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The Intersection of Mathematics, Philosophy, and Real-World Applications

Explore how mathematics shapes our understanding of the world through philosophical lenses. This course examines the application of functions to model real-life problems, project trends in finances and populations, and analyze data. Delve into how great thinkers like Plato, Descartes, Kant, and Einstein used mathematical concepts to affect their philosophical inquiries, culminating in practical examples such as the geometric proof behind the Declaration of Independence and the revolutionary ideas of non-Euclidean geometry in general relativity.

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The Intersection of Mathematics, Philosophy, and Real-World Applications

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Presentation Transcript

  1. Seeing Math in the World

  2. Application • Use functions to model real-life problems • Project trends based on models • Finances • Population • Data analysis

  3. Habits of Mind • Breaking big problems into steps • Justifying choices • Mathematic theorems originally used to understand the world

  4. Proof • Thomas Jefferson modeled the composition of the Declaration of Independence on a geometric proof; which makes it so powerful. • Albert Einstein’s theory of general relativity used non-Euclidean geometry to prove that the path of a ray of light, in the presence of a gravitational field, is not straight but curved. • Course Description: Mathematics, Philosophy, and the "Real World“ http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=1440

  5. Views shaped by math • human nature • religion • truth • space and time

  6. Key Philosophers • Plato: Flourishing in the 4th century B.C.E., Plato was inspired by geometry to argue that reality resides in a perfect world of Forms accessible only to the intellect—just like the ideal circles, triangles, and other shapes that seem to exist only in the mind. • Descartes: Writing in the 17th century, René Descartes used geometric reasoning in a systematic search for all possible truths. In a famous exercise, he doubted everything until he arrived at an irrefutable fact: "I think, therefore I am." • Kant: A century after Descartes, Immanuel Kant argued that metaphysics was possible by showing its kinship with mathematics. The perfection of Euclidean geometry led him to take for granted that space has to be Euclidean. • Einstein: Working in the early 20th century with a concept of "straight lines" that was different from Euclid's, Albert Einstein showed that gravity is a geometric property of non-Euclidean space, which is an essential idea of his general theory of relativity.

  7. My Project • Video/song that inspired me. • Driving questions: • How do I surround myself with positive things? • How do I contribute positive things to the world around me?

  8. How do you surround your self with positive things?

  9. How do you contribute positive things to the world?

  10. Connection to Parent Functions and Transformations

  11. Product • Symbolism • Medium explained

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