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morphism
#5
Jun10-07, 09:37 PM
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Quote Quote by Dr. Proof View Post
I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?
The view that mathematics is created purely for some "real-world application" is short-sighted, in my opinion. While it is true that a lot of good mathematics was created to solve "real-world" problems, sometimes we can reap great rewards by ditching "reality" and generalizing and focusing on the ideas instead of the applications. Incidentally, such pursuits might actually give rise to more fascinating applications down the road. For a famous example, think about how differential geometry started out, and what Einstein did with it decades later.

I could go on, but instead I'll direct you to a series of videos where Cambridge Fields medalist Timothy Gowers shares his opinion:
http://www.youtube.com/watch?v=BsIJN4YMZZo (Part 1)
http://www.youtube.com/watch?v=NyqiEMilyns (Part 2)
http://www.youtube.com/watch?v=bVgoHb73i7U (Part 3)
http://www.youtube.com/watch?v=FszlWrvyxPc (Part 4)
http://www.youtube.com/watch?v=gjA8S82Q810 (Part 5)
http://www.youtube.com/watch?v=4ivoaFLQ4vM (Part 6)
http://www.youtube.com/watch?v=NnXiCwI78wY (Part 7)
http://www.youtube.com/watch?v=xRfVYpaGtvQ (Part 8)

Enjoy!