Hi sparticus;

Mathematics is difficult but too a large degree can be done by the abandonment of total understanding.

In the words of the great John Von Neumann:

In mathematics, you don't understand things. You just get used to them.

If a person discovers that he can do mathematics and hang with the big boys by adopting a simpler idea than rigor and proof then he/she can begin to make progress.

One can do math in the way that scientists do experiments and this simplifies the usage greatly. To be able to play, "spot the pattern" is something that I do all the time. Proof comes later. This approach is gaining in popularity and I am one of its staunchest supporters here, it is called "Experimental Mathematics."

I think this approach is really what mathematics is, not the dry memorization of what theorems Cauchy or Legendre proved.

Using these techniques even if you have no talent, nothing extra going for you, you will do okay just because your approach ala Richard Feynman will be different.

It is not tough for me. But some of my classmates does.

bobbym wrote:

One can do math in the way that scientists do experiments and this simplifies the usage greatly. To be able to play, "spot the pattern" is something that I do all the time. Proof comes later. This approach is gaining in popularity and I am one of its staunchest supporters here, it is called "Experimental Mathematics."

I think this approach is really what mathematics is, not the dry memorization of what theorems Cauchy or Legendre proved.

It is interesting that you mention this.  I have a B.S. in mathematics, and this is the approach that I think was forced to learn in Calculus II (indefinite integration and infinite series).

I have derived the sums of power formulas from scratch, some Bernouilli number equations, and of course I figured out how to solve problems which my instructors and my book couldn't teach me well for courses during my time at school, all of which was by experimentation.

I have created an enormous amount of 4x4x4 Rubik's cube parity algorithms as well, and have explored different "cube theory" topics, but all still experimentation...at least at the beginning.

Once I find some pattern by using experimentation, then the proof/theory comes in (just as you said).  Once I start asking "why" and "how" I got the results that I did with experimentation, then I am already more than familiar with whatever subject matter it is that I am working on enough to beginning formalizing a theory.  Proofs are very useful because they give you no doubt that you aren't missing any details, but you first need to know the details (through experimentation) before you can even can talk about them and draw conclusions.  This is of course when you explore new unknown territory and have no choice but to experiment to see how something ticks.

But the questions of "why" and "how" also feed the experimentation process as well.  So I guess if you have a curious mind (and a stubborn one), then that attitude will give you the passion to drive you through experimentation and then to make intelligent conclusions about your experiments.