why do we study geometry?

Answers to why do we study geometry

The WHY of geometry depends on how you want to look at the world you live in.

If you are a pragmatist, geometry is a branch of practical knowledge which allows you learn more about the world around you, through surveying, measurements, and design, and then build more with accurate construction techniques.

If you are a philosopher, learning how to construct proofs will teach you how to think logically, and not make stupid decisions based on ignorance and faulty assumption.

If you are a student of history, then you know that the cultures with the smartest people, the best engineers, and superior technology, generally prevail over those without these assets. Geometry is part of the mathematics which underpins science and engineering.

And if you are just a plain student, who could care less about geometry or any other serious study other than the opposite sex, learning all that you can, while you can, may help you to prepare for a higher-income, satisfying job which will make you a more attractive partner for those you would want to date or marry.

Should none of these reasons satisfy you, then you need to study geometry because that is what you are required to do by whatever powers rule your life.

You need those skills for skilled craft trades such as carpeting, painting, tile laying and carpentry, for every technician job that requires digging holes, surveying, estimating materials required, and for every engineering job for building anything - buildings, highways, bridges, etc.

Digging deeper
At least at one level, the answer is quite surprisingly simple. Over most of the last two and a half thousand years in the European or Western tradition, geometry has been studied because it has been held to be the most exquisite, perfect, paradigmatic truth available to us outside divine revelation. It is the surest, clearest way of thinking available to us.

Studying geometry reveals – in some way – the deepest true essence of the physical world. And teaching geometry trains the mind in clear and rigorous thinking.

What I mean here is a little more complicated than it might first appear; it is easy for us to justify the study of geometry to ourselves (although perhaps not so easy to the man on the top of the Clapham Omnibus), and our reasons today are very deeply embedded in and reflect the science and scientific culture of late 20th century Europe. Yet European culture has valued and studied geometry
(and our benefactors have had their predecessors) over the last two and a half thousand years, reaching back to such institutions as Plato’s Academy in the Athens of the turn of the 4th century BC. What is this continuing need or this continuing stimulus to study geometry? What is interesting is that the answers of the ancient Greeks were certainly not those we would give today. What has
been the perceived value of studying, doing research into geometry? And – let’s not be mathematicians for a moment – why on earth should something so arcane and generally useless as geometry (done the way mathematicians do geometry) be so apparently important, and continuously important to Western learning and values over two and a half millennia? Clearly there is a history
here: a history of the role, status, the reasons past thinkers have had for the importance of geometry. And it might come as a surprise to some that past actors did not share the same scientific or intellectual values that we have today, and did not have anything like the same reasons for studying geometry as we have today.

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