Mathematical proof

remarkably, a cousin Magda Fredro had been sent to Auschwitz but had survived. In the end, one can say that Paul Erdős had many great life experiences, probably more than a classroom full of adults together. He contributed to, many of today’s mathematical theories and helped the growth of other great mathematicians. He did have his challenges at times, but he overcame them. On September 20th 1996 he died of a heart attack “only hours after disposing of a nettlesome problem in geometry at a…

The two authors I chose to compare and contrast are Charles Sanders Peirce and William James. One outstanding similarity between these two authors is that they both promoted the philosophy of Pragmatism. The Merriam-Webster dictionary defines pragmatism as: “A reasonable and logical way of doing things or of thinking about problems that is based on dealing with specific situations instead of on ideas and theories”. The core of pragmatism is what is known as the pragmatist maxim. This is…

focusing more on what they have to teach and not taking the time to explore their students’ claims. But, in contrast, teachers from schools like Grove City are being taught how to solve problems. Teachers should never just accept a claim. Using mathematical formulas and definitions, they should work with the student to find an example that disproves the claim, if any can be found. In this example, many of the SMPs can be found. SMP 1: Make sense of problems and persevere in solving them is…

The setting of Plato’s Euthyphro took place with a discussion between Socrates and Euthyphro which concerned the definition of Piety. This was an interest to Socrates for which he was being charged for impiety and facing a trail at the Athenian court to determine his innocence for the crimes he was accused for. Socrates wasn’t sure if the Athenian people actually knew what piety and impiety was. For this reason, Socrates asked Euthyphro “What is piety?” Euthyphro is arrogant and so his…

This method is a way of discovery by forming an idea and proving or disproving it. One important aspect though, is that the proof must be repeatable. Miracles, according to Hume, have no proof, because they do not have enough uniform experiences. This means that not enough people have observed miracles, to validate their existence. He claims that “a miracle is a violation of the laws of nature” (p 771). He…

The ancient Greeks have made many new advances in their lifetime. The ancient Greek culture has influenced many other cultures as well. Other cultures saw how well the Greeks were doing and wanted to share the wealth. They would take concepts of the Greeks and form it into their own. The Romans took concepts from the Greek such as the Greek gods; Romans made the Greek gods’ names into Roman names. The ancient Greeks contributed to the advances and discoveries in education, architecture and…

simply not know whether or not that there is an intelligent creator, and the universe could create itself through nothingness. Then again, it is impossible to know whether or not that the universe did create itself from the void. The cosmological proof is a both a valid and invalid argument in many ways. It is a valid argument for those who want to believe, and an invalid argument for those who are more dubious and…

Ramanujan’s main contribution in mathematics discusses on mainly in the analytic also game theory and infinite series. He made many in depth analytics in order for the aim to solve various mathematical problems by bringing to light new and novel ideas that gave impetus to progress of game theory. He was such a mathematical genius that he discovered his own theorems of different kinds. Ramanujan stands upright most of the time, he is one of the greatest minds who ever been born on Earth. in…

When we think of the mathematical disciplines learned in high school, algebra typically reigns supreme. We use algebra to explain geometric concepts, usually the geometry element in the process. This was never more evident than our discussion in class about completing the square…

were discovered, neither did their applications fail to hold. Therefore, mathematics is both abstract and absolutely consistent. In addition to math being the underlying description of everything, it is also a discipline of logical thinking. The proofs of even the most basic theorems are completely logical, and the solving of math exercises follows logical steps to obtain the answer. This logical requirement necessarily verifies the consistency of math since all theorems must be proved, and…