Most of us cringed every time we were forced to take a math class beyond algebra, all sighing the same phrase: “When am I ever going to use this?” According to our history, apparently, if you’re looking to make some incredible discovery, one of the first places you may need to look to is the ever dreaded math. The following 10 items will give us a look into the greatest predictions and discoveries ever made thanks to math and mathematical models.

## Happiness

See that long string of letters, numbers, and mathematical symbols? That’s the equation researchers from University College, London came up with during a study meant to predict the fluctuation of happiness in situations where expectations were either not met or exceeded. The study started with 26 subjects who were all given a game they could gamble with, that was also tied to an MRI machine. As they played and either won or loss, the participants rated their happiness level from 0 to 10 while the MRI registered brain wave activity. From this study, the researchers were able to deduce that happiness was in correlation with expectations but, most importantly, were able to devise this equation which, when tested on 18,000 people through a phone app, accurately predicted the fluctuation in happiness.

## Earthquakes

Did you know that you would be able to come up with a mathematical model that could predict earthquakes? No? Ah, that’s okay, because 14-year-old Suganth Kannan did, and he proved its reliability by predicting a magnitude 5.0 to 9.0 earthquake would occur at a specific point. Within the 6-month time frame he gave, a site near Napa Valley, only 50 miles from his prediction point, experienced a 6.0 quake. Kannan used the Spatial Connection Theory, which states that earthquakes within a fault zone are relative to one another, the Poisson Distribution, or the probability of a given number of events in a specific time interval, and Exponential Distribution to create a spatial connection model in Google Earth, leading to what geologists affirmed to be “remarkably accurate” results.

## Drug Discovery

As of April 2015, the prediction of pharmacodynamics activity, or how a drug will affect its target, has always been kind of a gamble, but a team of researchers from Stony Brook University in New York may have developed a mathematical model that could reduce the percentage of failed clinical trials and improve future drug discovery. The model, according to Dr. Peter Tonge, is said to accurately predict the activity of the drug based on how strong it binds to the target protein and how long it remains bound. The team was able to implement their mathematical method to accurately predict the activity of an antibacterial drug on the Pseudomonas aeruginosa pathogen, adding validity to their research.

## The Spread of Infectious Diseases

When the spreading of Ebola in 2014 turned into an epidemic, the world dove into a panic; but thanks to a tried and true mathematical model, SIR, the spread and growth of the disease was fairly accurately predicted. The model even showed a drop in cases in December of 2014 and, in areas like Guinea and Sierra Leone, by that December, case numbers had started to drop. SIR – which accounts for those susceptible, those infected and immune, and those recovered – isn’t the only model used in epidemiology. The SEIR and MSIR models include additional facts such as the population exposed to the disease and population born with an immunity while the SIS model removes the immune group altogether. An additional factor, known as R-nought, represents the reproduction number of the disease, or the number of people an infected individual can spread the disease to before becoming non-infectious.

## Terrorist Attacks

To be able to predict a terrorist attack would be an incredible step forward in the never-ending war against an invisible enemy. In March of 2016, researchers from University College, London believed they had stumbled across an unusual means of combating terrorism across the globe – math. While you may be picturing a “Math Off” between terrorist cells, that’s not quite what the team had in mind. The model reviewed over 5,000 terrorist attacks in a 28-year period during the Troubles in Northern Ireland and determined that within specific phases such as the negotiation of a ceasefire and the IRA’s formation of a cell-based structure, the probability of a follow-up attack decreases as time passes. This also applies to the likelihood of an attack, with the probability decreasing as time passes from the initial likelihood.

## Gravitational Waves

Gravitational waves are described as ripples in space-time’s curvature that are the product of gravitational interactions, kind of like the ripples created when a stone is dropped in water. That rather basic explanation is far from everything there is to know about gravitational waves, but what we’d like to focus on is Einstein’s prediction of gravitational waves, based on his theory of general relativity, and how his model of basic and advanced mathematics predicted something that took 100 years to finally observe. Utilizing his now-popular theory, Einstein was able to deduce that space and time are a measurable reality that can be physically affected by the materials of matter and energy, meaning that large amounts of mass or energy would cause a distortion in space-time. Using a correlation of the masses involved, the distance between objects, gravitational constant, and the speed of light in a vacuum, Einstein was able to accurately predict the existence of these gravitational waves.

## Ceres’ Orbit

It’s not entirely uncommon for astronomy and mathematics to cross paths, but it’s still a wonder when a mathematical method proves to be successful in determining, say, the orbital pattern of the dwarf planet Ceres. In 1801, Ceres was discovered by Italian monk Giuseppe Piazzi. Piazzi observed the planet for 41 days before falling ill and losing sight of the planet behind the Sun. With a considerably small sampling of time, astronomers attempted to relocate the object but were unable to do so. Enter 24-year-old German mathematician Carl Friedrich Gauss, who proceeded to use only 3 of the observations to create a new method of successfully finding the orbital pattern of Ceres. How Gauss was able to do so remains an unanswered question as his notes prove to be unclear.

## The Existence of Other Continents

So, who really discovered America? While some would argue Christopher Columbus, others may point to the Vikings; but there may be another name to throw into the mix. Abu Rayhan al-Biruni, a scholar from Central Asia, may have actually inadvertently predicted the existence of America - and other non-Eurasian continents - when his attempt to precisely determine the position of the qiblah, or the direction of Mecca, brought him to plot out a map of the known world, recording coordinates of locations he’d visited and additional data on settlements pulled from other sources. On a 16-foot or roughly 5-meter tall globe, Biruni mapped out the world and determined 3/5ths of the surface of the Earth were unaccounted for. While it was popular to believe Eurasia was surrounded by a world ocean, Biruni believed that the processes that created Eurasia would have been active across the globe, forming additional land masses.

## Antimatter and Antiparticles

English physicist Paul Dirac followed in the footsteps of history’s greatest theorists and, in 1933, earned himself a Nobel prize for physics. One of his crowning achievements was the discovery of antiparticles, which he stumbled upon while working on an equation that fed off of quantum mechanics and Einstein’s theory of special relativity. Dirac’s equation looked at the behavioral patterns of items that were both very small and fast, and it was then that he realized his equation brought to light the concept of antiparticles when it was shown to work the same for electrons with a negative charge and a positively charged particle that behaved like an electron. Dirac theorized that every particle has an antiparticle and that even the universe itself would have a mirror image of itself filled with antimatter.

## The Planet Neptune

Most of the planets in our solar system share the distinction of having been discovered through observational methods. The exception to that is Neptune, which was discovered by both French astronomer Urbain Jean Joseph Le Verrier and British astronomer John Couch Adams. The two weren’t working together on a joint effort to locate a new planet but were rather working independently on models that would explain the movement of Uranus. Adams was able to predict the location of the planet within 2 degrees after two years of research he started in 1843. Le Verrier’s discovery was confirmed in 1846, when European astronomer Johann Gottfried Galle, who La Verrier had sent his findings to, confirmed via Berlin Observatory’s 9-inch telescope the existence of a previously unrecorded celestial body. Rather than start a feud over who should be credited with the discovery, Adams graciously explained that Le Verrier’s research was published first, leading to the actual discovery by Galle.