Any Mathematicians here?

I am currently (and for the next year or two) bringing my maths skills back up to date, using Scottish school exam texts, then a pre university/first year maths book, along with a book on how to think like a mathematician.

Statistics, big data and related maths, Some Baysians maths, and some geometry and algebra online, aside, I haven’t really pursued maths since school (Scottish Higher level).

But I want a better grounding now, hence working through N4-Advanced Higher (gcse to A level), and hopefully onto first year Uni maths in due course.

My strategy is obviously revise the basics and build in old school maths, and it is going fine. I have a book coming on how to think like a mathematician covering stuff like proofs (my favourite part of my maths higher nearly 40 years ago) and logic, analysis etc.

Hence as I start on this journey I was wondering if any mathematicians here could offer any tips, words of wisdom, etc.

My aim is to be back at Advanced Higher/A level standard by this time next year. But I want a deeper understanding (as I have found maths to be everywhere) not to rote learn it. You can get formula etc easily enough so no need for someone at my stage in life to memorise them (but I will obviously be working my way through them).

So any tips on gaining a deeper, more conceptual understanding, as I work my way through the texts? I can already see the maths in pretty much everything, including my esoteric hobbies. Like a language that underpins everything.

I will never make a mathematician, but that isn’t my aim, I just want a better mathematical toolkit to explore with.

Thanks in advance.

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If this helps I’d say it’s important to understand the basics. Sounds obvious I know.
I’ve always been ok with Maths. Mental arithmetic and basic algebra. I studied engineering a few years back for work, and there was a Bridge Maths course. Genuinely starting from the beginning. Understanding how algebra works, not just how to simplify equations. Understanding what Sine was, not just a mysterious button on your calculator.
All I’d say is, unless you’ve previously had a strong grounding in maths, go back to the beginning. Right back to the beginning. Even if it’s just a couple of weeks. The concepts behind maths will help you no end when it starts to get heavier.
I realise this doesn’t answer you question but I guess we where in similar positions. Good luck.


How did the mathematician cure his constipation? He worked it out with a pencil.

My old maths teacher hated negative numbers. He’d stop at nothing to avoid them.

Etc etc etc

I liked maths at school and am now parent to 3 boys who have grappled with A level maths to varying degrees of enthusiasm. Seems like there is so much good stuff out there now, and free too. Khan academy etc. They all found online sites which helped them understand the different concepts. And like @Midlife_Trisis says, often retracing steps, and doing practice questions, until they really understood a maths tool & how to apply it to solve problems.

My brother actually went full nerd and did a maths degree. He said that the first lecture went soooo far back to basics. Literally, they went back to 1+1=2 and dissected it, then built from there. He went on to work in finance in Hong Kong and Switzerland, for what it’s worth. Sometimes when I have my gloved finger up an old man’s bottom, I question my life choices, but that’s another story.


I’m surrounded by some of the best maths/data modellers in the world.

Build a road but can’t cross it, is the term that springs to mind. :grin:


the son of some friends has a PhD in Theoretical Maths and he went on to post-doc research specialising in topology. now that is frankly weird shit stuff and pretty impossible for your average person to understand. it makes rocket science easy.


It depends a lot on your learning style. I’ve self taught myself a lot. For me reading a book or watching a video is fine. But the real learning comes for me from doing.

Not sure how you apply that to maths though

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I remember understanding this stuff at one point in time. Still have my final year book on metric spaces (the module that led to second semester topology) somewhere. It would no doubt be jibberish to me now though!

@SloggingScotsman I have two maths degrees, so can try and answer questions if you have anything specific, but in all honesty I was one of those annoying people where I just kind of “got maths”. It makes me a pretty rubbish teacher, or explainer, as I don’t really understand stuff in the way @Midlife_Trisis describes. It just always seemed to naturally make sense in my head. I also haven’t really done anything with maths since my Masters, and therefore have forgotten a lot!


:joy: That wouldn’t surprise me in the slightest.

I work with some of the smartest people in the world in their very specific fields at the Uni. Some of the things they do/believe when dealing with very basic commercial issues/suppliers would make your eyes water! :joy:


This. I’ve got an engineering degree and nuclear science masters. That’s a lot of Maths! I’m just proud I recognise equations these days.

I realise I’m very lucky to have a brain that just gets it. But when you look at it as a whole it’s the very gradual progression from 1+1=2 at the age of 6 through to neutron diffusion and transport theory.

Maths is very much a subject that unless you are using it every day, you’ll forget it. As others have said, go from the basics and you start to find things that’ll interest you. That might be applicable subjects like thermodynamics or fluid mechanics or the pure maths subjects going into the depths of applied maths and Laplace transforms or even statistics. Maths is the basis of so much but it’ll be down to your interest as to which works and which doesn’t.

For me I was absolutely hopeless at thermodynamics and Laplace transforms but I totally got fluid dynamics and some of the more pure maths theorems.


Didn’t get anything at school, hated it, not 1 O level let alone A! First person ever to leave my school with nowt :slight_smile:

Went on to do a maths degree and then MMath which is basically a 4 year honours degree, when I was about 30. I prefer these to my MBA but that’s another story for another day.

I would repeat all said on here about basics. I did find that sometimes if I didn’t understand something (that happened lots of times) I just carried on and sometimes clarity on a previous point ensued, or I was able to go back and then it clicked.

Having said that I only got a 2:1 and was gutted as I knew if I hadn’t have been a full time worker, I could have got a first. I still feel I owe it one!

If you have any questions just shout, it sounds like many of us are numerically minded.


I did an engineering degree too, so basically 3 years of applied maths. I was fine with the mech eng stuff, but some of the electrical and electronic engineering maths was just too weird :wink:. That was 26 years ago and even though I’ve got a very numerate job now, I’m pretty sure that most of the maths from my engineering days was pushed out of my brain years ago :rofl:.

We had quite a few Mathmos at my college and none of them ever seemed to be doing any work. One of them explained to me that they got one problem to solve each week for each supervision and if they could do it it took them no time at all and if they didn’t get it then they could spend all week working on it and still not get it :rofl:.

It seemed pretty binary - they were all either on for a 1st or a 3rd :grinning:


I teach physics, rather than maths - - but I’d echo Clive’s point as an important addition to all the other good advice in this thread. It’s really good to work at understanding but sometimes you have to settle for just being able to do it, first. For example, I was shown how to differentiate from first principles when I did Higher maths, but I didn’t understand it at all. Then I realised I could do it by just following the rules. And somewhere later on I finally connected the pieces and understood what I was doing.

Also, when people are learning, particularly if self-directed, they tend to move on a bit too quickly. Lots of people are saying go back to basics, but I’d add that you want to over-learn everything. When you think you’ve got the hang of something, do another hour or two before moving on, and schedule revising each new bit of maths - by doing some more examples and/or testing yourself - at regular but increasing intervals. Forgetting is an integral part of the learning process but you need to try to retain the useful elements and forget only the unnecessary details, and over-learning and revision is the way to achieve that.

Godd luck and enjoy!


my wife has a maths degree, however…

I scraped through my maths o-level…but have two science degrees…

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Only 10 types of people…


Thank you all. I do have a maths higher, I specialised in Econometrics at Uni, and have passed professional statistics exams in my time. I have also done some online maths courses, read up on Baysians maths (guessing that makes you phone and self driving car work, oh and it broke ww2 codes).

Just now I am working through a N4 (first year gcse) book, and it’s easy. But I also have the series up to Advanced Higher and while I will have to think I don’t think it will be beyond me. A first year Uni maths book does however look a bit daunting.

For almost all my life I have explored a very wide range of subjects, some in quite some detail, from economics, accountancy, biochemistry, oceanography, even a US pre med immunology course (I found that hard), and others, through to all the other stuff like conspiracy world and freemasonry, and the more esoteric stuff. I just enjoy learning. On any and every subject.

But what has become clear to me is that maths underpins pretty much everything, and I want to see if I can use it to help me gain better insights. Might be a strange thing for a bloke with Incurable cancer to do, but it gives me pleasure. Maths was my weakest school higher C as opposed to my 3As and 2Bs, and while it scares me a little, I am also beginning to appreciate its beauty.

Again thank you all.

Let’s see how it goes this year.

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Yeah, that would have been me. No idea how people managed to have a “good time” at uni with actual essays, and coursework, to do!



I worked the equivalent of 2 years full time employment (postman, glass collector, bouncer, shelf stacking in 2 shops and working in a bank and in a chicken factory) during my 4 year degree, and was Secretary and then chairman of a university (not student) committee. Oh and I enjoyed beer. Ok only got a 2:2 but it has served me well.


3k words required for Monday, 2pm… eeek!

Yeah, I did fill up my time running a sports club and various other wider Sports Association involvement.

I worked throughout my school years, and then through uni holidays, rather than through uni term. I’d saved up enough by then to fully self fund myself through uni with various jobs (on top of the full student loan of course). I did some part time bar work through term, but that was really just beer money.

Anyway, back to maths!

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Interesting post.

Full disclosure - like others I also ‘got’ maths; A at A-level before moving into engineering at university.
Since then I’ve moved a long way towards more general business - I have an MBA and a second Masters from Cranfield which was part of a mid-life crisis conversion to consultancy.
I’ve since moved back towards maths with a six sigma black belt (stats basically).

For your needs, more relevantly, I coached my wife to a C at GCSE which was eye opening as all the methods I used were irrelevant as she didn’t understand them. As I looked through her notes form evening class I suddenly realised there’s a hell of of a lot of different approaches (which you could argue are more systematic) to get to the right answer than the way I did things.
More systematic but generally a lot slower. I see a lot of them now in homework that my 8yo son does, they teach several ways of learning.

As you progress to A level (or whatever it’s called now), I think, like most subjects, it becomes harder and harder without some natural aptitude. FWIW I would say that there’s a rapid transition from easier and more useful to more complicated and less useful.
The other thing I remember clearly is that more complicated maths requires regular practice to keep techniques in mind - even a few days away from differential equations and I would become rusty (BTW I have never used a differential equation IRL).

What’s worth learning? IMHO algebra, trigonometry, basic calculus, accounting and stats. With a decent appreciation of those I’d say you can navigate over 95% of all maths problems you’ll ever encounter - everything else just ask a geek :slight_smile: