Who Was Nicolaus Copernicus?

When it comes to understanding our place in the universe, few scientists have had more of an impact than Nicolaus Copernicus. The creator of the Copernican Model of the universe (aka. heliocentrism), his discovery that the Earth and other planets revolved the Sun triggered an intellectual revolution that would have far-reaching consequences.

In addition to playing a major part in the Scientific Revolution of the 17th and 18th centuries, his ideas changed the way people looked at the heavens, the planets, and would have a profound influence over men like Johannes Kepler, Galileo Galilei, Sir Isaac Newton and many others. In short, the “Copernican Revolution” helped to usher in the era of modern science.

Copernicus’ Early Life:

Copernicus was born on February 19th, 1473 in the city of Torun (Thorn) in the Crown of the Kingdom of Poland. The youngest of four children to a well-to-do merchant family, Copernicus and his siblings were raised in the Catholic faith and had many strong ties to the Church.

His older brother Andreas would go on to become an Augustinian canon, while his sister, Barbara, became a Benedictine nun and (in her final years) the prioress of a convent. Only his sister Katharina ever married and had children, which Copernicus looked after until the day he died. Copernicus himself never married or had any children of his own.

Nicolaus Copernicus portrait from Town Hall in Torun (Thorn), 1580. Credit: frombork.art.pl
Nicolaus Copernicus portrait from Town Hall in Torun (Thorn), 1580. Credit: frombork.art.pl

Born in a predominately Germanic city and province, Copernicus acquired fluency in both German and Polish at a young age, and would go on to learn Greek and Italian during the course of his education. Given that it was the language of academia in his time, as well as the Catholic Church and the Polish royal court, Copernicus also became fluent in Latin, which the majority of his surviving works are written in.

Copernicus’ Education:

In 1483, Copernicus’ father (whom he was named after) died, whereupon his maternal uncle, Lucas Watzenrode the Younger, began to oversee his education and career. Given the connections he maintained with Poland’s leading intellectual figures, Watzenrode would ensure that Copernicus had  great deal of exposure to some of the intellectual figures of his time.

Although little information on his early childhood is available, Copernicus’ biographers believe that his uncle sent him to St. John’ School in Torun, where he himself had been a master. Later, it is believed that he attended the Cathedral School at Wloclawek (located 60 km south-east Torun on the Vistula River), which prepared pupils for entrance to the University of Krakow – Watzenrode’s own Alma mater.

In 1491, Copernicus began his studies in the Department of Arts at the University of Krakow. However, he quickly became fascinated by astronomy, thanks to his exposure to many contemporary philosophers who taught or were associated with the Krakow School of Mathematics and Astrology, which was in its heyday at the time.

A comparison of the geocentric and heliocentric models of the universe. Credit: history.ucsb.edu
A comparison of the geocentric and heliocentric models of the universe. Credit: history.ucsb.edu

Copernicus’ studies provided him with a thorough grounding in mathematical-astronomical knowledge, as well as the philosophy and natural-science writings of Aristotle, Euclid, and various humanist writers. It was while at Krakow that Copernicus began collecting a large library on astronomy, and where he began his analysis of the logical contradictions in the two most popular systems of astronomy.

These models – Aristotle’s theory of homocentric spheres, and Ptolemy’s mechanism of eccentrics and epicycles – were both geocentric in nature. Consistent with classical astronomy and physics, they espoused that the Earth was at the center of the universe, and that the Sun, the Moon, the other planets, and the stars all revolved around it.

Before earning a degree, Copernicus left Krakow (ca. 1495) to travel to the court of his uncle Watzenrode in Warmia, a province in northern Poland. Having been elevated to the position of Prince-Bishop of Warmia in 1489, his uncle sought to place Copernicus in the Warmia canonry. However, Copernicus’ installation was delayed, which prompted his uncle to send him and his brother to study in Italy to further their ecclesiastic careers.

In 1497, Copernicus arrived in Bologna and began studying at the Bologna University of Jurists’. While there, he studied canon law, but devoted himself primarily to the study of the humanities and astronomy. It was also while at Bologna that he met the famous astronomer Domenico Maria Novara da Ferrara and became his disciple and assistant.

The Geocentric View of the Solar System
An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568. Credit: bnf.fr

Over time, Copernicus’ began to feel a growing sense of doubt towards the Aristotelian and Ptolemaic models of the universe. These included the problematic explanations arising from the inconsistent motion of the planets (i.e. retrograde motion, equants, deferents and epicycles), and the fact that Mars and Jupiter appeared to be larger in the night sky at certain times than at others.

Hoping to resolve this, Copernicus used his time at the university to study Greek and Latin authors (i.e. Pythagoras, Cicero, Pliny the Elder, Plutarch, Heraclides and Plato) as well as the fragments of historic information the university had on ancient astronomical, cosmological and calendar systems – which included other (predominantly Greek and Arab) heliocentric theories.

In 1501, Copernicus moved to Padua, ostensibly to study medicine as part of his ecclesiastical career. Just as he had done at Bologna, Copernicus carried out his appointed studies, but remained committed to his own astronomical research. Between 1501 and 1503, he continued to study ancient Greek texts; and it is believed that it was at this time that his ideas for a new system of astronomy – whereby the Earth itself moved – finally crystallized.

The Copernican Model (aka. Heliocentrism):

In 1503, having finally earned his doctorate in canon law, Copernicus returned to Warmia where he would spend the remaining 40 years of his life. By 1514, he began making his Commentariolus (“Little Commentary”) available for his friends to read. This forty-page manuscript described his ideas about the heliocentric hypothesis, which was based on seven general principles.

These seven principles stated that: Celestial bodies do not all revolve around a single point; the center of Earth is the center of the lunar sphere—the orbit of the moon around Earth; all the spheres rotate around the Sun, which is near the center of the Universe; the distance between Earth and the Sun is an insignificant fraction of the distance from Earth and Sun to the stars, so parallax is not observed in the stars; the stars are immovable – their apparent daily motion is caused by the daily rotation of Earth; Earth is moved in a sphere around the Sun, causing the apparent annual migration of the Sun; Earth has more than one motion; and Earth’s orbital motion around the Sun causes the seeming reverse in direction of the motions of the planets.

Heliocentric Model
Andreas Cellarius’s illustration of the Copernican system, from the Harmonia Macrocosmica (1708). Credit: Public Domain

Thereafter he continued gathering data for a more detailed work, and by 1532, he had come close to completing the manuscript of his magnum opus – De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). In it, he advanced his seven major arguments, but in more detailed form and with detailed computations to back them up.

However, due to fears that the publication of his theories would lead to condemnation from the church (as well as, perhaps, worries that his theory presented some scientific flaws) he withheld his research until a year before he died. It was only in 1542, when he was near death, that he sent his treatise to Nuremberg to be published.

Copernicus’ Death:

Towards the end of 1542, Copernicus suffered from a brain hemorrhage or stroke which left him paralyzed. On May 24th, 1543, he died at the age of 70 and was reportedly buried in the Frombork Cathedral in Frombork, Poland. It is said that on the day of his death, May 24th 1543 at the age of 70, he was presented with an advance copy of his book, which he smiled upon before passing away.

In 2005, an archaeological team conducted a scan of the floor of Frombork Cathedral, declaring that they had found Copernicus’ remains. Afterwards, a forensic expert from the Polish Police Central Forensic Laboratory used the unearthed skull to reconstruct a face that closely resembled Copernicus’ features. The expert also determined that the skull belonged to a man who had died around age 70 – Copernicus’ age at the time of his death.

These findings were backed up in 2008 when a comparative DNA analysis was made from both the remains and two hairs found in a book Copernicus was known to have owned (Calendarium Romanum Magnum, by Johannes Stoeffler). The DNA results were a match, proving that Copernicus’ body had indeed been found.

Copernicus' 2010 grave in Frombork Cathedral, acknowledging him as the father of heiocentirsm.Credit:
Copernicus’ 2010 grave in Frombork Cathedral, acknowledging him as a church canon and the father of heliocentricism. Credit: Wikipedia/Holger Weinandt

On May 22nd, 2010, Copernicus was given a second funeral in a Mass led by Józef Kowalczyk, the former papal nuncio to Poland and newly named Primate of Poland. Copernicus’ remains were reburied in the same spot in Frombork Cathedral, and a black granite tombstone (shown above) now identifies him as the founder of the heliocentric theory and also a church canon. The tombstone bears a representation of Copernicus’ model of the solar system – a golden sun encircled by six of the planets.

Copernicus’ Legacy:

Despite his fears about his arguments producing scorn and controversy, the publication of his theories resulted in only mild condemnation from religious authorities. Over time, many religious scholars tried to argue against his model, using a combination of Biblical canon, Aristotelian philosophy, Ptolemaic astronomy, and then-accepted notions of physics to discredit the idea that the Earth itself would be capable of motion.

However, within a few generation’s time, Copernicus’ theory became more widespread and accepted, and gained many influential defenders in the meantime. These included Galileo Galilei (1564-1642), who’s investigations of the heavens using the telescope allowed him to resolve what were seen at the time as flaws in the heliocentric model.

These included the relative changes in the appearances of Mars and Jupiter when they are in opposition vs. conjunction to the Earth. Whereas they appear larger to the naked eye than Copernicus’ model suggested they should, Galileo proved that this is an illusion caused by the behavior of light at a distance, and can be resolved with a telescope.

1973 Federal Republic of Germany 5-mark silver coin commemorating 500th anniversary of Copernicus' birth. Credit: Wikipedia/Berlin-George
1973 Federal Republic of Germany 5-mark silver coin commemorating 500th anniversary of Copernicus’ birth. Credit: Wikipedia/Berlin-George

Through the use of the telescope, Galileo also discovered moons orbiting Jupiter, Sunspots, and the imperfections on the Moon’s surface, all of which helped to undermine the notion that the planets were perfect orbs, rather than planets similar to Earth. While Galileo’s advocacy of Copernicus’ theories resulted in his house arrest, others soon followed.

German mathematician and astronomer Johannes Kepler (1571-1630) also helped to refine the heliocentric model with his introduction of elliptical orbits. Prior to this, the heliocentric model still made use of circular orbits, which did not explain why planets orbited the Sun at different speeds at different times. By showing how the planet’s sped up while at certain points in their orbits, and slowed down in others, Kepler resolved this.

In addition, Copernicus’ theory about the Earth being capable of motion would go on to inspire a rethinking of the entire field of physics. Whereas previous ideas of motion depended on an outside force to instigate and maintain it (i.e. wind pushing a sail) Copernicus’ theories helped to inspire the concepts of gravity and inertia. These ideas would be articulated by Sir Isaac Newton, who’s Principia formed the basis of modern physics and astronomy.

Today, Copernicus is honored (along with Johannes Kepler) by the liturgical calendar of the Episcopal Church (USA) with a feast day on May 23rd. In 2009, the discoverers of chemical element 112 (which had previously been named ununbium) proposed that the International Union of Pure and Applied Chemistry rename it copernicum (Cn) – which they did in 2011.

Crater Copernicus on the Moon. Mosaic of photos by Lunar Reconnaissance Orbiter, . Credit: NASA/LRO
Mosaic image of the Copernicus Crater on the Moon, taken by the Lunar Reconnaissance Orbiter, . Credit: NASA/LRO

In 1973, on the 500th anniversary of his birthday, the Federal Republic of Germany (aka. West Germany) issued a 5 Mark silver coin (shown above) that bore Copernicus’ name and a representation of the heliocentric universe on one side.

In August of 1972, the Copernicus – an Orbiting Astronomical Observatory created by NASA and the UK’s Science Research Council – was launched to conduct space-based observations. Originally designated OAO-3, the satellite was renamed in 1973 in time for the 500th anniversary of Copernicus’ birth. Operating until February of 1981, Copernicus proved to be the most successful of the OAO missions, providing extensive X-ray and ultraviolet information on stars and discovering several long-period pulsars.

Two craters, one located on the Moon, the other on Mars, are named in Copernicus’ honor. The European Commission and the European Space Agency (ESA) is currently conducting the Copernicus Program. Formerly known as Global Monitoring for Environment and Security (GMES), this program aims at achieving an autonomous, multi-level operational Earth observatory.

On February 19th, 2013, the world celebrated the 540th anniversary of Copernicus’ birthday. Even now, almost five and a half centuries later, he is considered one of the greatest astronomers and scientific minds that ever lived. In addition to revolutionizing the fields of physics, astronomy, and our very concept of the laws of motion, the tradition of modern science itself owes a great debt to this noble scholar who placed the truth above all else.

Universe Today has many interesting articles on ancient astronomy, such as What is the Difference Between the Geocentric and Heliocentric Models of the Solar System.

For more information, you should check out Nicolaus Copernicus, the biography of Nicolaus Copernicus, and Planetary Motion: The History of an Idea That Launched the Scientific Revolution.

Astronomy Cast has an episode on Episode 338: Copernicus.


Mathematics: The Beautiful Language of the Universe

Let us discuss the very nature of the cosmos. What you may find in this discussion is not what you expect. Going into a conversation about the universe as a whole, you would imagine a story full of wondrous events such as stellar collapse, galactic collisions, strange occurrences with particles, and even cataclysmic eruptions of energy. You may be expecting a story stretching the breadth of time as we understand it, starting from the Big Bang and landing you here, your eyes soaking in the photons being emitted from your screen. Of course, the story is grand. But there is an additional side to this amazing assortment of events that oftentimes is overlooked; that is until you truly attempt to understand what is going on. Behind all of those fantastic realizations, there is a mechanism at work that allows for us to discover all that you enjoy learning about. That mechanism is mathematics, and without it the universe would still be shrouded in darkness. In this article, I will attempt to persuade you that math isn’t some arbitrary and sometimes pointless mental task that society makes it out to be, and instead show you that it is a language we use to communicate with the stars.

We are currently bound to our solar system. This statement is actually better than it sounds, as being bound to our solar system is one major step up from being bound simply to our planet, as we were

A defining moment for humanity: Galileo turing his spyglass towards the sky
A defining moment for humanity: Galileo turing his spyglass towards the sky

before some very important minds elected to turn their geniuses toward the heavens. Before those like Galileo, who aimed his spyglass towards the sky, or Kepler discovering that planets move about the sun in ellipses, or Newton discovering a gravitational constant, mathematics was somewhat  limited, and our understanding of the universe rather ignorant. At its core, mathematics allows a species bound to its solar system to probe the depths of the cosmos from behind a desk. Now, in order to appreciate the wonder that is mathematics, we must first step back and briefly look at its beginnings and how it is integrally tied into our very existence.

Mathematics almost certainly came about from very early human tribes (predating Babylonian culture which is attributed to some of the first organized mathematics in recorded history), that may have used math as a way of keeping track of lunar or solar cycles, and keeping count of animals, food and/or people by leaders. It is as natural as when you are a young child and you can see that you have

Ancient Babylonian tablet displaying early mathematics
Ancient Babylonian tablet displaying early mathematics

one toy plus one other toy, meaning you have more than one toy. As you get older, you develop the ability to see that 1+1=2, and thus simple arithmetic seems to be interwoven into our very nature. Those that profess that they don’t have a mind for math are sadly mistaken because just as we all have a mind for breathing, or blinking, we all have this innate ability to understand arithmetic. Mathematics is both a natural occurrence and a human designed system. It would appear that nature grants us this ability to recognize patterns in the form of arithmetic, and then we systematically construct more complex mathematical systems that aren’t obvious in nature but let us further communicate with nature.

All this aside, mathematics developed alongside of human development, and carried on similarly with each culture that was developing it simultaneously. It’s a wonderful observation to see that cultures that had no contact with one another were developing similar mathematical constructs without conversing. However, it wasn’t until mankind decidedly turned their mathematical wonder towards the sky that math truly began to develop in an astonishing way. It is by no mere coincidence that our scientific revolution was spurred by the development of more advanced mathematics built not to tally sheep or people, but rather to further our understandings of our place within the universe. Once Galileo began measuring the rates at which objects fell in an attempt to show mathematically that the mass of an object had little to do with the speed in which it fell, mankind’s future would forever be altered.

This is where the cosmic perspective ties in to our want to further our mathematical knowledge. If it were not for math, we would still think we were on one of a few planets orbiting a star amidst the backdrop of seemingly motionless lights. This is a rather bleak outlook today compared to what we now know

Johannes Kepler used mathematics to model his observations of the planets.
Johannes Kepler used mathematics to model his observations of the planets.

about the awesomely large universe we reside in. This idea of the universe motivating us to understand more about mathematics can be inscribed in how Johannes Kepler used what he observed the planets doing, and then applied mathematics to it to develop a fairly accurate model (and method for predicting planetary motion) of the solar system. This is one of many demonstrations that illustrate the importance of mathematics within our history, especially within astronomy and physics.

The story of mathematics becomes even more amazing as we push forward to one of the most advanced thinkers humanity has ever known. Sir Isaac Newton, when pondering the motions of Halley’s Comet, came to the realization that the math that had been used thus far to describe physical motion of massive

Isaac Newton
Isaac Newton

bodies, simply would not suffice if we were to ever understand anything beyond that of our seemingly limited celestial nook. In a show of pure brilliance that lends validity to my earlier statement about how we can take what we naturally have and then construct a more complex system upon it, Newton developed the Calculus in which this way of approaching moving bodies, he was able to accurately model the motion of not only Halley’s comet, but also any other heavenly body that moved across the sky.

In one instant, our entire universe opened up before us, unlocking almost unlimited abilities for us to converse with the cosmos as never before. Newton also expanded upon what Kepler started. Newton recognized that Kepler’s mathematical equation for planetary motion, Kepler’s 3rd Law ( P2=A3 ), was purely based on empirical observation, and was only meant to measure what we observed within our solar system. Newton’s mathematical brilliance was in realizing that this basic equation could be made universal by applying a gravitational constant to the equation, in which gave birth to perhaps one of the most important equations to ever be derived by mankind; Newton’s Version of Kepler’s Third Law.

You can still see where Kepler's 3rd Law remains, but with the added values of the gravitational constant G, and M and m representing the masses of the two bodies in question, this equation is no longer restricted to just our solar system
You can still see where Kepler’s 3rd Law remains, but with the added values of the gravitational constant G, and M and m representing the masses of the two bodies in question, this equation is no longer restricted to just our solar system

What Newton realized was that when things move in non-linear ways, using basic Algebra would not produce the correct answer. Herein lays one of the main differences between Algebra and Calculus. Algebra allows one to find the slope (rate of change) of straight lines (constant rate of change), whereas Calculus allows one to find the slope of curved lines (variable rate of change). There are obviously many more applications of Calculus than just this, but I am merely illustrating a fundamental difference between the two in order to show you just how revolutionary this new concept was. All at once, the motions of planets and other objects that orbit the sun became more accurately measurable, and thus we gained the ability to understand the universe a little deeper. Referring back to Netwon’s Version of Kepler’s Third Law, we were now able to apply (and still do) this incredible physics equation to almost anything that is orbiting something else. From this equation, we can determine the mass of either of the objects, the distance apart they are from each other, the force of gravity that is exerted between the two, and other physical qualities built from these simple calculations.

With his understanding of mathematics, Newton was able to derive the aforementioned gravitational constant for all objects in the universe ( G = 6.672×10-11 N m2 kg-2 ). This constant allowed him to unify astronomy and physics which then permitted predictions about how things moved in the universe. We could now measure the masses of planets (and the sun) more accurately, simply according to Newtonian physics (aptly named to honor just how important Newton was within physics and mathematics). We could now apply this newfound language to the cosmos, and begin coercing it to divulge its secrets. This was a defining moment for humanity, in that all of those things that prohibited our understandings prior to this new form of math were now at our fingertips, ready to be discovered. This is the brilliance of understanding Calculus, in that you are speaking the language of the stars.

There perhaps is no better illustration of the power that mathematics awarded us then in the discovery of the planet Neptune. Up until its discovery in September of 1846, planets were discovered simply by observing certain “stars” that were moving against the backdrop of all the other stars in odd ways. The term planet is Greek for “wanderer”, in that these peculiar stars wandered across the sky in noticeable patterns at different times of the year. Once the telescope was first turned upwards towards the sky by Galileo, these wanderers resolved into other worlds that appeared to be like ours. If fact, some of these worlds appeared to be little solar systems themselves, as Galileo discovered when he began recording the moons of Jupiter as they orbited around it.

After Newton presented his physics equations to the world, mathematicians were ready and excited to begin applying them to what we had been keeping track of for years. It was as if we were thirsty for the knowledge, and finally someone turned on the faucet. We began measuring the motions of the planets and gaining more accurate models for how they behaved. We used these equations to approximate the mass of the Sun. We were able to make remarkable predictions that were validated time and again simply by observation. What we were doing was unprecedented, as we were using mathematics to make almost impossible to know predictions that you would think we could never make without actually going to these planets, and then using actual observation to prove the math correct. However, what we also did was begin to figure out some odd discrepancies with certain things. Uranus, for instance, was behaving not as it should according to Newton’s laws.

Here you can see that the inner planet is being perturbed by the outer planet, in our situation, that outer planet was Neptune, not yet discovered.
Here you can see that the inner planet is being perturbed by the outer planet. In our situation, that outer planet was Neptune, which had yet to be discovered.

What makes the discovery of Neptune so wonderful was the manner in which it was discovered. What Newton had done was uncover a deeper language of the cosmos, in which the universe was able to reveal more to us. And this is exactly what happened when we applied this language to the orbit of Uranus. The manner in which Uranus orbited was curious and did not fit what it should have if it was the only planet that far out from the sun. Looking at the numbers, there had to be something else out there perturbing its orbit. Now, before Newton’s mathematical insights and laws, we would have had no reason to suspect anything was wrong in what we observed. Uranus orbited in the way Uranus orbited; it was just how it was. But, again revisiting that notion of mathematics being an ever increasing dialogue with the universe, once we asked the question in the right format, we realized that there really must be something else beyond what we couldn’t see. This is the beauty of mathematics writ large; an ongoing conversation with the universe in which more than we may expect is revealed.

It came to a French mathematician Urbain Le Verrier who sat down and painstakingly worked through the mathematical equations of the orbit of Uranus. What he was doing was using Newton’s mathematical equations backwards, realizing that there must be an object out there beyond the orbit of Uranus that was also orbiting the sun,

French mathematician who discovered the planet Neptune by using only mathematics
French mathematician who discovered the planet Neptune by using only mathematics

and then looking to apply the right mass and distance that this unseen object required for perturbing the orbit of Uranus in the way we were observing it was. This was phenomenal, as we were using parchment and ink to find a planet that nobody had ever actually observed. What he found was that an object, soon to be Neptune, had to be orbiting at a specific distance from the sun, with the specific mass that would cause the irregularities in the orbital path of Uranus. Confident of his mathematical calculations, he took his numbers to the New Berlin Observatory, where the astronomer Johann Gottfried Galle looked exactly where Verrier’s calculations told him to look, and there lay the 8th and final planet of our solar system, less than 1 degree off from where Verrier’s calculations said for him to look. What had just happened was an incredible confirmation of Newton’s gravitational theory and proved that his mathematics were correct.

Are There Oceans on Neptune
Neptune is more than just the 8th planet in our solar system; it is a celestial reminder of the power that mathematics grants us.

These types of mathematical insights continued on long after Newton. Eventually, we began to learn much more about the universe with the advent of better technology (brought about by advances in mathematics). As we moved into the 20th century, quantum theory began to take shape, and we soon realized that Newtonian physics and mathematics seemed to hold no sway over what we observed on the quantum level. In another momentous event in human history, yet again brought forth by the advancement in mathematics, Albert Einstein unveiled his theories of General and Special Relativity, which was a new way to look not only at gravity, but

Einstein's Relativity, yet another momentous advancement for humanity brought forth from an ongoing mathematical dialogue. Image via Pixabay.
Einstein’s equation for the energy-mass equivalency, yet another incredible advancement for humanity brought forth from an ongoing mathematical dialogue. Image via Pixabay.

also on energy and the universe in general. What Einstein’s mathematics did was allow for us to yet again uncover an even deeper dialogue with the universe, in which we began to understand its origins.

Continuing this trend of advancing our understandings, what we have realized is that now there are two sects of physics that do not entirely align. Newtonian or “classical” physics, that works extraordinarily well with the very large (motions of planets, galaxies, etc…) and quantum physics that explains the extremely small (the interactions of sub-atomic particles, light, etc…). Currently, these two areas of physics are not in alignment, much like two different dialects of a language. They are similar and they both work, but they are not easily reconcilable with one another. One of the greatest challenges we face today is attempting to create a mathematical grand “theory of everything” which either unites the laws in the quantum world with that of the macroscopic world, or to work to explain everything solely in terms of quantum mechanics. This is no easy task, but we are striving forward nonetheless.

As you can see, mathematics is more than just a set of vague equations and complex rules that you are required to memorize. Mathematics is the language of the universe, and in learning this language, you are opening yourself up the core mechanisms by which the cosmos operates. It is the same as traveling to a new land, and slowly picking up on the native language so that you may begin to learn from them. This mathematical endeavor is what allows us, a species bound to our solar system, to explore the depths of the universe. As of now, there simply is no way for us to travel to the center of our galaxy and observe the supermassive black hole there to visually confirm its existence. There is no way for us to venture out into a Dark Nebula and watch in real time a star being born. Yet, through mathematics, we are able to understand how these things exist and work. When you set about to learn math, you are not only expanding your mind, but you are connecting with the universe on a fundamental level. You can, from your desk, explore the awesome physics at the event horizon of a black hole, or bear witness to the destructive fury behind a supernova. All of those things that I mentioned at the beginning of this article come into focus through mathematics. The grand story of the universe is written in mathematics, and our ability to translate those numbers into the events that we all love to learn about is nothing short of amazing. So remember, when you are presented with the opportunity to learn math, accept every bit of it because math connects us to the stars.

We are connected to the universe through mathematics...
We are connected to the universe through mathematics…