Oddly enough. People frequently surprise themselves when discovering that I can’t do complex calculations faster than all non-mathematicians and without use of an electronic calculator. Yet, I call myself mathematician. I don’t have extensive knowledge in the subject, but I keep studying it because it’s something I discovered to bring me a lot of joy. And the acceptance came just after finding the real meaning of the topic.
In a given year I had opportunity to read some books: The Man Who Counted, Rich Dad, Poor Dad, Invitation à la physique, Alice in Quantumland and The Drunkard’s Walk. Each of them aiming different publics, talking about distinct subjects yet including some level of Mathematics. To understand which are they, you have to use one of the most important fields inside of it: logic.
The Man Who Counted appropriates itself from the most known fields: calculations and problem solving using numbers. Beremiz Samir, the main fictional character, is what we like to call nerd. From hyperboles like counting how many feathers are in a flock of flying birds, you may understand Mathematics as something out of reach, possible just for those who were born with a gift.
A personal finance book, Rich Dad, Poor Dad tells the story of the author and how he became rich. Between entrepreneurship lessons, you learn the importance of accounting for those following his path. The set of rules for taxes payments are part of Mathematics study.
Reading The Drunkard’s Walk you understand how randomness affect our lives. How an excellent soccer coach can see his/her team perform worst than all the others in a given season? And in all seasons of 5 years in a row?! Does this make the coach worse? Learning about Statistics and discovering that improbable events may happen (in previously known number of times), you end up discovering that even imperfect things are ruled by Mathematics.
On trying to understand basics of Quantum Theory, I read two books: Invitation à la physique and Alice in Quantumland. In Physics origins — before Aristotle, 384 BCE — the subject used to be part of Mathematics. Today, the reasoning of discovering and putting the rules defining our Universe down are written in Math language.
The book of nature is written in the language of mathematics.
Galileo Galilei
Starting to study Mathematics by itself and not parts of it used in other fields, you get how important it is in basically all existent subjects. Abraham Lincoln once gave a pause in his studies of law to master Euclidian Geometry before going back with more confidence.
In the course of my law reading I constantly came upon the word “demonstrate”. I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?
I consulted Webster’s Dictionary. They told of ‘certain proof,’ ‘proof beyond the possibility of doubt’; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man.
At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.
Abraham Lincoln
In the end, Mathematics is all of this. It is the basis of all sciences, a toolkit to discover and define patterns. Since we already have thousands of years evolving the subject, a lot of knowledge was acquired and divided between fields so you can learn them easier. Logic (the reasoning over a set of rules), Arithmetics (relations between quantities, usually represented by numbers), Algebra (discovering missing pieces in Arithmetics’ relations), Statistics (logic way of seeing data) and so on.
Arithmetics and Algebra — the so called “calculations” — are Mathematics because have patterns and logical rules. Yet, are just a small part of all you have available to learn and create in the field. So take the dust out of your brain, use your analytical thinking — the one all humans have — and go learn this new language. You will find incredibly rewarding to understand the only language spoken by all the things in the Universe.
If you still don’t have a clue of how start, a good way is reading the book Introduction to Mathematical Thinking or attending the homonymous course, by Keith Devlin. Putting all your effort over it is good, but just reading it is already enough to be able to know where you can find Mathematics and apply it in the world.