Exploring Math: Learning from the Originals vs. Modern Interpretations

[Howers]

I am wondering, is it worth studying math from the original papers as a means to learn a subject? What I am worried about is that some of the methods used to justify results is out dated, or even worse incorrect.

As an example, consider Conics. Should I attempt to learn the material by reading the original work as written by Appollonius via translation, or learn it from a modern book that makes refrence to analytic geometry?

I have read Euclid's work, and it contains some of the most beautiful mathematics I have ever read... even if the number theory is out dated. To my knowledge, most of Euclid's methods seem rigorous with few exceptions. At the same time, Newtons Principa is said to be out dated and primitive, and learning it would be a waste of time. Is this true of all original work? I am interested in Greek math in particular.

 

[Defennder]

Wouldn't the notation employed by the original authors be difficult to get used to? Try reading Newton's calculus for example. Why not find some modern classic textbooks?

 

[will.c]

The original texts are always a lot of fun and extremely interesting to read... but to learn from?

I heard an astronomy professor joke that he knew more about General Relativity than Einstein ever would, and I had a laugh, but his point was well made. It's not even a matter of notation, but of paradigm. As we discover more about any topic, we are better able to see the dead branches and trim them away. You won't be a better mathematician by learning from the "source;" in fact, the source is kind of an illusion. Once new mathematics is discovered, it's everyones. If someone can expose it better than the discoverer (often the case, imo) so much the better.

 

[jimvoit]

My opinion: Focus on the most modern exposition available, and when you have time, use the historical material as background information to augment your understanding of the subject. Then you will be better able to communicate your ideas to your contemporaries, who may be applied math types.

 

[chroot]

It'd be essentially impossible to learn from the original texts. The math has been reviewed, studied, rewritten, and expressed in new, better notation so many times that new treatments are inarguably easier to learn from.

- Warren

 

[tiny-tim]

Appollonius

As an example, consider Conics. Should I attempt to learn the material by reading the original work as written by Appollonius via translation, or learn it from a modern book that makes refrence to analytic geometry?

Hi Howers!

Yes, it is more beautiful than analytic geometry!

And the notation is more-or less modern (unlike in Newton's Principia ).

(But is it as useful? Depends what you want to use it for! )

There's a good Britannica Encyclopedia great-books-of-the-world translation of Appollonius.

I also suggest Hilbert's rather old book (I forget the name).

Yeah … go for it!

 

[TMFKAN64]

When I took undergrad electrodynamics, our professor had us read a few of Einstein's original relativity papers, translated from the German.

Let me tell you, manipulating Maxwell's equations without using modern vector calculus notation is downright *painful*!

I think it was still worthwhile, but don't underestimate the value of more modern notation!