Summary

People often say that mathematics is right, but useless. Let’s imagine a tale of time machine. 500 B.C. science class, reached through the time machine, taught that the Earth is flat, and that the sun is loaded onto the carriage of Helios and carried from the east to the west, and goes back to the east loaded onto a large ship. When the time travellers disputed this, they were ridiculed and kicked out of the class. 1,000 B.C. mathematics class, again reached through the time machine, while the order of doing multiplication was a bit different, was doing the mathematics that we do today.

Even if you don’t know poetry, you can still read novels or modern literature. Even if you don’t know nouns, you can still know gerunds, and even if you don’t know present continuous, you can still know past participle. But mathematics is built on top of what came before. If you don’t understand addition, you can’t understand subtraction, multiplication, and division, and if you don’t understand elementary arithmetics, you can’t understand operations of integers, rational numbers, irrational numbers, real numbers, and complex numbers, and thus can’t understand symbols and equations. If you don’t understand symbols and equations, you can’t understand functions which appear frequently in mathematics, and thus can’t understand calculus and engineering. Business administration and economics of humanities, because they have many mathematical aspects, can’t be understood as well.

So, if one intends to do mathematics since highschool, they have to first ascertain that their basis of elementary school mathematics and middle school mathematics are sound.

Implication

You have to review the past to learn the new. At least in mathematics.

Underlying context – Background behind

Not applicable

Notions – Key ideas

Not applicable

Index – Source(s)

How to Think Like Mathematicians / 피타고라스 생각 수업
03 Review the Past to Learn the New / 옛것을 알아야 새것을 안다 | 온고이지신

Trajectory – Where I’m headed now

Not applicable