Mathematicians: why do you like maths?

I've just been to a talk by Andrew Thomason entitled "Dirichlet's theorem of primes: a fresher's proof". It was one of those rare moments when, outside of mostly rather dry Tripos, I remembered why I chose maths in the first place. It pulled together areas of maths I never knew could possibly fit together, was perfectly understandable (if difficult), and yet it was natural and you could almost predict his next step at every move, and there was no point at which he said anything that threw me. I almost feel as if attending that talk has improved my whole outlook on maths again, which can occasionally feel as if it's just heading off in completely esoteric directions to answer questions no one's asking.

So why do you like maths, and what made / makes you realise this? What areas of maths do you specialise in / see yourself leaning towards (e.g. pure/applied), and why?

Curious.

Reply 1

Ariana123

12

i get a thrill off solving equations hahaha and i plan on studying pure at uni...... can't stand anything to do with the statistics side of things though, i loathe it. ^_^

Reply 2

in_jeopardy

Because it makes sense more than any other topic.

Reply 3

EvenStevens

17

in_jeopardy

Because it makes sense more than any other topic.

That, to be honest.

Plus there's that sense of achievement that what you've just done is ... just right.

Not like English or Philosophy where your answers are just merely opinions.

Maths is solid, hard, proof. Pure, even.

Reply 4

Zhen Lin

12

Hmm, didn't we have this thread before?

Reply 5

mikeski

3

It's challenging. Even though the same rules apply, you never really get the same question twice :smile:

Reply 6

generalebriety

OP

16

Not in principle. Most people who study maths do so because it'll help them get a good job, as part of a science / engineering degree. And if you study maths, you're not obliged to like it.

I'm disappointed that this thread has mostly been answered by A-level students. I don't mind that, of course (I deliberately didn't specify), I just think "if you say stuff in maths it's always right because of proof" and "it's satisfying being able to do it" rather predictable. :p:

Reply 7

Jake22

18

My answer as to why I like it is the same as that in the other thread linked above (by Zhen Lin). I can't be bothered retyping that at present.

The thing that got me interested in mathematics was the book Abstract Algebra by Whitelaw. I had no mathematical knowledge (beyond GCSE) when I picked up the book (I saw it in a charity shop - don't have a clue why I bought it) but the book was self contained and was the first thing that introduced to me what maths really was and I became quite interested as a consequence.

I don't know what area I want to specialise in; I am only at the second year undergraduate level at the moment. I think it would have to be something algebraic, but I am not sure whether that will be pure algebra or perhaps also combining something else like algebraic geometry or algebraic topology etc. I only know very basic things about those areas so it is too early for me to be conclusive but I guess I will find out more in the next couple of years.

Reply 8

Kolya

17

Is it just a coincidence that we both created threads on the same topic?...

Reply 9

Overmars

17

So why do you like maths, and what made / makes you realise this?

It’s weird. I’m doing maths at uni now and I don’t know if I made the right decision or not. Sometimes I hate the work, sometimes I enjoy doing it. Why do I sometimes like it? It feels like a game. When you’re asked to complete a proof or do a ‘show that’ question, sometimes you have to think ‘outside the box’ – find a trick and the satisfaction of doing that is great. Another thing that I’ve found I like from university maths from A-level maths is that when you’re writing answers there cannot be any ambiguity – every line of working must be logically consistent with the line above it. You can’t get away with messy work and it has to be precise. A very useful skill to develop, me thinks.

What areas of maths do you specialise in / see yourself leaning towards (e.g. pure/applied), and why?

At the moment, I am learning pure and applied maths but I didn’t like my stats module. I enjoyed analysis and discrete maths, and although I have found them fairly difficult, I’ll choose to continue with those topics next year.

Reply 10

generalebriety

OP

16

Lusus Naturae

Is it just a coincidence that we both created threads on the same topic?...

What are you suggesting? :p:

Reply 11

Kolya

17

generalebriety

What are you suggesting?

I'm suggesting that you are feeling similar to how I felt (and am still feeling). :smile:

To help I did something slightly similar to what you did: I picked up one of those easy "popular" Maths books which focus on the stories and ideas more than the dry Maths; however, feelings return. Only a couple of days ago I was thinking about what my answer would be to this very question, and my current answer would be different to any given on this thread: Of all subjects I could be reading, Maths is the most useful if one is interested in a variety of disciplines: Maths makes the study of Physics, Chemistry and other quantitative sciences much easier; I can still read and understand classic literature; I can play and appreciate music; I can understand and argue about philosophy, politics and religion. I submit that, of all subjects, there is none that would give me more freedom as easily as Maths. In what subject would the difference in difficulty and quality between a formal and individual study of said subject be greater than in Mathematics?

Reply 12

generalebriety

OP

16

Lusus Naturae

I'm suggesting that you are feeling similar to how I felt (and am still feeling). :smile:

To help I did something slightly similar to what you did: I picked up one of those easy "popular" Maths books which focus on the stories and ideas more than the dry Maths; however, feelings return. Only a couple of days ago I was thinking about what my answer would be to this very question, and my current answer would be different to any given on this thread: Of all subjects I could be reading, Maths is the most useful if one is interested in a variety of disciplines: Maths makes the study of Physics, Chemistry and other quantitative sciences much easier; I can still read and understand classic literature; I can play and appreciate music; I can understand and argue about philosophy, politics and religion. I submit that, of all subjects, there is none that would give me more freedom as easily as Maths. In what subject would the difference in difficulty and quality between a formal and individual study of said subject be greater than in Mathematics?

A convincing argument; why, then, do you think this argument only applies to mathematicians? In other words, if a mathematician told this to a historian, a philosopher or a biologist, why would they not suddenly drop their field of study and come and join us in maths?

I feel your argument is entirely correct, but somewhat artificial; it is only a mathematician that would feel like this, and therefore rather than being the reasons that you like maths, the above reasons are probably more a consequence of the fact that you like maths.

Reply 13

SsEe

13

About a year ago I read a book on Galois theory. This is the part of maths that answers the question of exactly when a polynomial is solvable by radicals, and also there's some stuff about straight edge and compass constructions flying about. It's basically linear algebra and group theory being used to answer very well known problems in a neat way. These are the best bits of maths for me. I love it when a classical problem is solved.
On the other hand, I took a course on Algebras before Christmas. That was exactly the "answering questions nobody asked" stuff you mentioned! Though it does lead the way to group characters which are one of the neater things I've seen.

Just finished the learning part of my 3rd year. I've done most of the usual undergraduate stuff (linear algebra, analysis, algebra, topology, prob, stats, logic, set theory). Next year I want to look at Godel's incompleteness theorems, algebraic topology, analytic topology, more set theory, representation theory of symmetric groups and some other stuff that I haven't decided. But it'll be pure. Because I'm no good at applied maths.

Reply 14

Kolya

17

generalebriety

A convincing argument; why, then, do you think this argument only applies to mathematicians? In other words, if a mathematician told this to a historian, a philosopher or a biologist, why would they not suddenly drop their field of study and come and join us in maths?

I think that the argument applies to different degrees depending on the subject. My argument was that Mathematics offers the most choice; the follower of another subject can still achieve the same breadth with sufficient willpower. If they have found that the subject that comes most naturally to them, and in which they have most interest, is History then I think they should study History. The reason for this is that many people have a main discipline which is their focus; their specialism allows them to find a job that requires skill and that few others can do. One who studies History informally is unlikely to achieve a depth of understanding that is comparable to one who studies it formally, and so the student who has the depth is a rarity - they have skills which we, as a high-functioning society, desire. I think the desire to excel in their specialism and its interesting heights will drive them to follow their line of study, even if it is detrimental to their understanding of other disciplines (and I am thinking of primarily quantitative scientific disciplines).

Furthermore, I do not believe that it is every students desire to gain a breadth of knowledge. On many occasions I have encountered students, many of whom were excellent students of their own subject, considering themselves to be "useless at Maths" or uncomfortable with complicated, abstract arguments that are presented in blocks of text. I do not think that such students - and I would place them in the majority - who are content with studying their own subject, and having a passing knowledge of current affairs, would be persuaded, as you suggest, to join us in the study of Mathematics.

I feel your argument is entirely correct, but somewhat artificial; it is only a mathematician that would feel like this, and therefore rather than being the reasons that you like maths, the above reasons are probably more a consequence of the fact that you like maths.

As I mentioned above: My argument would apply, in varying degrees, to students of different disciplines. A Physics student will find many concepts in other quantitative sciences to be simple to understand, while a History student would have to work much harder to understand those same concepts. While I think that my argument could be a reason that one might give for liking Maths, I would personally feel that it is a reason to tolerate the formal study of Maths, which itself forms only a part - albeit a large one, at present - of a much wider education in the many academic disciplines that one might choose to educate oneself in.

Reply 15

Zhen Lin

12

Lusus Naturae

Of all subjects I could be reading, Maths is the most useful if one is interested in a variety of disciplines: Maths makes the study of Physics, Chemistry and other quantitative sciences much easier

That was actually the main thrust of my personal statement - that mathematics is everywhere, or rather, can be and is used to model just about anything. But should we be distinguishing between appreciating mathematics and basic numeracy? I think what most people actually mean by "good/bad at maths" is "good/bad with numbers", though obviously that's not always the case and there is some correlation between the two...

Reply 16

studyboy

13

I like math because I seem to be able to understand it more than other subject! Basically, I think in numbers so math comes natural to me :biggrin:

I'm going to specialise in statistics, especially in the area of finance

Reply 17

mountainmetman

14

For one thing, there's an elegance to maths (and spelling matters less :biggrin:

)
Randell over at xkcd has another good point, but I mainly did maths at Swansea as a means to an end.
Now I'm going back into it with the OU because at the end of my first degree we were getting into some really cool stuff with index notation and multiple dimensions. The description with the maths didn't rely on physical existance, just topographical conservation. Now I want to know that that means! It's a VERY powerful tool and satisfying when it goes right.