"One of the serious problems in Chinese mathematics was the absence of rigorous proof. Chinese scientists lacked a standard of logical proof provided by Aristotelian logical and they had no system of deductive geometry. ... Western geometry and optical science books were translated and published in Ming China. ... Scholars pointed out that, despite the very well-developed state of Chinese technology, abstract mathematics was extremely weak - geometry was fragmented and ad-hoc, arithmetics was there but algebra was primitive (partly due to the failure of adopting the system of mathetical ...

• Word Count: 1756
• Approx Pages: 7

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

because of his constant questioning and arguing against anything his professors said that could not be backed up by solid proof? ... Even as a student, he could not tolerate superstition or claims not backed up by proof, preferably mathematical (Levinger 8). ... Unlike his predecessors, he had proof to back up his claims. ... Galileo wrote to him to correct his errors by using simple geometry (Machamer 29). ... He admitted in 1597 (albeit only in a private letter to his German contemporary Johannes Kepler) to his belief in the Copernican doctrine, but said that he would not come forward...

• Word Count: 4135
• Approx Pages: 17
• Grade Level: High School