It is a collective creation from cultures around the world and very well could be the oldest discipline. Recognizing patterns and sequences in nature with a desire to make sense of the heavens and our place in the universe might be where it all started. In the simplest of terms, it’s the science of numbers but more realistically, has become one of the most important tools to be used in science. Mathematics is involved in all fields and is also its own field. In the modern era, math not only helps formulate conjectures, it’s a key player in the scientific method when confirming and disproving them.
The importance of mathematics cannot be over stressed and we usually take it for granted. It’s in the infrastructure of our towns and cities, in hospitals with doctors and nurses saving lives and in times of war, it has made the difference between winning and losing. Cell phones, computers and the Internet, the modern home with all the luxuries, our various means of transportation and money are only some of the things we wouldn’t have, without mathematics.
There is no universal definition for mathematics. For instance, there’s a common feeling among mathematicians that new formulas and maths are discoveries of something that already existed, but if you’re an intuitionist then you believe these things are only a construct of our mental activities. There are even philosophical consideration that mathematics might be created like art. Axioms or postulations are beliefs, also known as self evident truths, that are based on common sense or logic, which by definition are not proven. The foundation of mathematics is created from axioms. Although mathematics as we understand it, consists of a sophisticated and highly respected structure, because it is built on axioms, it leaves itself open to a full array of debates and challenges from various opinions.
Math is even involved in the wild kingdom. Animals instinctively calculate amounts when they decide to fight or run if they are outnumbered. They are calculating distance when they decide it’s feasible to attack pray and they calculate the size of other animals to determine the amount of danger a potential interaction could have.
The Fibonacci sequence is an endless string of numbers where each number in the sequence is the sum of adding the two preceding numbers. Example, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21 and so on. From the mating of rabbits to the sequence of seeds in a sun flower, the Fibonacci sequence is found all over the place in nature.
First steps leading to the concept of mathematics began through enumerating, where quantities of objects were matched one to one, for example, pebbles or cut notches on a piece of wood. People also enumerated by matching them to body parts. Left five fingers, wrist, elbow and shoulder, counted for eight objects and on the right side, they would count eight more. It’s suggested these counting methods predate language, because in some of the oldest known dialects, the first names for the numbers now known as one, two, three, four, and so on, were the names of these body parts. When people began naming different amounts, which is called numeration, another step towards mathematics had been taken.
In the early stages of numeration the concept of numbers weren’t separate from physical objects. Eventually the knowledge of knowing how many object there were would evolve into numbers that were separate from anything physical. This was when numbers began to existed on there own in the abstract mind of humans. The next step from here was to create numeration systems. This was when symbols were created to represent each abstract number. There are many ancient numeration systems, Roman numerals are among the most known.
The first numbering system is called natural numbers. This involves counting, one, two, three, four, into infinity. By 500AD, the Hindu Indians had invented the modern concept of zero. When the zero was incorporated into the natural numbers, they became known as whole numbers. The next step from here was to realize negative one, two, three, four, into infinity. The negative numbers with whole numbers are called integers.
Rational numbers are fractions or decimals. These are the numbers to the right side of the decimal. Rational numbers can have terminating or repeating decimals. Terminating decimals have an end number. Repeating decimals have a number or group of numbers that repeat infinitely. Irrational numbers are decimals that don’t repeat and go on for ever. Some irrational numbers are the square root of two and pi.
In ancient Egypt and Babylonia they used arithmetic, algebra and geometry for taxation, financial calculations, building construction and astronomy. Throughout the years the topics and formulas in mathematics would soar into the thousands. These days, after learning the basic arithmetic operations addition, subtraction, multiplication and division, the educational road to becoming a mathematician will run you through algebra, geometry, trigonometry and calculus. If this sounds like a long trail it is, but it’s also just the beginning of what the world of mathematics has become.
In 1900, David Hilbert published a list of twenty-three mathematical problems. In one of them he challenged researchers to find an axiomatic basis to all of physics. In this problem he’s asking for what today would be considered a (TOE).
Because of the success it’s had in explaining reality, there is a strong belief that mathematics is the language of the universe. If it is, the formula for a (TOE) is still a vocabulary waiting to be revealed. This brings us back to the opening statement of this book and the story that leads to an interpretation and how it will be deciphered.