Saturday, August 18, 2007

 

JSH: Looking back, wondering

Wow, I didn't know the solution to the factoring problem would turn out to be that simple.

It seems strange to think back over the years since I first started looking at factoring one number by using another and consider all the failed approaches and all the other, with the actual solution now in hand.

But I got this feeling before with the proof of Fermat's Last Theorem and with the prime counting function, though I must admit this answer is the most succinct, the most definitive and probably the simplest result I have yet.

So why didn't some other person figure it out before?

That question is one that comes up time and time again, and growing up I would get amazed when I'd learn something like trigonometry or basic calculus and realized how easy it was and you wonder about why it took so long for people to figure it out.

Or ranging further, the Romans were playing with steam over two thousand years ago and even built simple devices that were novelties demonstrating steam power, but didn't figure out a steam engine.

If they had history would have changed. We might be in interstellar spacecraft today.

They had a mechanical computer as well and Archimedes had quite a bit of calculus which was mostly lost to be re-discovered much later by Leibniz and Newton.

With several major discoveries now under my belt I find myself thinking about history in different ways and I have a different perspective now on what it takes to make a major discovery and what it takes for it to be accepted where of course the big story here has been the successful fight by mainstream mathematicians to ignore my other discoveries.

There is that amazing difference between wanting to be something and actually being it, where I see most modern mathematicians as playing pretend, which is why they picked factoring anyway because they lacked the mathematical intuition that said a simple solution probably did exist.

Oh yeah, so it is amazing all the machinery and effort done around factoring, when people just didn't know how to do it.

Students who learn about the factoring problem in the future with the simple answer presented, say, in some textbook will not have the perspective many of you have had with BELIEVING it was a hard problem (many of you probably still believe it at this point with the solution only hours old) so it will be remarkable to see how they try to understand how it could have been such a big deal.

With so many mathematical questions now answered from FLT, to what I've learned with primes which cover the Twin Primes Conjecture and the Goldbach Conjecture, where I guess I haven't really bothered with going in detail with the Riemann Hypothesis because it doesn't interest me (I think it's false), there is an odd kind of closing of the door on the discipline of mathematics as it was.

Given that I have also presented the definition of mathematical proof and united mathematics and logic in doing so, as well as discovered the object ring, it is clear that a door to mathematical discoveries that were impossible before has been opened and with that a door to science that could never have been learned is now open as well.

I have joked about mathematicians ignoring my research maybe being aliens trying to destroy the future of humanity, but there is something to looking at it from that perspective as without the mathematics there is no way to get the science and no way to push technology into areas that seem like fantasy today.

After all to even Newton flying was a thing of fantasy. And going to the moon could only be imagined in dreams.

Our world today may be as primitive to a near future now possible because of crucial mathematical advances as Newton's was to us and could Newton have ever dreamed of our modern world?





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