Tcc - a mathematician's apology

A Mathematician's Apology is an essay by the great British mathematician, GH Hardy. It examines topics as diverse as careers advice, the motives behind mathematics, beauty in the sciences, and the evil that can be caused by them.



I found A Mathematician's Apology pretty damn interesting, especially as I find maths itself pretty damn interesting. I too am worried about peaking too early - it seems that once I finish a degree, I will have only a couple of years to add anything to mathematics before I become senile. The last section assuages my fear a little; I do enjoy maths for its competitiveness, as did Hardy, and he got along fine. Anyway, it's too early to think about such things really.

Oddly enough, the Maths A Level syllabus has been updated very recently, and from 2016 students will have to be able to prove the irrationality of the square root of 2. It's not too hard, clearly, but it's a very different proof method to what most people are used to. A Level Maths is fundamentally algorithmic, and when it becomes less so, everyone seems to panic. Hardy would clearly support this idea.

The comments on maths being harmless are a little unfortunate in the modern era of warfare, however.


Maths was always my most hated subject at school (other than PE), and I would also say it is the most important subject out there; it's the building block of our society, and although I can't stand the subject I still admire it. As well as talking about maths, Hardy also made a few comments about life in general, and those stuck out to me just as much as his comments on the beauty of maths.

He referred to maths as a "young mans game," and this idea of being creative when you're young is something I've heard time and time again. To be quite frank, this terrifies me. Does that mean my best work will occur over the next few years of my life? And after that, everything will just begin to decline? If anything, it makes me feel like I'm wasting my youth right now by not "achieving" anything. I always believed that my achievements would come in the future once I'd gained more knowledge and experience about my field, but I'm not sure if Hardy would agree.

It was also interesting to read the two reasons Hardy laid out for why people choose their career paths. I definitely fit into the second reason: "There is nothing I can do particularly well. I do what I do because it came my way." Which is perhaps a bit pessimistic, but I certainly didn't feel a calling towards my chosen career, nor did I have aspirations for one specific career when I was younger. I wonder how other people's experiences on here differ?

I was a little put out by Hardy's line "Good work is not done by 'humble' men." Although I do agree that questioning everything you do is detrimental, and a bit of self-confidence is always needed, I don't think humility is a negative quality. Perhaps you could argue that in our ruthless world you need to be arrogant to get where you want, and I guess if that's the case, I'll be very unsuccessful.

Ambition also seemed to come up quite a bit in the first few chapters, and I also disagree with the idea that ambition is the only thing worth pursuing - "A man's first duty .. is to be ambitious." There is more to life than your career, and I think that by engulfing yourself in your work you are missing out on so much that life has to offer. You can never enjoy the moment - it's always about meeting the next goal and winning the next prize. When I first entered university I was ambitious as hell. I had dreams of saving the world and winning the Nobel Prize. The main thing that quenched all these desires for me was a fear of failure. I have respect for those people who are able to pursue their goals relentlessly without letting this fear get in the way, and I wish I had that determination. In a way I can see what Hardy is saying - I guess ambition can give you the drive that you need to succeed.

Although no one can deny the usefulness of maths, I would argue that maths can be harmful at times. I'm sure this wasn't what Hardy was getting at, but I feel that STEM subjects are pushed down students throats a bit too much. Maths is seen as a subject in which only the intelligent do well in, and that sort of thinking can really lower your self-esteem. Doing well at Maths (and Science) at school does not mean you will be a failure in life, and I think there should be a bit more emphasis on the humanities - and this is coming from a science student.

I enjoyed reading Hardy's descriptions of the beauty of maths. For me the beauty lies in that moment when something clicks and it all makes sense. The numbers fit perfectly within each other and the equation hangs symmetrically. It's a concise subject, with no frills and extra bits hanging around. You have everything you need in front of you on the page.I also liked the way Hardy described pure maths as being "clean" - it's sad how we can taint things like science through their uses in war. Even a subject as noble as medicine can be used in horrific ways if you have the mind for it.

I noticed that Hardy rattled on a bit about the uselessness of pure maths, and I wish to point out that knowledge doesn't always have to be useful - it can be for pleasure. I enjoy reading about a variety of things, most of which I have no first hand experience in. I doubt I will use everything I read in my day to day life but the process itself is a stimulating. Everything I read makes me view the world a little differently, and although such thoughts will not lead me to make the next scientific discovery, it does not mean that these thoughts are useless.

I'm glad Hardy mentioned "mathematical reality" as it's something I've often wondered. Did humans construct equations to assist in their understanding of the universe, or did these equations already exist and were simply discovered? Hardy noted that mathematicians "observed" the world around them, much like science. But in science you also attempt to alter the world around you - can you do the same in maths?

It was certainly an interesting read, although I do wish we could have gained more insight into his mind: what's it like to be a mathematician? How does your brain process things compared to everyone else? We did get an insight into his personal thoughts in the last chapter with some raw emotion about the process of ageing. Overall I'd say it was a fascinating insight into a topic I know little about and a good way to let a layman admire the subject from a distance.