I'm not sure it is different than for humans, honestly. First, I should give a standard disclaimer that different students have different strengths and weaknesses in terms of mathematical problem-solving ability, as well as different aesthetic preferences for what types of problems they like to work on, so any overview like the one I am about to give is necessarily reductive and doesn't capture the full range of opinions on this matter.

As I recall from my own Math olympiad days (and, admittedly, it has been quite a while), Combinatorics problems were generally considered to be the most difficult/tricky/annoying for the majority of contestants. This was because, unlike the vast majority of other fields, Combinatorics problems required a certain set of intuitions that could be described as "combinatorial taste", and solving them required you to understand the particular problem in front of you deeply, on an S1 level. You generally had to "play around" with the set-up for a fair bit, developing a better and better picture of what's going on, before certain insights just clicked in your head and guided you on the path to a solution.^[1]

Geometry, by contrast, was much more straightforward.^[2] Not in the sense that the problems were necessarily easier from an "objective" standpoint,^[3] but because you had an essentially fixed set of techniques and configurations you needed to understand (and mostly memorize) that would solve the vast majority of problems. As Evan Chen has said:

Very roughly, there are three different ways I try to make progress on a geometry problem.

• (I) The standard synthetic techniques; angle chasing, cyclic quadrilaterals, homothety, radical axis / power of a point, etc. My own personal arsenal contains some weapons not known to many contestants as well, most notably inversion, harmonic bundles and quadrilaterals, and spiral similarity / Miquel points.For this part, it’s highly advantageous to be well-versed with “standard” configurations and tricks. To give an extreme example: to solve Iran TST 2009, Problem 9 one essentially needs only recognize two configurations: a lemma about the midpoint of an altitude (2002 G7) and another lemma about the line (USAJMO 2014/6). Not knowing either of these makes it more difficult to solve the problem synthetically in the time limit. As a reference, Yufei Zhao’s lemmas handout contains a fairly comprehensive list of these configurations.

You also often had the opportunity to turn a geometry problem into an algebra bash, through complex numbers, barycentric coordinates, Cartesian coordinates, trigonometry, etc. These were skills you developed naturally by practice, and in many cases, if you were an experienced and well-prepared contestant, whenever you were given a Geometry problem, you would be able to instantly remember related problems and ideas and figure out the rough plan of how you needed to go about solving the problem. This is completely the opposite of Combinatorics, where you did indeed sometimes have recurring patterns or broad themes,^[4] but you mostly had to take each (worthwhile, IMO-level) problem on its own terms, instead of falling back on previously-memorized ideas.^[5]

Rather interestingly, this phenomenon (the distinction between the aesthetic of Combinatorics being centered on "deeply understanding and solving one problem" and the rest of the fields as "applying general techniques that expand the understanding of the entirety of Geometry, Algebra, etc.") was also noted at the research level by Timothy Gowers in his excellent essay on "The Two Cultures of Mathematics."^[6]

So, from this perspective, I suppose it would make a lot of sense for a rather narrow AI system to be better at areas of olympiad Math that are more easily "systematizable" (such as Algebra and Geometry) and worse at the areas that seem to require a sort of deep understanding and problem-solving (like Combinatorics) that could plausibly get it closer to general intelligence.

1. ^{^}

   I think the standard example to illustrate this is problem 2 of the 2011 IMO (nicknamed the "windmill problem"), which had an average score of 1.5/7, which was roughly half of what the organizers generally aim for (meaning ~ 3/7, as in 2012), mostly because they underestimated how difficult it would be for the contestants to understand the (combinatorial) set-up properly given the time constraints.

2. ^{^}

   And so was Algebra, but to a lesser extent (although contestants working on inequalities, for example, also benefitted from a boatload of books filled to the brim with dozens of techniques and proof methods specifically geared for this).

3. ^{^}

   I'm not sure how such a thing could even be defined, anyway.

4. ^{^}

   If there actually was no structure to Combinatorics problems, then human minds would not be able to predictably perform better at solving them over time as they practiced more and more, which is false.

5. ^{^}

   To be fair, I have heard through the grapevine that this is getting less and less true as the years pass, because trainers are getting better and better at identifying and compiling books/documents, etc., for training specific combinatorial problem-solving techniques.

6. ^{^}

   Of course, there is a lot of nuance here that I am not getting into, and you shouldn't come away with the impression that Combinatorics is all just one-time tricks and the rest of math is just memorizing proofs that worked on previous problems. Reality is far more complex and multi-dimensional than that; there are parts of Combinatorics that work on the basis of deep theories (such as when using generating functions or the probabilistic method or when making connections with Statistical Mechanics, etc.), and also non-Combinatorial results that seem to have arisen from an almost purely individualized assessment of the problem (David Corfield mentions arithmetic progressions among primes as an example).