Relative, Intellectual difficulty of University Mathematics

I have often pondered the question of whether mathematics, as a subject, increases in relative intellectual difficulty, as one moves from GCSE right up to research level mathematics / mathematical physics.

At first glance, I think most people would probably suggest that this is really a none question and ask what nonsense I am spouting "of course, maths increases in difficulty, as you move through the subject and it becomes more complex and, oh, so abstract."

However, if one were to imagine, say, an index of relative perceived difficulty from 1 to 10; and then went on to examine how a student would rate themselves, at each stage of their maths journey; I wonder how they would rate themselves over time?

Would their perception of the intellectual difficulty of their studies, relative to their intellectual ability at that moment, stay fairly stable?

Let me give an example of my own perception of the intellectual difficulty of mathematics, as I have moved from GCSE, to my current level of understanding and studies.  I will then go on to discuss possible reasons for this and pose the question as to whether or not you would find a similar pattern in the general population.


My Perceived Intellectual difficulty index (1 easy -  10 difficult)


1988 - 1991
Pre- GCSE Maths (felt like I couldn't understand any of it, so switched off) --- Perceived difficulty: 10

1992
GCSE Maths (Grade C, but felt I could have got an A, but wasn't in the right stream to take the higher paper) --- Perceived difficulty: 5

2005
[Life event: Finally diagnosed with Irlen syndrome / Dyslexia, and treatment for Irlen's, improved study ability and motivation]  Read this blog post I wrote, for full details: 

Coping with Dyslexia 

2007
Pre-University self study (Equivalent to Further Maths A Level) --- Perceived difficulty: 8

2010
MST121 Using Mathematics (feels like I am coasting along) --- Perceived difficulty: 4

2011
Self Study via Standard text books (Number Theory / Group Theory) --- Perceived difficulty: 8

2011
Current Status (revisiting A Level skills and practising MST121, prep for M208 and M303) --- Perceived difficulty: 4


What does this all mean?  Well, I can feel a definite pattern in my own path.  Having done this exercise it seems very obvious to me now, that although higher maths is more complex and arguably more intellectually demanding; I find it no more taxing to meet for the first time, than some of the Pre-GCSE maths, that I met as a young teenager.

The only question that I can't personally answer at the moment, is whether this will continue, as I tackle advanced Undergraduate and postgraduate topics and texts, in the next 4yrs?  Will those 8's turn into 10's, as I meet post grad maths for the first time?  Will I be over-clocking my brain with 11's or 12's?


I think that as long as I can keep learning a chunk at a time, then I feel that I will cope intellectually with the later modules.  But does this type of pattern occur in the general population?  Without some research it would be impossible to say for sure; but I do wonder if it is the case that as long as you have average or above intelligence, that any person could apply themselves and achieve a certain level of university mathematics proficiency.

Unfortunately, I suspect that there is a ceiling to how high someone could reach, unless they were particularly gifted or very mathematically minded.

Do I have that ability?  Not sure; not enough data yet.  But I'll give it a bloody good go.