area that has brought about much debate among physicists as it is not entirely understood. Light, for example, can exist as both a particle and a wave in the quantum world. When this discovery was made, physicists deduced that not only light behaved in this way. All matter had a dual nature.

Quantum theory is used not only in physics but also in modern electronics. Memory chips are built of a crystalline material called semiconductors. These semiconductors have electrical conductivity and for people to analyze how electrons move through the crystal, they have to know about quantum theory. Thus all modern devices that contain memory chips depend on quantum theory.

## Key lesson five: Chaos Theory

Chaos theory has its origins in mathematical curiosity but has now become a common part of all science. In its simplicity, it shows that all theories can generate random behaviour or chaos.

A simple example comes from population studies in biology. There is a population model that exists for animals that says that the size of one generation is determined by the previous one. This means that the very first generation or generation zero will decide the size of each generation thereafter. However, it is very rare that biologists have accurate data regarding generation zero. Thus, with uncertainty comes unpredictability. Population numbers can grow exponentially and chaos has occurred.

Chaos theory has been applied to many areas such as the mixing of medicine and processes involving food ingredients. One of the most significant areas it is used is the way that weather forecasts are done. We all know how unpredictable the weather really is. As much as there are clear signs regarding the weather, chaos can come about quite quickly due to its complexity. This is why meteorologists run multiple models and if they all predict the same outcome, they go with it as it is most likely to be accurate.

## Key lesson six: Normal Distribution

When it comes to analyzing data, a normal distribution is what statisticians pray for. Normal distributions were only discovered in the nineteenth century by Adolphe Quetelet, a mathematician who noticed that his data had a specific shape when plotted. He deduced that the probability of observing a specific data value is greatest near the average or mean value. This is what gives a normal distribution the so-called bell-shaped curve which piqued Quetelet’s interest. What was even more remarkable at the time is that the data he was collating related to social variables which involved human choices. No one expected them to conform to mathematical law. What Quetelet’s data showed is that a large group of people had more predictable behaviour than individuals.

Normal distributions are widely used for hypothesis testing. They are, in fact, common in drug and treatment trials the trial’s reliability can be tested against the probability of errors in observational data. The normal distribution is undoubtedly the most important distribution in statistics today and can be applied to everything from blood pressure to IQ scores.

**The key takeaway from In Pursuit of The Unknown is:**

Mathematical equations play an important role in history much like any other historical event. They have changed the world and allowed humans to pursue new areas of science which was never before possible. The names behind these equations are known, but why do we ignore the equations themselves? Just because we are not experts in the specific field of study does not mean we should not strive to understand and appreciate these equations. Many modern techniques, devices and experiments would not be possible for these brilliant contributions.

**How can Implement the lessons learned in In Pursuit of The Unknown:**

It’s not that hard to use these equations in your daily life. If you want to do some renovation work at home, the theorem of Pythagoras can come in handy when you have to measure out your floors, walls or even when cutting tiles. You can surprise everyone with your accurate measurements in no time!