The Italian-American mathematican, Juan Carlos Rota (1932-1999) wrote … We often hear that mathematics consists mainly of “proving theorems.” Is a writer’s job mainly that of “writing sentences?” Mathematics is much, much more than just dealing with theorems.
Having said that, just as a good writer knows how to craft his/her sentences, a good mathematican builds their understanding on theorems. Theorems are the firm foundations, the principles upon which the rest of mathematics is built. Everything that we ‘know’ and every skill that we use in mathematics has been analysed and proven by someone … from the very mundane and practical to the amazingly abstract and beautiful.
Why does 1 + 1 = 2? Well, we know it does … but why? Such thoughts are not trivial. Entire books have been written about such matters. The great British astrophysicist, Sir Arthur Eddington (1882 – 1944), wryly observed, “We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about ‘and.’”
The image to the left is of Euclid’s proof of Pythagoras’ Theorem in Greek. In his day, all the Greek would have been written in capital letters and run together, but the text used here is easier to read. Why did I choose this image? Simply because Pythagoras’ Theorem is one of the most famous theorems of mathematics. Also, the fact that you can see it in its Greek form underscores the fact that mathematics is a discipline that transcends cultures and times. I found the image on a most marvellous site designed by J B Calvert called Reading Euclid. Let me encourage you to browse this site and learn something of the Greek (language) from which our geometry came. What J B Calvert shares about Pythagoras’ Theorem is fascinating!
Sadly, I could not find out how to contact him for permission to use this image (and his site was last revised on 16 June 2002) … but I hope he doesn’t mind.
I recently read that mathematicans today are expanding the numerous branches of mathematics at something like 250,000 published theorems per year! Obviously, no one can keep up with such rapid development. I certainly will not try. All you will see here are some key historical theorems presented and discussed … as I am able to add them.
Brilliant!!! This helps so much!!! So much easier than anything else I have found. This is now simple.
Thanks again for showing the simple way of doing this. I look forward to the next video!! Absolutely brilliant.
Once again, excellent! I’ve watched many others, that have not helped nearly as much as these. Thanks for making it so easy to understand. When things get complicated, it is easy to make a mistake, but your method of writing down the structure helps to prevent mistakes.
Thanks a million!!! I’ve watched many videos and read tutorials, but still could not get two in a row correct on Khan Academy. Your explanation was so clear and simple that it finally made sense to me and now I can get all of the problems correct!!! Thank you very much.
It all makes total sense now! Thanks very much for all the derivative videos!!! Very helpful.
MemorizeAndLearn (on four different CCM YouTube videos about Differentiation)
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