Type of paper:Â | Essay |

Categories:Â | Knowledge Mathematics Case study |

Pages: | 5 |

Wordcount: | 1205 words |

Mathematics involves a scientific language that has helped humankind in the advancement in technology. It is without any doubt that logic, as well as the order underpinning mathematics, has served in the description of the structure and patterns that are found in nature. The achieved successes from the cosmos mathematics down to the electronic devices at the micro-scale are much more important.

It has always been depicted scientists and mathematicians that there has never been any consensus on whether mathematics is either discovered or invented. To ascertain this, mathematics is seen to be a natural scientific language since the same order underpins the universe. Mathematical structures usually are intrinsic to nature. Hence in case of the universe disappearance, the eternal mathematical facts will always remain intact. Discovering mathematics as well as its workings, it will be significant in building models that will lead to a predictive power with the knowledge of the physical phenomena that people seek to control. Therefore form this information, mathematics is innate and hence it is a natural language of science.

Besides, mathematics is mankind's construct. The main reason why mathematics is suited for the description of the physical world is that it was invented to purely for that. It is as a result of the people's mind and this is made to suit everyone's purpose. If the world were to disappear, there would have been no existence in mathematics just in a similar manner that there would have been no games such as football and even chess (Lessel, 2016). Therefore, mathematics is only invented and not discovered. Besides the success of mathematics has been depicted to be unsuccessful since those that overstatements of the scientists' objectives have seduced marvel at the mathematical application's ubiquity. For the real world's description, the analytical mathematics equations describe the real world.

The debate on the mathematics' nature has been raged since the era of Pythagoreans. The anti-realism of mathematics holds that it was a product of human imagination and hence is engineered carefully in making of the formal statements about nature in order to help in knowing the universe behavior. The anti-realists claims that statements of mathematics have had truth values by the particular realm's correspondence of the non-empirical or immaterial entities. Math is our direction of making models of what we see as a general rule, making expectations, and recognizing the truth to a higher degree (Lessel, 2016). The numerical framework we are generally acquainted with is a lot of sayings, facts, and their consistent results. These operational images and the remainder of our mathematical language have become some portion of the human condition and are consequently deserving of the title innovation.

It is always a plain truth that 1+1=2, but no one knows how it was worked out since it could be somehow complicated. The fact that an infinite number of primes exists involves truths of reality which held before the mathematician's knowledge about them. These entail more of the discoveries but mainly they are done using the mathematicians' invented techniques (Putnam, 2010). For example, from the Pythagoras theorem, the sum of the squares of the two sides of a right-angled triangle is equal to the square of its hypotenuse. This is a fact that exist for all the right-angled triangles; hence, it is a discovery.

A proof in mathematics is a demonstration of the truth of a statement using theorems, postulates, definitions and even postulates. In mathematical proofs, there are no assumptions made since there is a need for the proof of every step in the logical sequence (Putnam, 2010). The proofs in mathematics mainly employ deductive reasoning whereby a conclusion is obtained from the multiple premises in which the premises make up statements in the proof. There are both direct as well as indirect proof (Voskoglou, 2018). In the case of the direct proof, statements are the only means of proving the truth of any conclusion. On the other hand, the indirect proof is a proof by contradiction where it starts by takes the opposite of the statement to be proven. On the other hand, the proof of otherwise is a demonstration that a given statement or theory or definition is wrong. This is the opposite of the mathematical statement's proof.

Truth in mathematical concepts reveals the facts about a statement. There are various kinds of mathematical truths dependent on what one wants in a notion of the absolute truth where some of them may either fit or not. In many cases, a defining feature of mathematics can generally arrive at the consensus relating to a particular mathematical statement's truth. This is done by criticizing its main weak points or by providing a putative proof. "There are no constraints on the scope of the direct consequence relation with which one starts and if one alters it one thereby alters the derivative division between 'logic-mathematical' and 'descriptive' expressions"( Voskoglou, 2018).

There are some of common instances where the proof, as well as truth in mathematics, are interrelated. Whereas any event has its truth, it also has proof of its occurrence. The mathematical proof, therefore, convinces people that something is true. The logical words such as 'or', 'if'etc underlies all the mathematical proofs. The two words mainly have their precise meanings where a slight difference is depicted in their daily use. The truth is most commonly used to refer to being following a fact of fidelity to the standard.

The proof is usually taken as sufficient evidence or an argument for the proposition's truth. The concept of this proof unlike in the case of truth, is applicable in almost various disciplines with the evidence nature, justification as well as the criteria for sufficiency being area-dependent (Reid, 2010). In many cases, the evidence is required to prove an absolute truth. Therefore any mathematical area bounded by its assumptions establishes that proof is a persuasive elocutionary speech demonstrating the truth of any proposition. For any statement's truth, the proof has always been presented since antiquity.Is proof of something that is "true" always possible? Yes, it is always possible. It has always been difficult to overestimate the significance of proofs in mathematics. In a case where one has a conjecture, the presentation of a valid mathematical proof is the only way that one can safely be sure that it is true. Another significance of mathematical proof is the insight that it may offer. Being in a position to draw valid proof is likely to indicate that one has a thorough knowledge of a problem. Sometimes the efforts of proofing the truth of a conjecture may require a critical deeper knowledge of the theory in question. In mathematics, any scientist trying to prove something may gain a great deal of knowledge as well as understanding even if the efforts of proofing the conjecture will fail.

## References

Voskoglou, M. (2018). Is mathematics invented or discovered by humans? Philosophy of Mathematics Education Journal, (33). https://www.closertotruth.com/series/mathematics-invented-or-discovered

Lessel, M. (2016). About the Origin: Is Mathematics Discovered or Invented? https://preserve.lehigh.edu/cgi/viewcontent.cgi?article=1038&context=cas-lehighreview-vol-24

Putnam, H. (2010) "What is mathematical truth?" Historia Mathematica 2.4 (1975): 529-533. https://philosophy.stackexchange.com/questions/48644/absolute-truth-in-mathematics

Reid, D. A., & Knipping, C. (2010). Proof in mathematics education. Research, learning, and teaching. http://www.acadiau.ca/~dreid/ridge/publications/Reid-Knipping-chr-11.pdf

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