another prime problem

Last weekend I wrote about Goldbach’s conjecture which involved the sums of prime numbers. Keeping with the theme of easy-to-state-number-theory-problems, I decided to mention the Twin Prime Conjecture this week.

We call a prime number a twin prime if you can reach another prime by either adding or subtracting 2. For example: 3 + 2 = 5, 13 – 2 = 11.

The conjecture is that there are an infinite number of twin primes. (We know there are an infinite number of primes.) Computers have been used to calculate twin primes which are very large (5,000+ digits) but it will take more than pure calculation to solve this conjecture…

memories and inspiration.

In highschool I had an old computer in my room. It was my journal for two years. Sure, I used it for other things – assignments, photos – but its primary function in my life was as a journal. It held my alternately miserable and optimistic poetry, detailed stories of “what happened at school today” and many pages of me trying to work out how I felt about things. Mostly boys.

I no longer have that computer. I saved some of the most interesting bits onto my laptop when I first changed computers and then, after a while, I deleted those too. They had too much emotion in them. They kept me holding onto a past that no longer existed. Every now and then I wish I could read them and laugh at myself and feel sad over old things but I know that, at the time, I needed to delete them to move on.

I’ve always kept journals in fits and bursts. I can’t count the number of notepads that have been, at one point or another, my diary. I’ve thrown out most of them and left the rest in Adelaide. I have a habit of starting them, keeping them regularly for a while, and then leaving them for months at a time. I used to think this was a failing on my part – a lack of commitment – and then one day I woke up and realised that it wasn’t.

I write as long as it is still good and fun and useful and doesn’t feel like a chore. I keep diaries when I need to think outside of my mind, when I’m having trouble keeping track or I’m scared of forgetting something. I keep diaries to help me make important decisions or to note when something feels so important that I don’t ever want to forget it. When I have my eureka moments, when I see something tragic… and so on. They serve their purpose and then I abandon them.

Now that I have decided to be a writer of stories – rather than a recorder and analyser of events – I sometimes wish that I had kept more of those records. I wonder how important our memories are. I wonder if it’s important to remember things correctly. I wonder if keeping all those old memories and emotions would have been an asset to my writing. I wonder if they would have been a detriment to my life.

Tell me, are you a hoarder of memories in physical form or do you let your brain sift through them as it will?

2nd draft woes: endings.

I have chopped and changed and rearranged my novel and now I’m feeling almost happy with it. There’s just one problem: the ending. I knew it wasn’t that great as I was writing it and now it’s even worse. I don’t know whether I’d be better off writing one really beautiful paragraph and leaving it open ended or writing an extra three chapters so that the ending in my head is another mini-adventure. Perhaps I need to throw out the ending in my head and try to think of a new ending that fits better. One thing’s for sure and that is that what I have is not good enough.

Fortunately I don’t think I’m alone because, as smirk inducing as this comparison is, Terry Pratchett‘s Discworld novels never seem to me that they end quite as well as they begin and continue.

So does anyone out there have any stories of endings gone wrong? Or methods for writing endings? Or examples of great endings? let me know.

Research in mathematics?

I am asked, regularly, how there can still be things to research in maths. How can there be new maths? Two is still two, right? What could there possibly be to discover?

So, for those of you who wonder how the career “mathematician” still exists, or what I could possibly spend three years researching, I have decided to create a weekly feature of famous unsolved mathematical problems/current research in mathematics.

The first thing that jumps to my mind is Goldbach’s Conjecture. Goldbach conjectured*¬† in the 1700s that any positive even number (>2) is equal to the sum of two primes. This is easy to see for the first few examples: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5 and so on. Using the amazing powers of computers we know that this conjecture is true up to ridiculously high numbers. But no one has ever proved that it must always be true.

This is such a great problem because it can be understood by anyone who knows what a prime is but it’s obviously incredibly difficult to solve.

Personal note: I was set this question as ‘homework’ by the head of the Adelaide Uni Maths Society a few years ago. He knew that it was a famous unsolved conjecture but I did not. I spent several hours trying to solve it but was sadly unsuccessful. My dad laughed when I told him what I was working on. He knew what it was too. Now you all know and can set the problem for your mathematically inclined friends.

*Actually he conjectured some very similar things, one of which turns out to be equivalent. Go look it up on wikipedia.