Philosophy of mathematics

In his Meditations on First Philosophy, Rene Descartes proposes the argument: “Nothing further now remains but to inquire whether material things exist. And certainly I at least know that these may exist insofar as they are considered as the objects of pure mathematics, since in this aspect I perceive them clearly and distinctly” (451) Essentially Descartes is putting forth the assertion that only the mathematical characteristics of objects can be clearly and distinctly perceived as being manifest of the true nature of them. The first premise of his claim is that I can infer mathematical qualities exhibited by objects are existent due to our systematic and regular perception and I cannot conclude that the non-mathematical properties I perceive…

Descartes’ journey through the realm of his mind and his internal exploration of all the things he previously thought to be certainly true, brings him to the subject of the existence of God in his Third Meditation. Before he touches on the existence of God, he concludes that there are three different types of ideas. There are fictional and adventitious ideas which Descartes’ creates on his own and finally there are innate ideas which are present in the mind at birth. With these types of ideas in…

Astronomy was particularly important to the Greek because it helped them understand the forces of life both practical and theoretical, and Ptolemy helped the Greeks with some progress of the universe around them. Since this was a long period of time ago they didn't have the intelligence advancement as we do now, so with the help of mathematics, science, and astronomy, Ptolemy helped try to explain what the Greeks couldn't. Astronomy became important to the Greeks because Ptolemy taught the…

one of the first women to make many contributions to mathematics. In this essay, I will be discussing her life and contributions to mathematics. Maria Gaetana Agnesi was born on May 16, 1718 in Milan, Italy. She had a very wealthy family, who in turn gave her the best tutors. While at a young age, she had learned 5 different languages. Growing up, Agnesi's father was proud of her wealth, so he would invite over intellectual people to debate with his daughter. She had to debate and give…

Mathematicians have been around for centuries. They have contributed great amounts of knowledge to the world. A mathematician is a person who excels or is an expert in mathematics. One specific mathematician that brought great ideas into the world was Gottfried Leibniz. He contributed a lot to mathematics, science, physics, philosophy and even his local government. Mathematicians are very important because without them we would not have many important theories that explain why certain things…

My intention to study Mathematics stems from my appreciation of the complexity and variety of the different branches which the subject encompasses. In my academic career I have particularly enjoyed the challenge of Further Mathematics, as many skills and disciplines are collated to reach a final and satisfying conclusion. Continuing my studies at Newcastle would give me the opportunity to diversify my knowledge and continue forming a solid foundation for further problem solving in my career.…

Scientists were now using the newly developed mathematics to describe natural science phenomena. They were no longer limited to forcing their math to fit a preconceived notion, and could now explore things as they were. Hume shows us a changed in the way people accepted new information. They were no longer accepting things on face value, but instead questioning them. They developed a curiosity to prove things for themselves, a notion that is still present today. Even today we still maintain a…

The Life of Leonhard Euler Leonhard Euler was born on April 15, 1707, in Basel, Switzerland. He was the first of six children in a minister's family. His father, Paul Euler, a Protestant preacher, taught young Euler mathematics but wanted him to be a minister. Paul Euler married Margaret Brucker, the daughter of another Protestant minister. He had two younger sisters named Anna Maria and Maria Magdalena (newworldencyclopedia). He died on September 18, 1783 from a cerebral hemorrhage. Euler…

He left his treasure for future generations with his crazy family background. Thanks to his father, Jakab, this astonishing mathematician made a mark in the mathematics world. It is beyond belief how even though his mind was not set of becoming a famous mathematician he became one. It is important to remember to never give up on anything, like George Polya he continued to look for what he loved to do until he found the sparkle he…

Descartes states “on the other hand synthesis, doubtless the method you here ask me to use though it suitably finds a place after analysis in the domain of geometry, nevertheless cannot so conveniently be applied to these metaphysical matters we are discussing” ( 102). Descartes states as clear as water that is there is a vast difference present between Mathematics and Metaphysics in regards to the synthetic approach. Firstly, Descartes points out that the hostility and obscenity present in the…