“Pure mathematics is, in its way, the poetry of logical ideas.” –Albert Einstein

When you start tracing the history of mathematics, you find yourself immersed in a tale as old as humanity. Though numbers as we know them didn’t exist during the early days of mankind, we began developing the concept right off the bat. Math seems to have been very limited at first based on the earliest examples to have been found so far.

Human though processes evolved, driven by need and curiosity, and those primitive numerical ideas branched out in hundreds of directions. Eventually, math became the complicated and diverse field we know today, defined as the theory of numbers, amounts, space and their relationships to each other. It has become a language all its own, and it’s the building block on which all other sciences are formed.

In the Beginning

Some of the oldest forms of math we’ve found are believed to have been created around 35,000 years ago. Ancient African tribes carved notches on bones resembling the tally marks many of us use for counting even now. We’re not exactly sure of what they were keeping track of back then. Perhaps they needed to keep up with how many members were in their tribes or how many animals roamed across their hunting grounds each day.

Variations of this tallying method have been discovered among cultures around the globe. No doubt, addition and subtraction arose from those first ideas. Over time, maybe tribes needed to figure out how much meat was needed to keep everyone fed for a certain amount of time or how to ration what food was available among their people. Multiplication and division sprang forth from there, and an unstoppable series of events was set into motion.

Facts eventually emerged, and plenty of concepts were formulated to help explain the why’s and how’s of it all. We begin learning these at an early age, giving us a solid foundation for more intricate branches later on in life. If you’d like to explore some of the basic math ideas further, Study.com offers a range of helpful explanations and videos.

The Plot Thickens

Thousands of years later, around 6,000 B.C., ancient Egypt and other civilizations around the world took matters to yet another level. Humanity had come to rely on organized agriculture more so than in the past, and we needed standard and reliable systems of measurement to help further the cause. Body parts, like the hands, fingers, feet and arms, were used to help divvy up plots of land. Since people aren’t all the same size, this wasn’t really an exact science, but it was a good start.

Incidentally, these cultures also started adding more rhyme and reason to their homes and other buildings. They decided bigger and more elaborate was the way to go; at least, this was the case where their royalty and authority figures were concerned. Someone had to figure out just how to build these structures, so the greatest minds of the time were called upon to lend their thoughts on the subject.

Engineering and architecture came about, concepts eventually responsible for the Great Pyramids, the mysterious and majestic Sphinx, the Roman aqueducts a few thousand years later and, ultimately, the towering cities, underground utilities and fast-paced transportation systems available to us today.

If you’d like to learn a little more of the history behind this aspect of math, the Fact Monster website offers a list of ancient measurements and their backstories. You’ll also find information on our modern-day equivalents there. While those are key elements paving the way to modern civilization, a few other branches of mathematics sprang to life during those centuries.

Looking at the World from Different Angles

Even as certain members of the human race were discovering the power of numbers, other inquiring minds were watching the sky. They realized aside from tracing paths across the heavens, the sun and moon had ways of gradually moving around over time. Though the sun was always there to brighten the day, the moon sometimes didn’t make an appearance at all.

Both these main celestial bodies had direct effects on life on Earth, and their impacts varied as much as their positions in the sky. These were significant discoveries worthy of further investigation. Patterns emerged, and though such revelations struck terror in the hearts of some people, others were fascinated. Entire religions were created around those entities in the sky, but mathematics made its way into the mix as well. By extension, so did science.

Glancing back to the measurement systems developed by the ancient Egyptians, we find a deeper idea beginning to take shape. Using certain units of measurement went a long way toward dividing up land, building some of the world’s greatest wonders and putting resources to more efficient use, but it also created plenty of questions and left a lot of blanks to be filled in. In time, a specific branch of “Earth measurement” came into play. Today, we call it geometry.

Shapes and Patterns Emerge

Geometry deals with shape, area, volume, distance and other relationships between objects. Several mathematically inclined minds had a hand in shaping this branch, but a couple stand out in the crowd. Pythagoras gets quite a bit of credit in the math realm although he’s considered more of a philosopher than a mathematician. Overall, he founded a school where students learned his views on religion, nature and the links between the two.

Pythagoras’ followers felt he had some good points where geometry was concerned, and they spent a great deal of time expanding upon them. One of his most famous theorems covers right triangles, stating the square of the longest side equals the squares of the other two sides combined. With a little rearrangement, you can also use this formula to uncover the length of the shorter sides. You’ll find a great explanation of Pythagorean Theorem at MathIsFun.com and a little background information on the man himself through Math Open Reference.

Another key player in the geometry game is Euclid. He realized a straight line segment can be drawn by joining any two points and all right angles are the same among other ideas. Wyzant Resources is a wonderful website for more details on Euclid’s Elements as they’re called in the geometry world. This website also offers in-depth lessons in geometry.

Both Euclid and Pythagoras were helping develop geometric rules around 300 B.C. Several hundred years later, René Descartes came along to introduce coordinate geometry. His contributions led to calculus and physics.

Beyond that point, matters became a little more abstract and began to deal with bending lines as well as the conventional rules. Non-Euclidian geometry arose, and this field may very well change the way you look at the world. If you draw a triangle on a flat latex balloon and inflate it, you’ll get an interesting little preview of where this branch takes you.

Taking Matters in a Different Direction

Geometry certainly brought about an endless array of advancements in down-to-Earth sciences like engineering and architecture, not to mention the real estate industry, but it also led to studies in more out-of-this-world fields. Here, astronomy and astrology enter the mix. Though they’re very different disciplines, both revolve around our planet and all things beyond our Earthly confines.

Using the Stars to Our Advantage

Referring back to ancient Egypt once again, it seems the pyramids of Giza are aligned with the three stars we know as Orion’s belt. Those and other celestial bodies had significant meanings in any number of cultures. Evidence has been found to suggest devices much like the ones used to ensure the pyramids were level and symmetrical also had a hand in tracking the stars, moon and sun across specific timeframes.

These studies and measurements ultimately led to the invention of calendars and clocks. They were also heavily relied upon to determine the best times for planting crops among other important occasions. Today, our Farmer’s Almanac is based on many of the theories and calculations from all those centuries ago, and it’s often more accurate than all the computer-aided meteorological instruments currently in play.

England’s Stonehenge is yet another example of mathematic and astronomical connections in early history. Construction began on this structure more than 5,000 years ago. Even then, builders and engineers had a thorough knowledge of shapes, angles and precise measurements.

All theories on otherworldly visitors aside, many believe Stonehenge was a calendar in its own right, using geometry to help predict cycles of the moon and sun as well as solstices and equinoxes. If we’re correctly interpreting its creators’ scientific know-how, their geometry actually counted out the lunar cycle a little more precisely than the modern-day calendar. Countless temples and gathering spots built centuries ago had the same basic principles incorporated into their designs.

Bowling Green State University’s website, specifically, provides a wonderful basic description of mathematics and its connection to astronomy and physics. You’ll also find some exercises allowing you to test your knowledge and understanding of the lessons covered in this resource.

Finding Out if the Stars Align in Our Favor

Those are aspects of astronomy, which is the study of the physical universe as a whole; on the other end of the spectrum, astrology deals with the movements of celestial bodies and their effects on us and our surroundings. Astrology got its start in geometry. While this field is as complicated as all other sciences, it’s essentially based on a circle divided into 12 pieces, one for each sign of the zodiac.

Astrologers use positions of the planets, sun and moon as well as our longitude, latitude and birth times to determine how all these elements might affect our personalities and even our futures. It’s a matter of precise measurements and angles. Opinions vary widely on this scientific and mathematic field of study, but a number of divisions have been developed dealing with everything from individual births to the fate of entire nations. All are centered on geometry.

The University of Singapore gives you a fairly complicated look at how astrology and geometry collide (http://www.math.nus.edu.sg/aslaksen/projects/kh-urops.pdf). Math Goodies and MathPlanet offer more basic explanations about circles and dividing them into equal pieces.

A World Both Divided and Intertwined

As mentioned, math started out in a very simple form. Notches on bones, rocks and other objects capable of being carved and withstanding the elements gave ancient mankind a way of keeping records. Over the years, the human mind expanded, and the world of math followed suit. Basic math is present in every aspect of our lives, but some of the more advanced branches often show up where we least expect them.

Those advanced scientific divisions, like algebra, calculus, trigonometry and so forth gave rise to engineering, architecture, physics, chemistry and any number of other disciplines. Even as they divide and go their separate ways, they all come back together at various points. Without the basics, our world would be a much different place. That being said, even the basics can make the world a bit more complicated for many of us.

We all need math skills whether we’re balancing ye olde checkbook, learning to read our own destiny in the angles of the stars or hoping to become one of NASA’s greatest assets. Some people seem to sail right through the most complicated and advanced concepts whereas others can’t grasp even the elemental facts. Even theoretical physicist Albert Einstein, who used advanced formulas to determine space is curved, develop quantum theory and stumble upon the photoelectric effect had trouble with the basics.

Back in 1936, the first functional computer came into being. Mathematics played a key role in its creation; from there, math was the fundamental building block of the internet we now turn to virtually every day. As it so happens, the internet is also a great resource for strengthening our understanding of mathematics. You’ll find a number of online courses are available regardless of your current level of mastery

From delving deeper into the history of each branch of mathematics to learning more about how all relate to everyday life, the internet is full of information. If you’d like to extend your skills or brush up on the ones you already have under your belt, plenty of options are geared toward those goals as well. Math has been around as long as the human race. It hasn’t stopped growing and evolving; no doubt, it never will.

No matter what advancements and changes come about in the future, resources will be available to help pass the new information along.