FO_Mathematics.pdf - IMTA Newsletter 109,2009 Page 29 THE...

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IMTA Newsletter 109,2009 Page 29 THE IMPORTANCE OF BEING BEAUTIFUL IN MATHEMATICS Fiacre 0 Cairbre, Department of Mathematics, NUI, Maynooth 1. Introduction In this article I will discuss beauty in mathematics and I will present a case for why I consider beauty to be arguably the most important feature of mathematics. However, I will first make some general comments about mathematics that are relevant to my discussion. Mathematics essentially comprises an abundance of ideas. Number, triangle and limit are just some examples of the myriad ideas in mathematics. I find from experience in teaching mathemat- ics and promoting mathematics among the general public that it's a big surprise for many people when they hear that number is an idea that cannot be sensed with our five physical senses. Num- bers are indispensable in today's society and appear practically everywhere from football scores to phone numbers to the time of day. One of my favourite football scores, which I refer to in some talks, is the 'celebrated' result: Louth 1-9 v 1-7 Cork in 1957 I will return to this football score later. The reason number appears practically everywhere is because a nuinber is actually an idea and not something physical. Many people think that they can physically see the nuinber two when it's written on the blacltboard but this is not so. The number two cannot be physically sensed because it's an idea. Mathematical ideas like number can only be really 'seen' with the 'eyes of the mind' because that is how one 'sees' ideas. Think of a sheet of music which is importailt and useful but it is nowhere near as interesting, beautiful or powerful as the music it represents. One can appreciate music without reading the sheet of music. Similarly, mathematical notation and symbols on a black- board are just like the sheet of music; they are important and useful but they are nowhere near as interesting, beautiful or powerful as the actual mathematics (ideas) they represent. The nuinber 2 on the blackboard is purely a symbol to represent the idea we call two. Many people claim they
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Page 30 IMTA Newsletter 109,2009 do not see mathematics in the physical world and this is because they are looking with the wrong eyes. These people are not looking with the eyes of their mind. For example if you look at a car with your physical eyes you do not really see mathematics, but if you look with the eyes of your mind you may see an abundance of mathematical ideas that are crucial for the design and opera- tion of the car. So what is this idea we call two? If one looks at the history of number one sees that the powerful idea of number did not come about overnight. As with most potent mathematical ideas, its crea- tion involved much imagination and creativity and it took a long time for the idea to evolve into something close to its current state around 2500 BC. Here is one way to think of what the number two is: Think of allpairs of objects that exist; they all have something in common and this common thing is the idea we call two.
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