what’s up with the phd?

I don’t post about my work much for a whole lot of reasons (the main one being that I’d rather talk about the actual content but you really need an undergraduate degree in maths for that to be interesting reading) but today I thought I’d break that streak a little bit. I’m nearly half way through, so why not?

  • That’s the main scary thing: being nearly half way through. I feel like I haven’t learnt a lot, and haven’t done very much, but when I look back at who I was and what I knew at the start, I know my feelings lie to me.
  • Knowing that my feelings lie to me has probably been essential in not quitting. Moving interstate helped too. Something’s got to be pretty horrible for you to quit after dragging your husband halfway across the country.
  • I’m having a good week. That needs to be said when it happens because so often I forget that any good weeks happen.
  • I am still struggling to work out what the point of my phd is, where the research is going, but I have more of an idea now and I’m less worried about the fact that I don’t know the things I don’t know.
  • I’m looking forward to this year of research. After that I guess it will mostly be panic and writing but this year is looking interesting.

Yeah that’s all for now. I just like to remind the blog part of myself that she is doing this whole phd thing.

I’ve been away

I went to Sydney for a maths conference.
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And then to Brisbane for a wedding.
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I returned to Perth and then headed off to Adelaide for Christmas almost immediately.
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It’s been pretty crazy in my head lately. There’s been so much going on, so many things to do, places to be and people to see. All of it was great but also tiring and today we returned home to 40C, a car with a coolant leak and an air conditioner that is out of action. The photos make the present a little easier and I’m hoping for some relaxation on the horizon.

I’ll be back in a few days with NY resolutions, something I am newly keen on.

Young Writers Prize

I did not make the shortlist and I must be getting thicker skin because that doesn’t bother me too much. I know my work has improved significantly since I sent it to them and I knew from the start that my topic was a bit too Australian to translate well internationally. I am obviously disappointed but it is safe to say that my world is not ending.

In other news, I gave my talk at Combinatorics12 this afternoon. It went well. I have ideas to investigate and a conference dinner to attend.

Life is good.

Italy in summer.

The beauty of Italy in summer took me a little while to see. Everything was dingier and more ordinary than photography books had led me to expect. Yes there are incredible cobble-stoned, tiny alleyways but they are lined with garbage bags. Yes there are hundreds of white houses in the cities but they don’t have grass like nice houses in Australia: just dust and tiles. Yes there are lots of old buildings but they are dirty and falling apart.

It didn’t help that I was exhausted from 17 hours of flying. It didn’t help that I’m not really a fan of crowds. It didn’t help that it’s just plain hot. Once I got a good sleep and really looked around I realised that this place is incredible after all.

The beaches are warm, maths is going well, the food is beyond exceptional and most days I wander around barefoot. (This house has grass because it’s out of the city.)

Love from Ischia.

the four colour theorem

How many colours does it take to colour a map? The title probably gives you a hint.

When I was a kid (no, I don’t know how old exactly… around 10), my dad set me and my brothers a challenge. Could we create a map which required more than four colours to colour it in? Here are the rules:

– no two adjacent “countries” can have the same colour,
– if two “countries” meet only in a point then they are not adjacent, and
– each “country” must be completely connected (Alaska, for instance, couldn’t count as part of the USA)

At the time I had no idea that this was a world famous mathematical concept, I just thought it was a frustrating problem. We didn’t find a map requiring 5 colours and, indeed, we couldn’t have. It was proved in 1976 that 4 is the maximum number of colours needed and, importantly, it was proved by using a computer.

In 1976 this was revolutionary, groundbreaking and contentious. Lots of mathematicians refused to accept the proof because it couldn’t be checked by hand. It has since been proven by a computer program we know to be reliable but it was a point of argument among mathematicians for many years.

 

stage fright? not me.

I like a big stage. I love to perform and my favourite way to experience a crowd is from the stage. But there are times that I have trouble with speaking in front of people and I’ve been called shy more than once. I get nervous when I’m not given time to prepare or when something is so casual that I’m not even expected to have prepared for it.  In middle school the idea of being in a conversation with five people was incredibly stressful. I was always stuck for things to say and terrified I would say the wrong thing. Speaking in front of the whole school would have been a much easier task. It could be the adrenalin of the situation, or maybe it’s that you don’t need to make eye contact with anyone, but there is definitely something about being on stage.

I’m going to be travelling to Europe soon and, while there, presenting my work at two separate conferences. The actual presenting-the-work aspect does not worry me at all and even if they ask me questions after the talk I think will cope. However if they ask me questions over dinner I suspect I will get very nervous.

I know I will need to constantly remind myself to stop, breathe, and remember that one person’s opinion of my opinions will not destroy my life.

a change of area

The last two weeks I’ve discussed fairly simple (to understand) mathematical problems which were both relating to prime numbers. I don’t want to give the impression that number theory is all there is to do in maths so today I thought I’d talk about something completely different…

The brain!

Yes, the brain. Specifically how it transmits information. About this time last year I was finishing off my honours year. One of the coolest things about honours is that everyone does different projects. We were all working in the same room, and discussing our work, but there was pretty much no crossover between research areas. So anyway, one of my friends was studying the neuron firings of the brain.

How do you study that? What is there to do? Well, in the world at the moment we have a lot of data. We record a lot of things without knowing what they mean. The world of mathematical modelling is about finding the mathematical equations that govern the things we have measured.

Mathematical modelling often ties into other subject areas like biology and physics.

Equations are about plugging some facts in and receiving another fact out (that is, describing the relationship between two or more things, if you’re being fussy). To find out your average speed on a trip you plug in the variables of distance and time taken. With the neuron firing of the brain you plug in physical factors like the current in the brain and the action of other neurons.

As I was writing that last sentence I felt like a fraud. I have no idea what those things really mean. That’s the crazy thing about it all. I could probably understand the equations and even work with them (at a stretch!) but I have no idea about the biology behind them.

But this stuff is really cool. Why are we still researching it? Because we don’t have a perfect equation, like we do for average speed, yet. We have approximate models that are improving – that is they are getting closer to the measured data – but none accurately represent what’s going on.

And I think it’s pretty cool that there are people researching the mathematical equations behind how our brain transmits information…

NB: This stuff is too complicated to really get into the details of it but if you’re interested in mathematical modelling then click here, and if you’re particularly interested in modelling the neuron firing of the brain then you probably know more about it than I do but here is a link anyhow

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…

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.