Four is awesome two. 2+2 as well as 2*2.
Tough problem. Finding numbers like that is actually a problem about elliptic curves, which have a lot of deep mathematics surrounding them. These are elliptic curves because you can write them in the form y^2=x^3+ax+b:
391=17*23 which makes it a semiprime.
Hmm...I went to verify my second solution and I got a strange result. All of my other solutions seem to give me 0 (not 2) when I go to take the difference. This is quite odd. My code looks like this:
So yeah I think you're probably right.
My guess is people hate math because they have never been introduced to playing with it. Instead school larning has forced kids to learn boring rules against their will. If one misses one day of learning it's likely to set one behind and from there on in things can get worse and worse.
Advanced math is just the other way around, frankly.
Practical math such as engineers and statistical people use requires and provides answers. "Pure mathematics" is different. It is the exploration of patterns, possibilities and the unknown. We don't know what is true, what can be put together in a pattern. Things are suspected and the idea is to prove them true or false or pull them together in a new structure. We just don't know. Graduate math is required (for new stuff but there is plenty of known stuff) unless you happen to be a genius and I don't think there are any more of those:
I did math only from books and the professor. Can you display some of those wikipedia sites? I'm curious to know where your are at or even if you're doing math.
You don't need to understand most of what is called "pure mathematics" to understand physics. Off the top of my head you need algebra, trig, calculus, linear algebra, and differential equations. Fourier analysis, numerical analysis, and prob/stat would be huge pluses. Abstract algebra, topology, and tensor analysis all might have uses. Those first few are definitely necessary, though (linear algebra is probably the only one of those that is made optional in a lot of physics curricula, which to me is really, really stupid, because it is used so much.)
I'mProbablyanINTP also and I tend to be all over this forum but not everywhere. This is the sucking math thread. When I asked for your wikipedia sights I thought they were for sucking up math. Your list reminds me of this book I had where the guy was telling his story of reading the Encyclopedia Britannica. I think I got through his experience up to the D's and then I had to give up. There was nothing to pull it all together.
Well I think because there is more than one way to enjoy something. The ability to freely play around with something is only one. History could be the stories or the explaining where the present came from. English the stories or anything. You tell me.
Well I think because there is more than one way to enjoy something. The ability to freely play around with something is only one. History could be the stories or the explaining where the present came from. English the stories or anything. You tell me.
Sorry Lobstrich. I'm waiting too. Can't recall. My mother used to say, "If you can't remember it, must not have been important."
Eh...not quite. There are mathematical concepts that take some effort to be reduced back down to real things, and then there are things in physics and chemistry that still don't have mathematical treatment. For example, the divergence theorem in multivariable calculus has a physical manifestation in Gauss's Law in electromagnetism. This isn't all that obvious at first, and the existence of this universal constant epsilon naught is also not that obvious. For another example, there are plenty of things that are very poorly understood in chemistry. Lots of reactions are well known and documented and their mechanisms are completely unknown.
