Mathematics is a way of thinking

As the famous mathematician Gauss put it, “Mathematics is the queen of science.” Mathematics, with a long history, is the foundation of all modern science. Such subjects as physics, chemistry, biology and computer can never develop without mathematics discipline backing them up. Though mathematics has been contributing to human civilization, its development is not smooth and it is constantly shaping our thinking.
The ups and downs in its development is evident from the 3 well known mathematical crises with the first one about irrational number, the second one about calculus and the third one about sets, dated from 500 B.C. to nowadays. Throughout history people have to face countless paradoxes, some of which may make mathematicians’ previous efforts seem in vain and even destroy the mathematical foundation. Let’s take a look at an interesting paradox:
“Motion---is impossible, because whatever moves must reach the middle of its course before it reach the end; but before it has reached the middle, it must have reached the quarter mark, and so on, indefinitely. Hence the motion can never start.”
This paradox is raised in the 5th century B.C., bringing the philosophers to their knees, and was not solved until early 19th century. It used to be so confusing because people’s ideas were confined by the rules set by themselves.
To me it is not just a paradox. To some extent it shows that we tend to think about a matter in a fixed way and wish math to be accurate and definite. Actually this idea is against the spirit of science. When doing study and research, we should not be restricted to our old thinking styles which may shadow the truth. Instead we must jump out the circle and learn to see a problem in a new angle and accept new ideas.
Mathematics is a rigorous subject. For so many years people are trying to build the edifice of math cautiously without ignoring even one brick. Even so different problems and leaks jump out and challenge our views. Some people sighed that mathematics is a building based on sand. However the real situation is far from that pessimistic. If we think in depth, we will realize that it is those very conflicts that push mathematics forward and make it enriched. The first mathematical crisis brought people in a world of irrational numbers; the second one made calculus complete and rigorous; the third one---having given birth to some advanced theories but not solved completely yet---is waiting to be explored further.
Mathematics is growing. New theories are being established and old ones modified and even abandoned. In this way the kingdom of mathematics prospers. Conflicts are not obstacles. On the contrary, it is where the beauty of mathematics lies. We should have a right attitude towards studying mathematics and then apply it to all subjects. Science emphasizes the significance of deception, and so does mathematics. Just like great men have their shortcomings, mathematics---with a great system---can hardly avoid mistakes and needs a process to become mature. Whenever we meet conflicts during its promotion, we will not pretend to see nothing but solve them instead.
The history of mathematics is one full of conflicts that form a main force that pushes mathematics forward. We should study and explore them without any prejudice. Thanks to the conflicts and changes that build our ways of thinking, making it mature and rational. As we are exploring, we need the right attitude and thinking ways to gain “real knowledge” and to march toward truth.