A proposal for girls and others
To young people, especially for girls, I propose being a friend with mathematics if you are not sure what to do in your life or want some insurance that never fails.
Here are the reasons.
1. While mathematics is a language which takes time to learn, even if you only like a part of it, you can start anything from that point because mathematics can help you in identifying and solving problems in your life.
2. Mathematics makes you learn how to get to the bottom of anything you are involved with, since it gives you a language to describe what is going on and what must be done with the situation.
3. Mathematics expands your views so that you could motivate yourself to conquer the problems because mathematics contains many strategies for tackling problems; including some that seem at first like nonsense or meaningless, but end up providing rich results.
4. You can find a reasonable path to reach something unbelievable by using a mathematical method called conjectures.
Let me explain my claims in order.
#1. I remember I was sitting in a train and thinking how I could handle a stressful situation; at the time, I was a student in topology and recalling there is no measurement in topology. That is, the size of my stressful problem is meaningless or I change the size of it as large as or as small as possible. I was so released and felt free; even I do not remember what the problem was. Since then, I have learned that I am in charge of deciding the size of a problem and mathematics helps me to not get overwhelmed by that stress.
#2. I had been struggling to decide whether I should live a safe life or take a risk to live my dream. I asked myself how I was living my life; and I found I was taking a job merely to pay the rent and was suppressing my dream. I decided to leave and to prepare to live my dream somewhere else. First, I started learning English and looking for a graduate school I could attend and earn a degree to find another job.
#3. Probably, it is enough to mention the value $X$ satisfying $X^2=-1$. Who thought this would open the doors and provide languages for electrical engineering and the new mathematical area of complex analysis and algebraic geometry? Let me add one more example in algebra. If we have a polynomial with one variable, you may think it is ridiculous to change it to a polynomial with two variables or three variables; this expansion seems to make the situation more complicated and to be useless. However, there are many occasions where this strategy works in mathematics. For example, you can see the amazing development by changing chromatic polynomials (single variable) to dichromatic polynomials (two variables). This expansion did not stop here and people are considering further expansion with three or more variables successfully. Thus, in math or in life, thinking expansions is a basic and meaningful strategy to try, even if it seems ridiculous at first.
#4. You describe what situations would be idealistic to reach your goals or to conquer (those idealistic situations may be called conjectures); then you continue to think what are idealistic to prove the conjectures (called sub-conjectures). You keep doing this until you reach something familiar. Now you see a path between familiar ones and unbelievable goals. As mathematicians do, you do trial and error and change the conjectures anytime because they are certainly yours.
As Galileo said, “the universe is written in the language of mathematics”; so why not learn that language?
＊The information in this article is as of the time it was written, and may have changed since.