4000 word essay on math

[NEGROWPLEASE]

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?

[xrayspecs]

Do the work yourself! If you can't then you should give some serious thought as to your suitability to the subject.

[bernardo]

It was discovered.
You'll have to do the other 3,997 words yourself.

[bob_builder]

Fermat's last theorem states that if n is a whole number strictly bigger than 2, then you can never find three whole numbers x, y and z such that xn+yn=zn

That's about 30 to get you started you lazy little tyke!!!

[tommy666]

bob if thats what the theory is, its f****d. i found xn and yn that equal zn on my first go. n = 3. x =3. y =4. z=7 3 x 3 + 4 x 3 = 7 x 3.

maybe x and n cant be the same, but if they can, it works.

[bob_builder]

Your maths are perfect Tommy, unfortunately it is not quite as it reads - the actual formula is where 'n' is the power of. So if x=2 and n=3 then xn = 8

Apologies for my poor illustration, but I would of thought Negrowplease should at least of known that bit!!

[bob_builder]

If your wondering what its all about - in simple terms (I believe). If you constructed 2 cubes from 1cm3 blocks, say 1cube 2x2x2cm and another 3x3x3cm you would have used a total of 35 (8+27) 1cm3 blocks - which is not enough blocks for another cube. Hence the theory revolves around 2 cubes added together will not make a third larger cube. I think!!!

[Buenchico]

Fermat's last theorem would prove to be an extremely difficult subject to write about. It forms part of the study of Diophantine equations which certainly isn't easy to 'get your head around'. ('Diophantine Equations' was the title for my university thesis. Much of the mathematics is well beyond that normally encountered at first degree level. Additionally, I had to translate many of the most important texts from the form of German used several centuries ago).

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

[NEGROWPLEASE]

thanks chris
your answer was the most help

[fo3nix]

if you want to write about Fermat's Last theorem (a good topic, could easily fill 4000 words), then I would suggest going to your library and getting out a copy of "Fermat's Last Theorem", by Simon Singh.

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

[fo3nix]

ahh, was writing at the same time as Buenchico :)

[NEGROWPLEASE]

thanks too foenix

so i would write about math in ancient history huh?
there should be a lot of books and sources for that right chris?

[Buenchico]

(Multi-part post):

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').

[Buenchico]

Any decent book about the history of mathematics - of which there are many - should have plenty of information about early civilizations. (The Babylonians, for example, invented measurement systems for both time and angles. We still use these systems, based upon the number 60, for these measurements today. The concept of the numerical measurement of time, other than by naturally occurring units like days or years, was an important advance for both mathematics and science).

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.

[Buenchico]

So the early civilizations have a great deal to offer in terms of your essay. This is because there's quite a bit of 'invention' during this period, whereas it tends to become largely 'discovery' later on. This doesn't mean that later periods are totally invention-free. I've already mentioned the invention of 'i' to represent the square root of -1. (Without this we wouldn't have complex numbers and many advances in mathematics would not have been possible). There have been plenty of other inventions, however. I'm thinking of such things as symbolic logic, Karnaugh maps, Venn diagrams, etc. Indeed, there could be a good case for arguing that algebra is an 'invention' which has been used to facilitate many 'discoveries'. (Much the same could be said for calculus - plus you could examine the conflicting arguments for attributing the invention of calculus to either Newton or Leibniz).

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

[NEGROWPLEASE]

Thanks a lot Chris.

I just wanted to make sure that there was no definite answer on whether or not Math was discovered or invented, and if I there were enough sources to be able to back up my position.

Thanks again

[NEGROWPLEASE]

Like when Bernardo posted that it was discovered, I began tohave doubts that I could do a research paper on this topic.