• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Is Mathematics Invention or Discovery?

Extracts from this document...


Tso William 12B Is Mathematics Invention or Discovery? The question on mathematics being invention or discovery has long been debated. In the ancient Greeks, Pythagoras and his school of thinking, Pythagoreans, considered number in mathematics to be a representation of reality. Plato, one of the most important Greek philosophers in the Western Philosophy, reasoned mathematics being the only way to understand the true reality of the world or the form. Thus they both suggested math being the ultimate reality that must be discovered by human. On the other hand, there are three fundamental questions about the nature of mathematics itself. First, we must know where mathematics exists and where it is operating. Secondly, we are not sure how we discover the so-called reality of math. We must take a closer look on the system we are using to find the mathematics laws that represents the reality. Finally, since mathematics laws must correspond with the reality if it's discovered. Therefore we will find how and why the real world will obey the mathematical laws. The most reasonable answer might be mathematics being operating and existed in our mind. We processed the abstract idea, such as numbers and logarithm, in our mind. This is an obvious answer but it suggested mathematics being invented by humans themselves. We use our reason and logic to arrive a conclusion to describe what we know and the idea we have. ...read more.


Therefore this sometimes leads to theorems that are bizarre and not likely to present the reality. One of the most noted example is the Banach-Tarski paradox. A sphere in the size of a tennis ball is split into many little pieces. Without changing their size, they could be re-arranged into another sphere in the size of the earth. This conclusion is odd and hard to accept. However this is derived from the obvious axioms in mathematics. Sometimes obvious axioms could even lead to contradicting theorem. A German mathematicians David Hilbert started to search a theorem that could prove if a theorem is true or false in a axiomatic system. Thus he wants to find a step-by-step recipe which could simplify the whole process of theorem from the beginning of the first axioms. On the other hand, another mathematician G�del derived two theorems. They stated that there will always be mathematical theorems which are true. However they are impossible to be proven right or wrong from the beginning of the axioms. However the axioms in which mathematicians chose are supposed to be true and self-evident. Their consequences still lead to a range of different results. If mathematics discovers the reality of the physical world, this world of nature will be in contradictory. Since there are paradoxes in mathematics, this world is in constant conflict between different theorems. Furthermore, mathematic is also a creative art like other so-called uncertain subject. ...read more.


We then use these axioms to derive more complicated theorem to describe the world. In other words, we create mathematic to describe the physical world that allows us to make the world more meaningful. On the other hand, the patterns we have created from the observation could be after all what we discover in the nature. Thus those patterns are in fact the reality of the physical world. Thus axioms will then be the reality also. Therefore we have discovered the mathematics in the nature. Physic laws, such as Newton's second law rely heavily on mathematics and they correctly predict the result. However, the process of finding scientific truth is based on falsification by peer-review. Also numerous and differed experiments are done to confirm the effect and the theories. Wrong theories, such as phrenology, were discarded. Thus the role of mathematic must not be exaggerated in finding truth in science. For example, Newton's famous three laws were later all experimented by other scientists in later times before they are accepted being truth in describe the motion. If the mathematical theorem could not be applied to the nature, then it could not be discovered. Since the mathematical laws should be hidden in the nature in which human discover. Thus we are invited to observe the chess player playing the chess but we are not told what the rules are. However the rules are contradictory. Thus by observing the nature, human used axioms to deduce theorem that are possible to describe the nature. Therefore mathematic is invented by people to describe the world. ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our International Baccalaureate Theory of Knowledge section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Theory of Knowledge essays

  1. TOK summer assignment - Art Questions. Experiencing art, artists reputations and "what is ...

    The artwork to me seemed quite appropriate in the contemporary section because of its modern technique. There were many puzzling pieces; however, this one seemed to me the most perplexing, because of the material used and the way it has been placed in the room.

  2. A historian must combine the rigour of the scientist with the imagination of the ...

    This is peculiar, considering the fact that both sides had access to the same material, and begs the question what the reason is for the difference. Ideology? Culture? Nationalism? Personal interests? All of the above are variables with the potential to influence the force of imagination, and affect historical conclusions.

  1. TOk Discussion - Do we impose mathematics upon nature or is it naturally inherent ...

    A: We are trying to impose a mathematical construct onto the physical world. It may be that in the pursuit of trying to explain perception of beauty, mathematics was used as an attempt to describe what we yet did not know, the reason why certain proportions look better than others.

  2. work based project

    warm weather outside, furthermore many of the patients were excited at the prospect of having a little time outside as they very rarely had the chance to do so because of health and safety issues conveyed by the senior members of staff.

  1. Moral Laws

    that is, the possibility of it's corruption was present. In this case, possibility of corruption soon became reality of corruption, and original Purity and uprightness was lost when Adam sinned . Our moral laws are not born with us , yet we grow to make our own laws and choose to follow them , for example we can choose

  2. Belief System or not?

    and after (New Testament) Christ's birth. Therefore, we can conclude that Christianity is a religion, following the definition previously given. The question that must now be asked is whether Christianity is also a belief system, or whether it is simply a religion.

  1. Is Mathematics a Tool or a Toy?

    Also in social sciences, such as economics and sociology, at least basic mathematical knowledge is necessary. For example, the economics' program of International Baccalaureate includes also calculations of elasticity of supply and demand. When acquiring the topic, we were required to calculate percentages and use also others skills obtained during

  2. Does the nature of our sense organs authoritatively determine the nature of our ultimate ...

    Furthermore, perception contains an element of interpretation: we inevitably interpret the information we gain. Thus, perceiving is not only about observation but a complex process composed by sensation plus unavoidable interpretation. Moreover, as human beings are not purely rational, we cannot stop ourselves from including our values and judgments in our interpretations.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work