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You Guys, It’s a Language, Not a Science

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Hi all,

It’s been a very long while since I’ve been actively blogging, which I’m going to put down to the intensity of second year and a heavy rehearsal schedule, but in reality is probably due to crippling laziness and my Dad giving me the Netflix password. I’ve been thinking about this post for a while, but I haven’t ever got round to actually putting proverbial pen to paper (fingers to cracked phone screen), and since I’m currently on a very long tube journey from Fulham Broadway to Camden Town I figure now is as good a time as any to start.

“What is this thing?!”

As most scientists and mathematicians will discover, at some point you reach a stage in your academic career where showing your work to someone outside your chosen discipline prompts a despairing cry of “What the fuck is that?! I have literally no idea what any of this means. What is this thing?! Jesus Christ, I could never do physics/maths/chemistry/engineering”. It would be lying to pretend that this sort of reaction isn’t, deep down, quite welcome – it gives you a sort of smug, superior “my subject is hard” glow – but, less superficially, it reveals a common misconception about mathematical subjects which, in my opinion, is a key factor in preventing kids from doing STEM subjects at a higher level.

“Imagine you’re reading a book in Cyrillic…”

Think about it this way. If you skim through a difficult history book, not being a historian yourself, your reaction might be a despairing one – “this is so dry and the vocabulary is overcomplicated, I could never finish this!” – but you would probably be able to power through it, maybe with the aid of a dictionary. Similarly, with a book in a foreign language, you accept that you’ll need google translate (or a dictionary, if you’re a purist or you don’t have the internet). Now imagine that you’re reading a book in Cyrillic, except it’s not regular Cyrillic, it’s just a meaningless string of Cyrillic symbols which are typeset seemingly at random with a couple of incongruous English words tossed in there like confusing croutons on a salad of misery. This is what maths looks like.

“People are told that mathematics is ‘the science of numbers’”

The problem lies in the fact that people are told that mathematics is ‘the science of numbers’ or something, when, in fact, it is a mix of language, inductive thinking and formal logic, and it’s not a science at all. To carry on with the maths/foreign language analogy, we can think of the symbols in a formal statement as the ‘words’ of the language, while being able to put them together in a way that makes logical sense is the ‘fluency’ that you get when you’ve been studying that language for a really long time. The problem is only in the fact that you only realise this much later on in your mathematical life – nobody tells you at school that it’s ok to be mystified by equations, because you’re not good enough at the language to understand them yet.

The easiest way to show my point is with a couple of examples – my favourite by far for illustrating the complexity of formal language is the Intermediate Value Theorem. Have a look at this. (I was going to latex this stuff, but I can’t be bothered and I prefer good old fashioned pen and paper anyway)

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THERE ARE ONLY THREE ENGLISH WORDS IN THIS *explodes*

 

This is the Intermediate Value Theorem in its most condensed form (including the definition of continuity, for completeness purposes). Nope? How about this:

“If a continuous function f with an interval [a, b] as its domain takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval”

That was poached directly from the Wikipedia page on the IVT. Let’s simplify this some more:

“If you draw a wiggly line that doesn’t cross itself from the bottom left of a rectangle to the to the top right corner of a rectangle, without taking your pen off the paper, then any horizontal line you draw on the rectangle will cross the wiggly line at least once”

And finally, here is a picture:

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Oh, that makes sense now, cheers

 

There. That wasn’t so hard. What we’ve done here is essentially put the maths through a three-step translation process – taking the formal symbols and turning them into the wordy statement, then interpreting that in layman’s terms, and then thinking about it pictorially – and it’s this sort of visualisation which is absolutely crucial to the understanding of mathematics as a whole. It’s not universally possible to visualise something in pictorial terms in higher level maths, and it’s then where you have to revert to using axioms and theorems rather than trying to think intuitively (topology, for example) but as a general rule, it always helps to try and think what the statement is actually trying to say before you work with it.

What I’m trying to say here is that kids are taught implicitly that maths is hard because it looks hard, and that only serves to further the thought that maths is like marmite – you either ‘get it’ or you ‘don’t get it’ – which is one that stops so, so many kids from doing A-Level maths. Of course, this isn’t helped at all by the fact that “good at maths” in kid-world (and most of the adult world, as I’ve discovered too many times in bars: “you study maths? What’s 347*892?” GO AWAY) directly translates to “being able to do lots of big sums in your head very quickly” which is not the same thing at all. “Lightning calculator” and “good at maths” are not tautological statements, far from it – plenty of people who can do lots of sums very fast couldn’t recognise an epsilon/delta proof if it punched them in the face. Teach maths it as what it is – a formal language and logical reasoning – not as ‘magical number science’ and I guarantee that the bright, well-reasoned kids who would end up being lawyers or historians might well end up being mathematicians instead. Think about it, anyway.

Edit: I may spend the rest of my academic life compiling a giant “Maths to Easy English” dictionary

A loss of identity/Thr(equals)?

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Term’s started again, and the combination of an incredibly light timetable (thanks, Imperial!) and the fact that I am loathe to make the 5 mile round trip twice in one day (it’s getting cold, and biking to college makes my ears hurt) means I have a delicious four hours to kill and not very much work, so I’m in the library, and I’m going to write a post that I’ve been planning for a while.

“When do you use equals, and when do you use threquals?”

One of my best friends is a theoretical physicist at Imperial, and we often have the stereotypical “Physics v Maths” arguments, where he tells me that “Maths is like a hammer, you just use it to do other, more useful things” and I shout back that “PHYSICS MATHS IS MESSY AND MAKES ME EXTREMELY ANXIOUS” and so on. One day we were both travelling back from Fulham to Cambridge quite late at night, and Tom asked me a question, which was, “When do you use equals, and when do you use threquals?” (‘Threquals‘, by the way, for anyone who’s unfamiliar with this little colloquialism, is another word for 3 parallel lines on top of each other, or, the identity symbol, ‘≡’). This was in the middle of August, and we have still yet to reach an agreement about who is right or not.

What tom said:

What Tom said (and I’m paraphrasing), is that if you set two functions equal to each other, say, f(x)=g(x), then that means that for some value(s) of x, the outputs f(x) and g(x) will be equal, for example, x² = x. If you say f(x) ≡ g(x), then it means for all input values in the domain, the functions are the same. He then went on to say that he uses threquals as a defining operator – that “equals does not have the power to define functions”. So if he was answering a question involving functions, he might start by saying “y ≡ x²“.

Why this makes me anxious:

This way of using threquals makes me incredibly nervous, and I told him that – I think I said something along the lines of “You’re bandying about with the identity like it’s nothing and it makes me very, very distressed”. The way that I see the identity(/threquals) is as follows. One can use the identity symbol when the expression that you write down is true for every value of x. No matter what you put in, the expression will remain the same. Hence, “cos² x + sin²x ≡ 1” is an identity, and so is “(x+y)² ≡ x² + 2xy + y²“, because whatever you stick in there, you’ll get out the same answer, but, the functions on either side are non-trivially different. (i.e. obviously 1≡1 but this helps nobody).

In addition, Tom being a physicist means he doesn’t know (or isn’t taught, certainly) about congruence classes – the ‘≡’ symbol also being used to denote two numbers being congruent modulo n, (for the non mathematicians: a ≡ b (mod n) simply means that n divides the difference (a-b), or, even more simply, if you divide a by n, you get the remainder b). While this doesn’t fit with my strict usage of identity, it does actually compliment it nicely. Usually, when you do modular arithmetic, you do all your calculations in a single framework – i.e, you start working in mod n, and you don’t switch halfway through. It is as if, for the purposes of your working, you enter a world where there are only n integers, and you forget about all the others until the end of the problem. Hence, when we do calculations of this kind, mathematicians often omit the mod n on each line, instead preferring to start with “working mod n…” and then just using ‘≡’ from then onwards. This is a very interesting thing to note. When we work in this world, a ≡ b means exactly that – “a is identical to b“. In mod n, there is no difference. So really, this is not a notation issue at all. It’s using ‘≡’ exactly as I think it should be used.

≡, ∀, Let, :=

The usage of the identity as a defining operator made me fret a lot in a sort of vague, worried way, where I couldn’t really explain why I hated the concept so much. Personally, if I were to define a function, I would either say “Let y = x“, “Let y = x, ∀x” or “y := x“. (I think this might be a difference between physicsy maths, which (I imagine) is quite calculation heavy, and pure maths, which is often very wordy, but I’m just hypothesising). ‘∀’, by the way, means “for all“, and ‘:=’ is the defining operator, though I’m not sure how widely its used. The distinction between all of these symbols is a bit of a grey area. I can’t imagine replacing the identity with any of these, for the simple reason that, in my opinion, an identity is something that transcends your current problem or line of reasoning. For example, you can start a question by saying “let x = 1“, and for the rest of the question, every x is also 1. But once you finish the question, x is no longer 1 – you cannot then start the next question taking x to be 1 as well. However, cos²x + sin²x is always 1, no matter what question you’re doing.

0 ≡ 0

I spoke with my other very good friend Richard about this (also on the London to Cambridge train, though going the other way). Richard is a mathematician as well, just about to go into his first year at Oxford (and also one of the smartest people I have ever met), and we had a nice chat about it, in which he sympathised completely with my irrational anxiousness about using identity in such a careless and irreverent way, and agreed that ‘≡’ was a powerful and elegant thing and deserved more respect. He then went on to say another very interesting thing – that, in his view, an identity is something that reduces down to “0 ≡ 0“. Think about this for a second. While it may seem unhelpful to work with statements that are essentially “0 ≡ 0“, this is exactly what the identity does. If you expanded out the Taylor series’ for cos²x and sin²x, and cancelled them, you would arrive at the statement “1 ≡ 1” (which directly implies “0 ≡ 0“, just subtract 1 from both sides!) with fairly little effort, and yet, the identity is widely considered to be a pretty nifty one. I think it’s an incredibly good way of explaining it, which also prevents you from using it as a defining operator, because “y ≡ x” doesn’t reduce down any further than that, so it’s an equation, not an identity.

Richard’s theory made me extremely happy, and also helped me justify my insistence that ‘≡’ is somehow grander and more royal than just a defining operator. So there we go. The threquals/equals debate rages on, but I feel like I’ve won.

 

To Infinity and Beyond

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I’ve been very very ill recently, and to pass the time I’ve been doing a number of things, but one of those things has been watching Morgan Freeman present “Into the Wormhole” or whatever it’s called and the other not entirely unconnected thing has been planning my post-degree meteoric rise into the upper echelons of the BBC where I have my own sophisticated niche TV program which makes maths accessible to people with a brain and everyone thinks I am very smart and I get to do lots of cool maths stuff and also sleep in late. So while lying in my bed of pain feeling sorry for myself, I thought about what I could do to start trying to gently probe my future career path, and then I remembered, I have a blog! That some people looked at, before I ran out of things to post about! (don’t worry though, anyone who is reading, it is a bit harder for me to post during the summer because I don’t really have any intellectual stimulus to keep me going and I tend to just lie about in the sun going “aaaaah” rather than exercising my grey matter, this will of course change once I arrive back at college in October…) So after testing the blogging waters with posts about the library and revision and how much my head hurts, I’m now going to start venturing into talking about actual maths. Brace yourselves. (Oh, and I got a 2:1! How cool is that?!)

“…our first hurdle of realising what a weird concept “infinity” is, is realising that “infinity plus infinity equals infinity”.”

One thing that amateur mathematicians, or laypeople, or your average joes (or however you choose to call them depending on your personal level of egoism) seem to have quite a considerable difficulty in comprehending is an understanding of the infinite, particularly the limit. Many books and TV programs have tried to give us all a taste of how big infinity is (like the classic analogy “A grain of sand is halfway between the size of an atom and the size of the universe” or whatever it is), and there are lots of ways to try and think about it but at the end of the day, comprehending something that big is very difficult. Once you get into the realms of the infinite, normal everyday things like addition just don’t really make sense any more. When you ask a particularly precocious 8 year old (say, me, eleven years ago) what the biggest number is, s/he might say “infinity, but then someone else might say “infinity plus one”, and it keeps going until it all ends in an infinity of infinities plus infinities and everybody goes home in tears. So our first hurdle of realising what a weird concept “infinity” is, is realising that “infinity plus infinity equals infinity”.

 “The real challenge comes when you start thinking about infinity in a set theory context”

So we move on. By the time I was about thirteen, I was happily (and more than a little vindictively) spouting the phrase “infinity isn’t a number, it’s an idea” at anyone who claimed they had “infinity lives” in a game of I genuinely can’t remember. So at some point we make this jump from thinking of infinity as a number, to thinking of it as something which can’t really be manipulated or quantified and ESPECIALLY NOT ADDED TO, RACHEL, YOU CAN’T HAVE INFINITY PLUS ONE BECAUSE IT IS NOT A NUMBER IT IS A CONCEPT AND YOU CAN’T HAVE INFINITE LIVES ANYWAY BECAUSE THAT RUINS THE GAME.  The real challenge comes when you start thinking about infinity in a set theory context, which I ended up doing when I was 16 and writing my Academic Research Project (sounds impressive? It isn’t) for my AS year on various bits and bobs of maths that I’d read about and thought were interesting. Alex Bellos’ brilliant book Alex’s Adventures in Numberland introduced me to the weird and frightening concept that some infinities could be somehow ‘bigger’ than others – like the naturals, the integers, and the rationals are all the same size, but the reals are bigger, somehow. Once I started doing maths at university the infinite became something we dealt with on a daily basis – as carefully as possible in analysis and with slightly more bravado in methods, and this ‘weirdness’ that we feel about infinity as a thing sort of gets swept away and forgotten about.

 “It takes a good teacher to be able to make an analogy that makes you go “Oh, that’s so simple!” when actually, it’s not”

When I first looked at cardinality when I was 16, I couldn’t understand it until I read the Hilbert Hotel Paradox, and in a way, it was that neat little way of describing something big and complicated that really made me sit up and think “maths is pretty cool stuff”. While the purists among mathematicians may laugh, because I needed someone to tell me a little story before I could fully understand countability, I think that analogies are really clever. It takes a good teacher to be able to make an analogy that makes you go “Oh, that’s so simple!” when actually, it’s not. Paradoxes, stories, analogies, puzzles and word problems absolutely delight me –which is probably why I still enjoy Murderous Maths books. I thought, upon entering into undergraduate maths, that the time where analogies could help me was over – but, to my surprise, I discovered an enormously helpful (and hotel based!) analogy that completely fixed my confusion over the Bolzano-Weierstrass theorem in analysis. Since everyone with any interest in popular mathematics will know the Hilbert Hotel paradox (and if you don’t, a quick google will remedy the situation, go on, I’ll wait), I’ll move straight onto the Bolzano-Weierstrass theorem.

Our second term analysis course was all about sequences, series, limits and continuity. The Bolzano-Weierstrass Theorem is a particularly important result that states that “every sequence in n-dimensional space has a convergent subsequence”. Have a think about it, it’s not initially obvious. To prove the Bolzano-Weierstrass Theorem it is necessary to use a lemma: that “every sequence in n-dimensional space has a monotone subsequence” (monotone meaning strictly increasing or decreasing). It is this lemma for which this cool analogy arises. To prove the lemma, we need to consider peak points in the sequence – discrete points for which all corresponding sequence values to the right of the points are lower than the sequence value of the peak point. I.e., a point in the sequence x_n is a peak point if m>n implies x_n > x_m. Then there are two cases, either there must be infinitely many peaks, or a finite number of peaks, etc, etc, and I imagine a lot of you have already decided to stop reading by now. But here is the clever bit!

Proof that every sequence on the real line has a monotone subsequence:

Imagine a seaside resort town where hotels compete to provide rooms with the best view of the sea. A hotel is said to have the “sea view property” if it is higher than all the hotels following it – the windows of its penthouse suite poke out over the top of all the other hotels closer than it to the sea. In our weird mathematical world, the hotels are all built along one strip, and we have an infinite amount of them (obviously!). There are either an infinite number of sea view hotels, or there are not. In our first case, there are an infinite number of hotels with a sea view. If we demolish the hotels without a sea view (bankruptcy), then the remaining hotels form a strictly decreasing subsequence of the original sequence of hotels and we are done. The second case is a little trickier. If there are a finite number of hotels with a sea view, then there must be one hotel which is the last one with a sea view. After that hotel, we can pick any hotel and find another hotel which is higher than it closer to the sea. We can jump to this hotel, and from this hotel, find another hotel which is higher than it and closer to the sea, and so on, and so forth, and in this way pick ourselves an increasing subsequence of the original sequence of hotels, starting from the first hotel without a sea-view. This works for any and all configurations of hotels on our strip. Therefore any sequence on the real line has a monotonic subsequence. Isn’t that neat? 

Why Maths Needs Public Speakers

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Hello everyone! Again apologies for leaving such a gap, I realised the other week that finding a house in London is stressful as hell and I spent about a week and a half on the phone to estate agents. But that’s all sorted now, so I can come back to making posts.

The Thursday and Friday before last was presentation day, where all of the maths freshers had to stand by their posters for two hours and present to any markers who were just wandering around quizzing people. I was in the Thursday AM session and I had a brilliant time, maybe mostly to do with the fact that there was free tea, danishes and doughnuts. I am very easy to please I think. But I digress.

“…but ask them to present to people and they turn into terrified stuttering mice, unable to form a coherent sentence”

Presentations made me think about something which I think is a big issue for mathematicians. There are a lot of kids in my year who are prodigal geniuses when it comes to maths, but ask them to create a visually attractive, well structured and easy to understand poster and then present it to people with varying degrees of knowledge and they turn into terrified stuttering mice, unable to form a coherent sentence. In my opinion, it’s people like this who give maths a very bad public image, and they are exactly the stereotype that we should want to avoid.

“I’m pretty average at the actual mathematics side of things, but I can yarn about ‘interesting maths stuff’ until the cows come home”

This brings me to the only career path I’ve actually thought seriously about in the past year – I’m pretty average at the actual mathematics side of things, but I can yarn about ‘interesting maths stuff’ until the cows come home, and I’m fairly confident I can do it in a way that makes it interesting for other people. (and I invented my own green in LaTeX for my poster, which counts for a lot in my book) So why shouldn’t I use that ‘skill’ to try and make maths interesting for people who never considered it an option? It can’t be denied that we need more students taking STEM subjects (science, technology, engineering and mathematics). While a liberal arts degree is all very well from a personal advancement point of view, it is the computer scientists and the genetic engineers who are making the huge advancements that improve our daily lives every day.

 “…you suddenly realise you’ve actually just learnt Benford’s law”

There are a few people who inspired me to try and inspire other people to enjoy maths, and I think they should probably be mentioned here. The first is Matt Parker, ‘stand up mathematician’ and 1/3 of the comedy-science trio The Spoken Nerd. I first saw him speak at a maths in action day in my lower sixth year, and since then have seen him a few times in the Festival of the Spoken Nerd. Matt is great because he approaches maths in a lighthearted, comedic way, which sneakily draws you in and makes you comfortable with web of jokes and anecdotes until you suddenly realise that you’ve actually just learnt Benford’s law and how did that even happen I swear he was just

 “Very few people can resist the charm of someone talking about something they truly, truly love”

The second person is actually two people, Dara O’Briain and Marcus du Sautoy, who I had the enormous fortune to spend four days filming with during the production of School of Hard Sums. School of Hard Sums itself brilliantly challenges people’s perceptions of maths, and it was incredibly gratifying to read the tweets from various people who had seen the program and were actually getting really involved with the problems without really realising that they were doing homework. Dara and Marcus (and the talented problem setters of the show, including Kit Yates) play a big part in this, and should be commended for it. While Dara was funny and charming as expected, I was extremely pleased to find out that Marcus is just as much of an unashamed nerd as he is portrayed (apart from his interest in football) and we had a lovely geeky chat at the aftershow drinks where he admitted that he actually doesn’t like writing books, his first love obviously being the actual maths. But watching him talk about maths is watching someone talk with true passion and excitement, and there are very few people who can completely resist the charm of someone talking about something they truly, truly love.

 “What are you going to do, be a maths teacher?”

This brings me nicely to the third person, one of my sixth form double maths teachers Mr Leslie. Before anyone accuses me of being a wet wipe, you can talk to anyone who has ever been taught by Mr Leslie and they will wax lyrical about what a brilliant and inspiring teacher he is. A lot of people laugh at teachers (and a lot of people have sneered “What are you going to do, be a maths teacher?” at me when I mentioned I didn’t want to use my maths degree to go into finance), but I think being a teacher is a really noble job. If you can inspire a 16 year old to work hard, get good grades, and go off to do something that you introduced them to, then you’ve done a very very difficult and a very good thing.

 “In an ideal world, in ten years time being a mathematician will be the sexy new thing”

So anyway I think that for mathematics to truly shake its nerdy, antisocial stereotype, we need more inspiring teachers, more public speakers and more media attention – in an ideal world, in ten years time being a mathematician will be the sexy new thing and we’ll improve our public image as well as getting a lot more intelligent, dynamic personalities into the subject. And maths is really cheap to fund. Just saying, all we really need is a lot of paper and some pens.

Welcome Back, Me – My Angry Letter To Amazon

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Hello guys, I’m here again! It’s been a long time.

I took a brief hiatus from blogging once I finished my exams because I didn’t really have that much to say – I attempted to write a blog post about our five introductory project lectures but decided it was feeble, and I tried to write one about when all my friends decided they didn’t really want to hang out with me any more, but that descended too much into the emotional, self indulgent kind of rubbish that is seen far too often on blogs of people my age, so I gave up and waited. I wanted to keep this relevant to people who don’t know me: students, academics, and particularly people who like maths, and talking about how I slept for 35 hours and went to some nightclubs with some people who I hadn’t originally planned to go to nightclubs with is not even interesting, let alone relevant. I hope you all feel the same way. I’ve finished my project now as well, and I’m planning to post tomorrow about some of the maths that went into it, but today is just a little mini-post to tickle your tastebuds so you keep checking back for the next one.

So, for my project, I ordered a book called “A Topological Aperitif” by Stephen Huggett and David Jordan. It has a nice little chapter on the winding number which I planned to use as a reference for some of the stuff I was looking into. I have an Amazon Prime membership, which is nice because it’s pretty cheap and it gets me free unlimited one day delivery, and so I ordered it for delivery on Monday 10th June, a full week before my project was due in. Obviously, it didn’t arrive, because a story about how I ordered a book and then it arrived on time would not be worthy of a blog post. Anyway, I won’t spoil the details – I have pasted below a copy of my email to Amazon. My family have often said of me that I have a knack for writing angry emails, and I must say as someone who prides herself on being nice, polite and generally non-confrontational, writing acerbic complaint letters is a beautifully British way for me to let off a bit of steam. So here it is – My Letter to Amazon.

I must say that I am usually very pleased by Amazon’s speed of delivery and general efficiency, which is why I continued my Amazon Prime membership past the trial period. As a university student, delivery of textbooks often needs to be snappy, and I can say that for the most part, Amazon has come through. 
However. 
I recently ordered this book as research material for my first year undergraduate end of year project, a piece of work which I am required to pass to enter the second year. There were no copies in the library available, and, being slightly tight for time (it was Saturday 9th June, my deadline is today) I decided that my interest in topology was worth the spend and I looked up the book on your website. To my surprise and delight, it was eligible for Prime delivery. I ordered it and it was scheduled for delivery on Monday 10th of June. 
 
I should probably note here that I ordered another item from an independent seller registered on Amazon, on the same day at the same time, with express delivery, that was scheduled for delivery on the 15th of June and arrived on the 11th. Please bear this in mind as you read the following.
 
Monday 10th rolled around and, at the end of the day, I checked my mailbox to find no delivery. (Our delivery system works as follows: big packages are delivered to the security office, who leave a slip in our postboxes telling us we have a delivery and to go and get it). By Friday, I was starting to get nervous, even asking security if they had forgotten to send me a note because “I’m sure it should be here, Amazon are very reliable”. Let’s just recall that this item was scheduled for one-day delivery, a service which, had I not had a prime membership, would have been fairly expensive. 
I rang you on Friday afternoon to explain the situation. I needed the book for a very important project, it was scheduled for delivery on Monday, was very disappointed due to lack of efficiency, more than just “inconvenient” as I actually needed it for a deadline, expected better, etc. To his eternal credit the gentleman I was speaking to (perhaps noting the slight hint of desperate ‘deadline’ panic in my voice) immediately replaced the item, scheduling a dispatch date the very next day (Saturday) for delivery that afternoon. While most of the groundwork for my project would have been completed by then, I acquiesced, thinking that I could read the book on Saturday night and add to my work on Sunday, the final day before the deadline. 
 
Congratulations, Amazon, for your superb grasp of urgency. I got a call at 6pm on Sunday evening while I was in the mathematics department putting the final touches on my project saying that I had a delivery and would I come and sign for it please. I directed them to security and have not been to collect it, because, and this is the important thing here, I’ve already finished. The book was almost a week late with guaranteed one-day delivery and even your urgent replacement arrived well past the time that I actually needed it for. I have paid £16.14 for a book that is now, essentially, useless. What is the point of having a premium service if that service is sub-par? I paid £49.00 for the privilege of “fast and unlimited one-day delivery” (quoting directly from your website here) and while I may be missing something here, failing to deliver one item within six days of ordering while promising to deliver it in two (where is it, anyway? The first book? Where has that got to?) and then delivering an urgent replacement a day and a half late as well is, frankly, taking the piss. 
I sent this about an hour ago and I’ve already been fully refunded and my membership for Prime extended one month. Amazon are very nice about things like that and it almost made me feel bad, and then I remembered that if it had been a textbook that I urgently needed for an exam (or something which I really could not have done without) then unlimited extension of Amazon Prime would still not be adequate compensation for a failed year.
Anyway I hope you enjoyed my little rant, I’ll post more maths soon. All the best!

“…but everyone says I’m the funnier one” – How to accept that some people are just better than you at stuff

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Hello! I couldn’t really post properly yesterday because I had an exam today. It went well! I think mainly because I wasn’t nervous, but also mainly because it was algebra.

Today I wanted to talk about success and failure in the academic world and how difficult it is to accept that some people are just better than you. Just before anyone starts getting frowny this is not a post whining about everyone’s mean to me because I’m fantastic, it’s a post about a general attitude, and it couldn’t be about me anyway, because nobody can call getting a bare pass in your exams successful. However, I kind of have writers block, because there is a lot I want to say about attitudes to success but I’m worried that I will end up either writing about rude assumptions I’ve made about successful people or just listing some wide sweeping stereotypical statements that everyone is bored to tears of already. (Edit: I didn’t!)

“The first reaction [to academic success] is not one of admiration or respect but incredulity and disgust”

I think the current attitude to academic success is toxic. When told about someone who got full marks in all their exams, or has a double first class degree, or did their A-levels two years early, the first reaction is not one of admiration or respect but incredulity and disgust – “what, are you serious? They must have no life. I mean seriously. Come on. That’s just ridiculous.” If we actually step back and have a look at this kind of thinking, what does it say about us? Unable to comprehend that someone could possibly have beaten us in academia, our forte, we hopelessly scrabble around trying to find one thing that we can cling onto that makes us ‘better’ than them. I can happily admit that I have justified my average ability at mathematics by the “at least I have a social life” excuse. The actual fact is that while maybe preventing me from crawling to a few 9am lectures, my social life probably has little to no effect on my academic prowess (especially considering I really don’t go out at all any more) and all I’m trying to do is subtly put myself on a higher pedestal so that I can justify it to myself: while such and such a person has just got a first in mechanics, I could be better than them, I’ve just decided not to be a stupid dumb nerd. Lol. Work is for dorks.

“I can go home without feeling inadequate because I can sing better than them”

It is absolutely astonishing to me that this kind of mentality (my mentality!) exists amongst people doing maths degrees, but it does. When you hear about someone doing all their work, or doing well in a test, you don’t say “fuck, better work harder” you say “jesus christ, are they mad?!”. It creates this vicious cycle where you tell yourself that there is no point trying because this person or people will always beat you academically so you may as well start trying to be the best at doing other things, like eating a foot long chicken temptation subway in twenty seconds flat (getting there) or expanding your mould collection (the cleaner threw my prize specimen away :( ). The thing is that in this environment everyone is an overachiever, and, if you are a chronic overachiever, you always have to be the best at something. I hope my friends don’t mind me saying this, but for example, none of my best pals in maths do musical theatre, and I do, so while they are ridiculously gorgeous and smart and funny and some of the coolest people I have ever met, I can go home without feeling inadequate because I can sing better than them. Isn’t that stupid and childish? But I challenge anyone who is an overachiever, anyone at a top university especially, to name a friend of theirs who is miles better than them at everything without itching to say something like “he’s got huge muscles but, you know, everyone says I’m the funnier one”.

“Don’t mate with her. Mate with me. Look how quickly I can eat this subway”

I think it’s partly biological. I only did biology AS (which still obviously makes me an expert on the subject, see above), but I think that the subconscious desire to put everyone else down is a tactic to make yourself seem like the most genetically advantageous individual. “Don’t mate with her. Mate with me. Look how quickly I can eat this subway. I could put on a hundred pounds of fat in a week. Look at my childbearing hips”. I’m not at all saying that everybody is horrible and everyone is out to get everyone else and no compliment is genuine and all your friends secretly want you to embarrass yourself in public so badly that nobody will talk to you again except them, but I think there is a grain of truth there. Nobody ever enjoys someone telling a story about how they had a day when everything just went so perfectly and they found twenty quid on the street and then they were scouted by a modelling agency and then they got a first in a test.

“I am absolutely not interested in your stories unless they involve you, or someone else, having a terrible time”

I started on success, but this also reminds me of something that a friend of mine said to me once about hearing stories from his friends about when they were on MDMA. He said (and I’m paraphrasing): “All their stories are the same. They had a brilliant time and they loved everyone and they made hundreds of new friends and everything was great. It’s so boring, I don’t want to hear it”. If you step back, what that statement says is “I am absolutely not interested in your stories unless they involve you, or someone else, having a terrible time”.

“It is completely human to feel like you need something that’s ‘yours’”

I would imagine that everyone would like to think that their friends would be happy and proud of their successes, and I am in a unique position because I have been on both ends of this kind of mentality. During my A-Levels I was frequently called a dick because I did a lot better than my peers and expected, naively, that they would be equally as thrilled for me as I was, and now, I admit that on one occasion I have unconsciously blustered something about “well, I didn’t even try, I hate mechanics, I didn’t even do the problem sheet” when I was beaten by almost my entire year group on a particular mechanics test. I have learnt, since then, that it is better to keep your scores to yourself. If it means letting someone think they beat you, so be it. Be the bigger person. Go home and eat a foot long subway and beat your personal best and then sing some musical songs or do a handstand or label your mould samples or something. It is completely human to feel like you need something that’s ‘yours’, something which you’re better than your friends at and that you’re fond of doing, but I would caution you not to let it turn toxic. If you ever find yourself saying even a single “yeah, but” after someone mentions that your best friend did really well in a test, stop, and think about whether you would like it if someone said that about you. And then don’t say it. Just be nice. Nice costs nothing.

"She might have a blog but her head looks like a spoon"

“She might have a blog but her head looks like a spoon”

My brain on exams

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9.45 am

“Hello everyone! Is everyone ok? I feel fine. No, I haven’t brought my notes, because there’s literally nothing we can do now!!!! Hahahahahahaha. Put your notes away. Please, seriously. What’s an integrating factor? Hahaha no kidding of course I know what it is.”

9.57 am

Good seat, right at the back, nobody can see me but I can see everyone else. Pity the girl next to me has such tiny writing, she’s so selfish.

10.02 am

Do I need a wee? I should have gone for a wee.

10.03 am

Ok. Question one. I’ve seen this question before!!!! Hahahaha. I’m going to look up at the exam room and smile knowingly so everybody knows just how much I know about this question. Nobody can see me. Ok. I know exactly what to do, just fiddle about with this and it’ll all fall out and I’ll get a first and everybody will love me- oh, shit, wait, this isn’t working at all

10.10 am

I’ll try part b).

10.11 am

You need part a) to do part b).

10.50 am

This is horrible. I’ve bitten my fingers so much that I am bleeding all over my paper. Look at my lecturer standing at the front smiling and watching all of us flounder. Arsehole. I hate him.

11.15 am

Are there really supposed to be that many cosines and sines in one question? I must have gone wrong somewhere. I can’t even write this fraction on one line it’s so big. I’m frightened of it. I wish my mum was here.

11.30 am

Is there really any point?

11.31 am

I may as well start trying to make a spring with those bits of plasticky paper that you peel off to seal the exam paper

11.34 am

If I fold over the paper at an angle, I can make a spring that is ALSO A SPIRAL

11.40 am

Should probably check my answers.

11.53 am

I think my sketch is wrong. No, it’s right, it’s definitely right. The guy to my upper right is just wrong.

11.54 am

And the girl next to him. She’s probably just wrong as well. I’ll laugh at them when I get my first.

12.03 am

Well that wasn’t so bad.

12.04 am

What am I talking about? That was the single worst exam I have ever sat in my life. As soon as they take my paper I’m going to sprint out of the door before any of my smart friends can ask me how it went and I have to admit that I think I got about 3% of it right and that I’m not even sure I wrote my name on the right bit.

12.07 am

MY SKETCH WAS WRONG OH MY GOD

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