Many philosophers made up information in order to try and prove their theories, but this did not work since there was no proof. ... This is still used in schools and geometry classes around the world to this day. ... They expanded upon the fundamentals of calculus and geometry and taught their discoveries to others. ...

• Word Count: 1375
• Approx Pages: 6
• Has Bibliography

Sciences as such geometry and mathematics are certain and indubitable for Descartes. ... What about mathematical proofs and geometric theorems? ... He is saying that spiritual people search for miracles from the heavens when there is a definite miracle present in the form of their overwhelming faith in something that has no concrete proof of existence. ...

• Word Count: 1541
• Approx Pages: 6
• Has Bibliography
• Grade Level: Undergraduate