Math is hard, just like learning any OTHER language is hard.

Sigfpe Says: Think of subjects like algebraic topology where much of
the fancy machinery is just a way to allow formal notation
to get a handle on things that a child already knows
intuitively.

You know a lot children with an intuitive grasp of homological algebra?!?
I mean, the 5 lemma sure, but I am sure most of them have a little trouble with the snake lemma.

Math is easy. Like many of my colleagues I sailed through my degree hardly lifting a finger to work. Once you grok a theorem, say, it becomes obvious and more or less unforgettable. I used to feel sorry for people studying a subject like chemistry who had to memorise an immense body of empirically determined facts to get anywhere. There’s little to memorise in mathematics and no need to work late into the night cramming arbitrary facts.

Math is hard. Just look at how much effort it takes to explain even the most elementary mathematics to a non-specialist. Pick up a mathematics textbook you’ve never read before. It’s not at all unusual for anything just one page beyond where you have already read to be completely incomprehensible. Mathematics texts pile up layer after layer of definition and abstraction which you have to ‘get’ before you can proceed. I can pick up a textbook in a subject like genetics, say, and get the gist of just about any chapter. Conceptually, he subject is more or less trivial and mastering it is just about learning some details.

Math is easy. Time and time again when you get to what appears to be a difficult result you realise it’s fancy language for a trivial intuition or concept. Think of subjects like algebraic topology where much of the fancy machinery is just a way to allow formal notation to get a handle on things that a child already knows intuitively.

Math is hard. I can’t tell you how many times I’ve been stuck there looking at a theorem knowing that everything I need is spelled out there in front of me and yet not being able to put the pieces together. It’s not like I can blame it on a missing fact that I need from another book that requires the work of going down to the library to look something up. This is a completely different kind of work – just you battling against your own mind. I don’t know of anything harder, sometimes, than trying to put those pieces together so that they fit together as a logical whole. You can’t just try to memorise the theorem. If you don’t get it then you won’t be able to use it. There’s no guarantee that if you just spend 12 hours looking at it you’ll have done the required work. No other subject begins to compare with the difficulty of doing this for a challenging proof.

Math is easy. Of course it is, I’m a lazy ba*tard and couldn’t have studied anything else.

Math is whatever you like.

Probability is an interesting case, since most people who studied it these last 300 years thought they knew what it was. There have, however, always been dissidents (starting with Leibniz), who have argued against the standard view of probability (that formalized with the Kolmogorov axioms) as the only or best model of uncertainty. The most recent dissidents have been people in AI trying to build expert systems, who have since the 1970s developed several formal alternatives to the Kolmogorov axioms (although most statisticians and probabilists seem ignorant of this work). The concept is not an easy one at all, IMO.