All posts by Paula Rowińska

I'm a PhD student of Mathematics of Planet Earth CDT, based at Imperial College London. My research focuses the impact of renewables on electricity prices. I'm doing my best to explain maths and climate science to non-scientists, so if you get lost, it's definitely my fault. Please don't hesitate to contact me!

Let’s make Earth great again

When in November 2016 Americans played their trump card, climate scientists faced a new challenge: how to persuade conservatives to start caring about our planet? Even though this task seems to be hopeless, research is being done – and I recently came across some very interesting results.

Researchers from Cologne discovered that conservatives are more likely to act against climate change when the problem is presented with reference to the past, as opposed to the future. We usually focus on future degradation of the environment, which doesn’t appeal to them. However, conservatives tend to be more concerned about the global warming, when we point out that the planet isn’t as “great” as it used to be.

German sociologists conducted a series of experiments on self-identified liberals and conservatives. As a part of the study participants were asked to donate money to one of two fictitious environmental charities: the one preventing future degradation or the one striving to restore the past state of the Earth. In all experiments conservatives were more likely to support the second organisation.

Does it solve our problem? Of course it doesn’t! Riley Dunlap, a sociologists from Oklahoma State University, commented on this study: “If you’re a good conservative, you need to be a climate change sceptic. Global warming has joined God, guns, gays, abortion and taxes. It’s part of that ideology.”

Even though sadly I must agree with Dunlap, I also believe that we should study ways of communicating climate change effectively to various social groups. One size doesn’t fit all – but we can find a good approach for many. If someone is blind in his or her scepticism, we probably can’t do much. However, I believe that with new communication methods we can persuade many people, who are ready to at least listen.

To make Earth great again.

Source: https://paularowinska.wordpress.com/2017/04/12/lets-make-earth-great-again/

 

Money blowing in the wind

I bet you’re not looking forward to receiving your monthly electricity bills. Can you predict how much you’ll be charged this time? Short answer: assume that more than you’d be willing to pay. Long answer: spend a couple of years studying how electricity prices evolve in time. Yes, that’s exactly what my PhD is about.

Power markets are surprisingly complicated. Trading energy is a relatively new idea, increasingly important because of the gradual liberalisation of the EU electricity industry. Not only do market rules in various countries differ significantly, but relevant laws change frequently. Therefore if you’re interested in any details, please don’t rely solely on my article, but refer to the website of the appropriate market (eg. European Power Exchange).

From the mathematical point of view, modelling any financial processes is an extremely difficult task. Stock values change in unpredictable ways, they also strongly depend on political events and human behaviour. Because of that, financial mathematics attracts increasing numbers of mathematicians with different backgrounds. Actually, not only mathematicians. For example, a building block for many financial models is a so-called Brownian motion, first used by physicists to describe chaotic movement of particles. The tools we can use are limited only by our imagination!

Energy markets are problematic, as they behave differently than traditional stock exchanges, so we have to come up with completely new ideas to model them. The main difference is that the supply and demand for electricity must always match. Storing electricity is almost impossible, in the best case very expensive, so we cannot produce (or buy) more and leave it for later. On the other hand, the supply is inelastic, because industry and citizens require a specific amount of power for their regular activities. You don’t like blackouts, do you? And they happen exactly as a result of a significant imbalance in the energy market.

Thankfully many people work very hard (this is how I like to think about myself) to make sure that you don’t have to dig out these candles too often. Mathematical models help producers decide how much energy to generate and traders to buy and sell its appropriate amounts. Most of trading takes place in electricity markets.

Two main types of contracts are traded. First, spot contracts (traded at noon) oblige producers to deliver a specified amount of energy for 24 hours, from midnight of the following day. Second, one can also trade futures contracts for a specified delivery period: a week, a month or a year. For example, if a producer signs a “2 months ahead” contract today (June 2017), she or he would have to deliver the electricity between 01/08/2017 and 31/08/2017.

However, predicting the prices so far in the future is a difficult task. We don’t know the general state of economy or if Donald T. decides to build a *huge* bridge from New York to the Moon (which would require a lot of power, I guess). And, what interests me most, what the weather will be.

Weather conditions significantly influence electricity prices, both the demand and supply. In countries like the UK or Germany, in general the demand is higher in cold months, when we need to heat our houses and offices, as well as use more light due to shorter days. In warmer places, also in the summer a lot of energy is needed for air-conditioning. On the other hand, renewable energy production strongly relies on the weather. We can’t generate wind energy without wind!

This is why in my models I have to take into account weather forecasts. As you know, they’re pretty useless a few weeks in advance, not to mention a few years. Therefore the models need to account for uncertainty related to these forecasts.

You might wonder if these factors really matter. They actually do! Now many markets even allow the prices to be negative, which means that we get paid for the electricity usage. It happens rather rarely, so you won’t even notice. However, it’s interesting to note that almost all negative prices are observed in early morning hours after a windy night. This means that a high level of wind energy generation, combined with a low demand (most factories are closed at night, we also tend to sleep), can significantly decrease electricity prices.

In other words, the chance for a lower electricity bill is literally blowing in the wind.

Source: https://paularowinska.wordpress.com/2017/06/11/money-blowing-in-the-wind/

A tale of a statistician without an umbrella

You should have seen our office today – our cycle to work resembled swimming rather than biking, so wet clothes were hanging everywhere. Well, I can blame only myself, since a normal human being would assume that 98% probability of rain means “it WILL rain, take a bus”. However, being an incurable optimist, I counted on these 2%. In the end, improbable things happen a lot, as Jordan Ellenberg (a mathematician, of course) says. But how improbable was a bit of sunshine in London today? And why on Earth do I try to squeeze some maths even in the weather prediction?!

If you live in the UK, chances are that you begin your day checking your favourite weather app. Based on the information you gained, you know what to wear – unless you’re a proper Briton, then you wear shorts, no matter what, don’t you? Regardless of the website you use, the forecast is probably provided either by Met Office or ECMWF, who constantly compete to produce the most reliable weather prediction in the world. Despite, or maybe because of this rivalry, their forecasts are more and more accurate. So again, why can’t they just get it right, why do they give us percentages?

Weather is chaotic. You might associate chaos with the butterfly effect, a term coined by Edward Lorenz. If you think that it means that a butterfly in Asia can create a tornado in America, then please, please forget this concept; or, even better, read an excellent book by Ian Stewart, Does God Play Dice?, or request an article about it in the comments. The bottom line is that weather forecasting centres will never be able to predict the weather with the accuracy of 100%, no matter how hard they try. Never. Ever.

lorenz
A chaotic system: a slight change in the intial conditions can lead us to a different “wing” (by Computed in Fractint by Wikimol [Public domain], via Wikimedia Commons)
Instead, they calculate their confidence in a particular weather forecast. For example, 98% PoP (probability of precipitation) between 8 am and 11 am in London means that there is 98 in 100 chance that in this period we’ll get at least 0.1 mm of some precipitation. Basically, if you kept going back in time and went for a walk in London today between 8 and 11 one hundred times, twice you would be lucky and came home completely dry.

What?! It doesn’t make any sense! We can’t go back in time! But computers can. Even better, they can look into the future. Because weather is chaotic, small changes in the initial conditions (so the temperature, pressure, clouds etc. in the moment when we start simulations) can lead to big changes in the outcome. This is why Met Office and ECMWF use so-called ensemble forecasting. They run many simulations starting from slightly different conditions and look at their outcomes; it’s a bit like in Groundhog Day, but less creepy. And this means that today I believed in these 2 measly forecasts out of 100 – and that’s why my neighbours asked me if I cycled into the Thames on my way home (not funny).

Learn your probabilities and figure out your chances for a dry day. Or take an umbrella, just in case.

Source: https://paularowinska.wordpress.com/2017/08/09/a-tale-of-a-statistician-without-an-umbrella/

 

One fine day

I finally got a chance to listen to the new album of Sting, one of my favourite artists: “57th and 9th”. By definition, it’s good – Sting has never recorded any unsuccessful songs! But why am I talking about some CD on a blog about maths and climate science?

Because this album contains a single that drew attention of my inner climate activist. In “One Fine Day”  Sting touches on the problem of the climate change. The artist points out at different types of climate sceptics. So we have optimists, histories, apologists and even scientists, who believe there’s not much we can do.

The singer makes an appeal to political leaders to heal the planet quickly. Some say it’s rather wishful thinking but, come on, we’re talking about a song, not an IPCC report! Although “Three penguins and a bear got drowned” part is a bit too cheesy for me to handle.

The lyrics aren’t the best and I know that Sting can do better. I mean, he’s the author of such jewels as “Englishman in New York” or “Fragile”. So why did I get so excited about this particular song? Because people like Sting and listen to him. This is what we need right now: a casual message about the dire issue of climate change, conveyed via a catchy song. I don’t care how people realise that we have a problem, as long as they DO realise is somehow. Buying a new CD is as good a way as any other.

Some criticise Sting for hypocrisy. Well, the truth is that an owner of eight residences scattered all over the world who travels between them on a private jet does contribute to the climate change quite significantly. However, as I stated before: it’s ok not to be perfect. It might be the case that Sting’s popularity will raise awareness of climate change, which can do more good to the planet than his flights to numerous concerts.

I hope we won’t see the times  “when snakes can talk and pigs will fly”. It’s up to us!

Image from MetroLyrics. Article originally posted here: https://paularowinska.wordpress.com/2016/12/20/one-fine-day/.

Think grey

Recently someone told me that they believe in the climate change but are not doing anything to help the planet because they do not want to sacrifice everything. That there are things they could not possibly give up. Conclusion? They might as well change nothing.

To prevent the climate change or at least to reduce its negative impact, we have to work together. In an ideal world, every inhabitant of our planet would change their behaviour and live an environment-friendly existence. However, it is not going to happen. We have too many climate sceptics and people who, while accepting that the climate change is a jeopardy, do not believe it is worth it to worry too much. Their main argument is that next generations will suffer most of the consequences – so why should we care?

Explaining to climate sceptics that they might be wrong is one of my main goals. I am not a psychologist but to my mind the other group will be also very hard to persuade. In this article I will focus mostly on the majority of the society: people who believe in climate problems, would like to change something but do not want to sacrifice their whole life to save the world. Please bear in mind that when I say majority, I base it only on my observations, not any data. Even if I am wrong, it is still a large group that should be targeted.

Where does that black and white thinking come from? Why can’t we accept that we do not have to be perfect? Perfectionism has been researched in numerous psychological studies. Yet, still so many people have to deal with consequences of this character trait in many areas of their lives. Instead of helping us to do an amazing job, it hinders all our efforts. Better is the enemy of good. Even when we are saving the planet.

You might think that we, climate scientists, young researchers who care a lot about the dire situation in which the Earth is now, are doing everything right. It is not exactly true. Yes, we are trying to do what we can – but not more. We are still human beings, with all our flaws.

Remember that we work together. This often means commuting quite far, many times even flying. What can I do about the fact that the conference relevant for my research takes place in Philadelphia? I have to use the plane, no matter how badly I want to avoid it. Because planes are one of the worst enemies of our planet, this is the fact. However, in order to do my research, I need to know about results of other scientists all over the world. In principle we could use video conferencing. And we do but it is far less effective than meeting other researchers in person. Because most of the ideas are created when we talk outside the official conference events.

Some universities tried to introduce travel funds not according to the money one spends on the travel but on the carbon footprint produced by the journey. I hope they will forget about such ideas soon. Yes, we should encourage alternative ways of travelling when they are feasible, for example one can get from London to Paris in a reasonable time by train. However, if one is unlucky enough to have a meeting in the U.S., it is just not fair.

Let us assume that we are already in the meeting. We switch on the lights, the computer, the projector, the air condition… There is coffee and water served in plastic cups. There are biscuits prettily wrapped in plastic bags. Another coffee break, another cup (because I managed to lose mine). And it continues…

These little things are what matters. I am not happy that they happen and I think we should change them. However, I still attend these meetings because I find them valuable for the climate research. Also, in my everyday life I try to waste as little as possible, save electricity etc. I know I could carry a mug with me and use it instead of plastic cups. But you know what? I would rather carry my laptop so that I can do some work on the train. Especially now that I cycle to the train station (no greenhouse gases produced!) and I do not want my backpack to be too heavy.

Later we go to the lunch. I do not remember a meal without any conversation about vegetarianism and its impact on the climate. I believe that reducing the meat consumption is an important part of helping the planet. Veganism is even more environment-friendly. Having said that, I do not think that meat eaters are doing something wrong. Especially when they are aware of how much greenhouse gases are released in the process of meat production and they try to reduce the amount of meat they consume. Cultivating the myth that we have to cut everything out in order to make the positive impact does not help our planet. Of course if we all went vegan, the release of CO2 would decrease but a traditional (in some countries) meat-free Friday has a good impact too. Why would we condemn them people for indulging in a favourite steak once a week? Every little step counts!

When it comes to the actual research, there is no weather and climate prediction without computers. Supercomputers. Super-power-hungry-computers. We cannot forget that every weather prediction releases large amounts of greenhouse gases. Should we then stop doing our research to prevent it? I doubt it would do us any good. Work is being done to develop more effective and less harmful algorithms but the problem will persist.

Can we be fully environment-friendly then? Yes and no. There are people who take it to the extreme. They eat only unprocessed plant-based foods, they live completely waste-free, do not travel, do not use electricity etc. It seems to be doable and if this lifestyle works for them, then it is great, but… I refuse to live like that. I am sure that we can live quite relaxed and pleasant lives and still do not do too much harm to the planet. The point is that we all have to do that. We all have to make some changes, no matter how small they would be.

You do not have to be perfect. If you feel that you can change something, then go for it! Do not beat yourself up for taking a super long shower because it was so pleasant. Do not feel like a failure for using a car when you were too tired to cycle to work. Just think about what you can do to reduce the harm that we, the whole of society, do to the planet. Listen to Paul McCartney: Don’t carry the world upon your shoulders. Do what you can – and enjoy what you do not want to sacrifice.

Article originally published on my personal blog.

Fasten your seat belts!

Recently I was flying back from New York to London and as soon as we took off, I heard the magical phrase: “Please keep your seatbelt fastened during the whole flight. We expect a bumpy ride”. The pilot was right – it was so bad that I couldn’t sleep, watch any movies, not to mention complete any work I had planned to do. To be honest, I was sure we would crash, so I’m happy just because I can write this blog post today.

This adventurous trip reminded me of one of seminars I attended during my first year of Mathematics of Planet Earth program. I should have paid more attention to Dr Paul Williams from the University of Reading, who claimed that due to the climate change we can expect more turbulence while flying over the Atlantic Ocean.

Most of us associate global warming with increased temperatures on the ground. However, as the above mentioned atmospheric scientist reported, it also makes the jet stream even stronger.

According to the Met Office, jet streams are ribbons of strong winds around 9 to 16 km above the Earth’s surface (so right below the tropopause). They move weather systems with the speed of up to 200 mph. The temperature difference between tropical and polar air masses is their main cause. Meteorologists care about jet streams a lot because waves and ripples formed along them can dramatically deepen Atlantic depressions while moving towards Europe.

Jet streams make flights from America to Europe faster than westbound journeys. Indeed, my flight ticket to the USA states that the journey lasted 8 hours 27 minutes while on the way back it took 7 hours 10 minutes. The pilot could have done even better, because the record on this route belongs to Boeing 777 operated by British Airways that in January 2015 landed at Heathrow after 5 hours and 16 minutes. They took advantage of the jet stream that brought heavy rainfalls and winds to the UK.

While jet streams work in favour of passengers travelling to the capital of the UK, they also make flights towards Big Apple longer. Especially because these winds are getting stronger due to the climate change causing increased differences between temperatures of troposphere and stratosphere. The stronger the jet streams become, the shorter the eastbound and the longer the westbound flights. The problem is that quicker journeys from America won’t compensate for the increased flight time against the wind. Williams estimates that each airplane flying over Atlantic will spend extra 2000 hours in the air, which means millions of gallons of jet fuel burnt. This will lead to the emission of 70 million kilograms of carbon dioxide, about as much as annual emission from 7100 average British households. It’s a vicious cycle: climate change causes more carbon dioxide burnt, which causes climate change, which causes…

The increased time spent in the air isn’t the only unfavourable effect of the climate change on aviation. Research shows that passengers should expect more turbulence incidents. Every year hundreds of people suffer injuries due to unexpected “bumps” during the flight. In 2016 videos such as the one taken on the flight from Abu Dhabi to Jakarta went viral. During this flight turbulence was so strong that 31 passengers and crew members had to seek medical help after landing in Indonesia. Such incidents make me think that my flight wasn’t as traumatic as I believed!

Jet stream is one of the common causes of the clear-air turbulence, a turbulence not associated with a cloud. This type of turbulence can be dangerous because radars aren’t able to detect it; this is why it’s usually unexpected not only by passengers, but also by pilots. And Dr Paul Williams with Dr Manoj Joshi (University of East Anglia) pointed out that we have to prepare for more such surprises as the level of carbon dioxide in the atmosphere increases.

Apart from obvious discomfort and dangers, increased turbulence leads also to considerable financial problems. Williams’ report states that airlines spend millions of dollars to repair damage caused by turbulence. Moreover, sometimes airlines have to find longer routes avoiding places notorious for occurring turbulences, which leads to even more money spent and more pollutants emitted. For us, passengers, it means delays as well as longer flights.

So fasten your seat belts – just in case. And have a safe flight!

Image: http://www.nytimes.com/2007/06/12/business/12turbulence.html?_r=0

Article originally published on my personal blog.

Programming is a piece of cake

When I think about famous mathematicians born in previous centuries, I imagine a handsome young man (well, my gender-biased imagination probably confirms the statements from my last article). He is sitting under a blooming tree with a quill and a scroll of parchment covered with equations. I must have lumped together mathematicians and poets, with the romantic charm.

With this image in mind, eighteen-year-old Paula went to her first lecture at the Faculty of Mathematics, Informatics and Mechanics (University of Warsaw). Full of expectations that I would do great things in the field of mathematics, I started copying down the words from the blackboard. “Baking a cake – the algorithm” – this is what they said. Was that a joke? No, just Introduction to Informatics.

You might wonder why such a course was obligatory for first year mathematics students. We just need a pen, a piece of paper and a great mind, right? Not quite. We can stay away from computers if we want to focus on abstract algebra or number theory. However, things get much more complicated if we would prefer to actually apply maths to other sciences. Like to weather prediction.

Lewis Fry Richardson tried to predict the weather on 20 May 1910 by hand. Don’t get me wrong, I admire his attempt, he was one of the pioneers of the weather prediction. Having said that, I am happy that scientists have developed more sophisticated techniques; Richardson failed quite badly.

Other examples? The model I am working on involves simulating the behaviour of population of worms. Without a computer I would have to give up, it is just impossible to calculate by a human being, not to mention more complicated systems, such as climate models.

The world of Four Colour Theorem

Computers even help us prove actual theorems from pure maths, for example the famous Four Colour Theorem. One of versions of this theorem states that any political map can be coloured using only four colours (or even less). The rule is that no bordering countries can have the same colour. The statement is very simple but the only way to prove it was to find all the possible configurations of countries (we are not talking about the existing countries but every map you could draw). I am pretty sure that without computers authors of the proof, Kenneth Appel and Wolfgang Haken, would be still checking all the possibilities.

I hope you understand now why the computers are so essential in mathematicians’ work. But what do they actually do for us and what does the cake mentioned in my first lecture have to do with maths?

Computers are like dogs and programming is just instructing the puppy to sit/stay/stop-stealing-my-favourite-socks-so-that-I-have-to-chase-you. You must know what you are given (input or your dog’s personality) and what you want to achieve (output or yay-I-can-wear-my-lovely-blue-socks). Anything in between is called the algorithm. Believe me or not, you are using algorithms every day. A recipe to bake a cake is one of them. Or your morning routine. When you forget one of the points or switch the order, you might have to eat a slack-baked cake or be late at work. Algorithms structure how we think about the problem.

How do we tell the computer what it is supposed to do? First we need to know in which language we are comfortable communicating. We can learn programming languages in similar way as we learn German or Spanish. The all have specific words, syntax etc. It takes practice to become fluent in one of them. And even if you are almost a native, you still need to consult a dictionary once in a while.

The problem with programming is that the computers are, paradoxically, very stupid. This is my personal view and I hope my laptop won’t take revenge on me for saying this (I still have to finish my project!). Why do I think so? If you confuse words in a foreign language, there are good chances that you will still be understood (unless you ask someone to turn you on, confusing it with turn around, which happened to me once). Computers just take what you give them and do not think. If your code is not working, it is entirely your fault. They will not try to guess what you wanted to do — do not count on their empathy. Life is brutal (and computers definitely are).

The first time you see a code – the instructions for the computer – you might be very surprised. It took me a while to accept that it is ok to write “a=a+1”. It means that we add 1 to a variable called “a”. Although if you accept “taking something with a pinch of salt”, why would you struggle with programming? We do not have to take everything literally!

I definitely think programming is a useful skill to acquire – and an essential one when you are a mathematician or a scientist. It can be hard, it can be exhausting. But trust me, the day when I managed to persuade my computer that I know what I want – and when I got it – was one of the best moments in my life. So keep calm and hello world!

 

When the mathematicians meet…

What’s the difference between an introverted mathematician and an extroverted mathematician? The extrovert looks at the other person’s shoes. You probably have heard this joke (very funny) many times and might believe that mathematicians work stuck in their offices (and their own heads). It was probably true a couple of centuries ago. However, things have changed after the rapid development of maths, especially applied maths. Why?

Nowadays we have to specialise, at least a little bit. We don’t have Da Vinci’s any more; it’s just impossible to fully understand more than your very narrow area. But while mathematics research narrows more and more, it tries to tackle more and more complex and multidisciplinary problems. What do we do now?!

We, as mathematicians, must get out of our comfort zones and collaborate. We need to accept our lack of understanding of certain aspects of each maths problem while, at the same time, being aware of how we can contribute to the solution. We have to identify what kind of experts we need to ask for help to make some progress. This is how it all begins.

When I started my adventure in maths, I certainly didn’t anticipate this. I was prepared for working alone and talking to colleagues only in my free time. While it could possibly work in pure maths, I would totally fail to succeed in applied fields if I tried to do so.

Examples? Mathematics of Planet Earth Centre for Doctoral Training! Yes, we pursue our individual degrees and work on our own projects. However, we operate as a cohort too. Sharing experience, tips and asking for help are essential for this programme to exist. I can’t even count how many times computer science experts saved my life (or at least my precious laptop) by preventing me from running a code that would destroy the system1 . In exchange I could give them a hand when they got lost in abstract multidimensional spaces (although I don’t claim I can visualise anything in more than three dimensions, though it disappoints my first year lecturer!). We all learn from one another.

Recently I realised that it’s not just a fake academic set-up, this is how the “real world mathematics“ works. I spent 5 days at the 116th European Study Group with Industry in Durham, UK (http://www.esgi.org.uk/). This event brought together about hundred mathematicians, physicists and industrial partners. The latter proposed eight problems they wanted to solve in fields as diverse as agriculture, banking and sepsis diagnosis. We divided ourselves into groups according to our interests — I chose the problem proposed by a digital bank. They needed help with marketing their product to the best target audience (of course the ultimate goal was to spend less and earn more). We sat down in a room and…well, and started thinking, talking, brainstorming and arguing. Within 3 days we managed to produce whole models and get some useful results for the industrial partners. Something infeasible for one genius became a reality for a group of people with different backgrounds.

Yes, you might still meet a mathematician staring at her/his own shoes while talking (or avoiding any contact) to you. But this is not a norm anymore. And definitely not the only way to succeed. We can tackle real world problems together because together impossible becomes possible!

  1. Note, not everyone is as lucky as me, you can read what happens when you’re not careful while programming here.

Not “too silly”, not “too girlish” for maths

– “What do you study?”
– “I’m doing PhD in maths.”
– “Wow, you must be so smart! And you’re a girl!”

I hear it so often. I’ve done a small amount of research and my results are sad: my friends studying linguistics, architecture,medicine and so on don’t get such a routine reaction. Why is it the case? Where does the assumption that a mathematician must be smarter than the rest of the society come from? And why are we still surprised that women are capable of pursuing this career path?

I had thought the same before I decided to study mathematics. It shouldn’t be surprising. As a ten-year-old I fell in love with John Nash (or rather Russell Crowe starring in A Beautiful Mind). Than I laughed at how nerdy and out of touch with life the characters of The Big Bang Theory were. Media portrayal of mathematicians didn’t make my decision to study maths easy. Would I become like them? Would I spend my adulthood bending over equations, unable to engage in social life and relationships?

Moreover, I was afraid that I wasn’t smart enough, that one needs a brain of Gauss or Newton to be a mathematician. But I took up the challenge and… I’m still here! Even though my IQ isn’t high enough to join Mensa. Even though I’m a GIRL!

Einstein nailed it: Genius is 1% talent and 99% percent hard work.During my undergraduate studies I’ve seen apparent geniuses being expelled from the university because talent and intelligence aren’t enough. Nobody is born with maths knowledge, it takes years of hard work to gain enough experience  experience to earn a diploma.

I believe that talent is helpful but what counts most is your interest in whatever you’re doing and determination to work hard. Although if you truly enjoy maths, the work might be turn in to fun, as crazy as that sounds. I’m not claiming that I loved every evening spent going through some complicated proofs (especially the ones beginning with the words “It’s obvious that…” – maybe it’s obvious for you, author, but it isn’t for me!). But some problems and ideas were really my thing. I even kept reading about them after the exam!

Ok, but what about the girl part? Is mathematician really a job just for men? Does the gender matter at all? Personally, I get very annoyed when someone admires me for studying maths despite being a female. There’s no correlation between the excellence in mathematical subjects and gender. Neither positive nor negative – I don’t agree with the common statement that girls are more hard-working so they get better results than “smart but lazy” boys.

Unfortunately not everyone agrees. Last year I went to my first mathematical conference. The organiser (male) came to me the day before my talk just to say something along the lines of: You don’t need to worry about your talk. You’re a women, you can’t be as good in mathematics as your male colleagues so nobody expects you to give a good talk. I was shocked! I did well because my research was of good quality, not because of or despite the fact that I’m a woman.

To sum up, if you feel that you like maths (or some parts of it) but are afraid of pursuing the degree because you’re not a genius or (even worse!) you’re a girl, don’t hesitate to give it a try! You have every chance of success and you don’t want to regret not having done something you really wanted. It’s far better to regret something you’ve done!

If you’re interested in articles about the need (or lack of need) for extraordinary mind to do mathematics, take a look at:

 

What on Earth is Mathematics of Planet Earth?

Until recently I had no problem explaining what I was studying; I was just an average maths student. I could reliably predict the reaction of a person informed of this fact: “How can you do that? I’ve always been hopeless at maths. And anyway, what are you going to end up doing with that degree”? Things got much more complicated when I started a PhD at Mathematics of Planet Earth. The first reaction is now usually the question used as a title to this article: what on earth is mathematics of planet earth?! After a brief explanation that I am learning how to use and develop maths for climate and weather predictions, I just get a reassuring statement: “I know that this whole climate change thing is very dangerous/rubbish” (choose the option that applies to you) and a question: “But why did you resign from doing proper maths?”

Actually, I am more involved in studying mathematics than ever. No science would exist without mathematics, in particular climatology or meteorology. Some people can predict the rain by feeling it in their bones; I can “predict” the rain more or less based on the fact that we are in UK. But do we really want to risk our life on someone’s body niggles? No, I do not exaggerate. Our life really can depend on it. Do not forget that a bad weather prediction not only can get you wet, but also farmers might not prepare for a drought (and the crops would get extremely expensive next year), local authorities might not decide to grit ice-covered roads (so you might get stuck in traffic or even have an accident) or a dangerous storm might hit citizens completely not ready for it. It is something worth looking at, is it not?

To get more reliable predictions about the state of atmosphere in the next couple of hours, days or even centuries, we need… mathematics. No, not that boring multiplication table, but nearly every field of very advanced mathematics. Let us take a look at a couple of examples.

Chaos Theory

You will have heard of the “butterfly effect” which allegedly can provoke a hurricane. This is all about the chaos. The intuitive definition, given by E. Lorenz, the creator of chaos theory, is [1] when the present determines the future, but the approximate present does not approximately determine the future. It means that if we were given infinitely precise initial conditions (i.e. full description of the state of the weather now), we could predict the weather at any time in the future. So why do meteorologists sometimes get it wrong? Because this is just wishful thinking. In reality we are not able to get perfect measures of the weather components, for example due to the limitations of measuring devices. Thus mathematicians need to choose the most important measurements with the available precision and try to get the best prediction they can. However, chaos theory states that, under some conditions, starting from almost the same state we can get completely different results. It complicates weather prediction so chaos theory is still something we need to study.

Numerical Analysis

There would be no weather forecast without very advanced computers we are using. Some of them are even supercomputers, such as the one used by Met Office. It costed a trifling £97 million. Why do governments invest such enormous sums into such equipment? Before we understand that, we have to see how the weather prediction works. As mentioned above, we cannot forecast it exactly. Hence mathematicians have to get rid of some parameters that seem to be less important (by the way, deciding which are those is far from obvious) and, using the ones that are left, build a model. This is a set of equations (sometimes thousands of them!) that describe the system. Do you remember solving systems of two equations at school? You might have struggled with it. So now imagine solving thousands of much more complicated ones. Yes, this is exactly why we need supercomputers; they make this job feasible. However, mathematicians still need to make sure that the result produced by a computer is sensible. They do it by carrying out a numerical analysis, checking the properties of the system.

I’ve mentioned only a tiny fraction of the whole range of mathematical tools used in the weather prediction. Next time when you listen to your favourite weather forecast, keep in mind that it would not make any sense without mathematics. And if you happen to have a child, encourage them to study maths. Just in case.

 

[1] Danforth, Christopher M. (April 2013). “Chaos in an Atmosphere Hanging on a Wall”. Mathematics of Planet Earth 2013. Retrieved 27 January 2016.