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I need to write a 4000 word essay on math

Extended essay for IB

Fermat's Last Theorem

Was Math Discovered or Invented?

these are two possible topics that i may do, but am not sure if i can write a lot about it

anybody have any suggestions?

Extended essay for IB

Fermat's Last Theorem

Was Math Discovered or Invented?

these are two possible topics that i may do, but am not sure if i can write a lot about it

anybody have any suggestions?

Best Answer

No best answer has yet been selected by NEGROWPLEASE. Once a best answer has been selected, it will be shown here.

For more on marking an answer as the "Best Answer", please visit our FAQ.If you were to attempt to write anything about Femat's last theorem without reference to the higher levels of mathematics, you'd find that essestially, there is only one source of reference. i.e.Simon Sigh's 1997 award-winning book. (There are other books but they cover much of the same ground). Using one (or a very limited number) of reference sources would be unlikely to impress whoever is to assess the essay.

"Was Math Discovered or Invented" is a far more general topic. There many different ways of tackling the topic. There's plenty of scope for examining mathematics across the ages (starting with the ancient civilizations). I'll let you do the hard work but I hope that your conclusion will be that, while most of the development of mathematics has come through 'discovery', many of the most important advances have come through 'invention'. (The most important invention of all time is thought, by many people, to be the representation of the number zero. Until this invention, both mathematics and science could only make very slow progress. Afterwards, great strides were possible. Another important invention was the concept of 'i' to represent the square root of -1. Without such a concept, much of mathematical research would have stagnated).

Ignore Fermat. Go for 'Discovery vs. Invention'. It'll be easier, more interesting and more rewarding.

Chris

A great book, explaining everything about the historical aspects of the theorem, explaining the maths very well (though missing out the harder maths).

I'd certainly start with the ancient civilizations. It will give you the opportunity to expound upon the differences between the discovery of mathematically-based principles and the discovery of the underlying mathematics. For example the Egyptians knew that a 3-4-5 triangle is always right-angled and used this knowledge to help construct the pyramids. So the discovery of the simple mathematical principle had occurred prior to the construction of the pyramids. The discovery of the mathematics behind the principle, however, is usually attributed to Pythagoras (although there are many historians who assert that it may well have been known before Pythagoras was born). So the discovery of the mathematical principle is attributed to the Egyptians but the discovery of the actual mathematics is attributed to the Greeks. (There's also the possibility of referring to the way that the Egyptians used this principle - a length of rope knotted into 3 lengths with a 3:4:5 ratio - as a mathematical invention, which will help with your discussion of 'discovery vs invention').

As I've already indicated, the number zero is frequently cited as mankind's greatest ever invention. Although it was originally conceived by the Mayan civilization, its real usefulness only came about when the early Hindu civilization, quite independently, also invented (or re-invented, depending upon your viewpoint) the number zero.

Hang on a minute. Who's meant to be writing this essay? You or me? :-)

I hope that I've given you some useful suggestions. The history of mathematics is a fascinating subject and has much to offer in respect of your essay.

Chris

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