Hi everyone. We went through every problem the International Olympiad on Astronomy and Astrophysics has set between 2007 and 2025, worked out what each one asks you to know, and drew the result as a map. Explore it below, or read how we built it further down.
Click a section to show it alone, shift-click to add more. We colour mathematical method grey to set it apart from astronomy.
We split every IOAA paper into the smallest pieces the marking scheme scores. Sometimes that means a sub-part and sometimes a whole problem. We ended up with 800 units across 402 problems. We read each one next to its official solution, wrote down the concepts you actually need to solve it, and matched those concepts to the 175 topics the official syllabus lists.
Marks do not mean the same thing from one year to the next. The median 2007 problem carried 2 points and the median 2008 problem carried 20. So we divide each unit's marks by the total for its year, which makes every olympiad count the same.
Pooling a year's marks in one lump would still get the balance wrong, because it lets whichever round we happen to hold more parts for take over. IOAA scores theory, data analysis and observation 2 to 1 to 1, so we normalise each round inside itself and then hand it its official share of the year. Pooling gave theory 59 per cent of the weight. It now gets the 50 per cent the statutes give it.
Two years gave us trouble. The 2012 and 2014 papers never published marks and 2015 published only three, so we give those problems the median value for their year. Where a problem shows no per-part marks we split its total evenly. The book carries no observation round for 2010, 2013 and 2020, so in those years we spread the observation share across the rounds we do hold and the year still counts once. We record all of this for every unit, so you can check us.
The area of each dot follows m(A). The percentage we show divides that by the total weight of whatever you have selected. These percentages do not add up to 100. They add up to roughly 400, because a unit that needs four topics counts toward all four. Read a number as coverage. It tells you what share of the marks sit in parts that need that topic, not what slice of a pie the topic owns.
We link two topics when the same exam part needs both. We measure the strength as a conditional probability and we keep the direction.
Read that as the share of marks testing A that also demand B. Direction matters, so we keep both readings. Of the marks on orbital energy, 39 per cent also need Kepler's first law, while only 21 per cent run the other way. For the layout we average the two. We also work out normalised pointwise mutual information for every pair, which asks whether two topics turn up together more often than their separate rates predict. That stops a topic appearing everywhere from faking a strong link.
We took this measure from Sun, Ting et al. (2024), who built the astro-ph knowledge graph by asking what share of the papers cited by work on A discuss B. We ask the exam version of the same question.
We laid the map out with ForceAtlas2 using logarithmic attraction. Linked topics pull together, everything pushes everything else apart, and heavier topics push harder. There are no axes and no units here. Only nearness means anything. We grouped topics with the Leiden algorithm. Syllabus topics that nothing tests have no links to place them, so we park each one next to its own Content group and draw it as a hollow ring. 31 syllabus topics have nothing in our map pointing at them, and 60 concepts the exam tests have no home in the syllabus at all.
The IOAA problem book sorts the same problems into 14 chapters of its own, which is an editor's reading of the material rather than the syllabus's. Every exam part sits in exactly one chapter, so chapters never share a part and a part-based graph of them would have no links at all. What they do share is concepts, 204 of our 337 turn up in more than one chapter, so at this level the concept does the linking and a link reads as the share of one chapter's concept mass that another chapter also examines. We colour each chapter by the syllabus section it draws on most, which is where Compact Objects and Gravitational Waves show up as sitting outside the syllabus.
Mark weight adds up across exam parts, so we store every quantity per round and period cell, then add up whichever cells you leave selected. We never add ratios. We work them out again from those sums each time you change something. That is why theory on its own, data analysis on its own, or any mixture over any stretch of years gives you exact numbers rather than an approximation.
We wanted to know whether links stay inside a syllabus section more often than chance allows. So we measured the share of link weight whose two ends sit in the same section, then compared it against 200 rewirings that keep every topic's degree and shuffle the weights. Rewiring breaks the syllabus structure and leaves everything else alone.
| What we measured, links inside one section | 40.4% |
| What rewiring gives | 11.5% |
| z | 24.5 |
If we count the dashed links too we get 35.9 per cent against the same rewired baseline, so the answer does not hinge on that choice. Newman's assortativity on section labels agrees at 0.27. Our Leiden groups agree only weakly with the syllabus sections, but that tells you more about how partition-matching scores behave on overlapping structure than about the result above.
The exam follows its syllabus much more closely than chance. It strays in one direction, into relativity, compact objects and gravitational waves, none of which the syllabus names. Those topics carried 1.4% of marks between 2007 and 2012 and 3.5% between 2019 and 2025.
Reading down the topics that gained and up the ones that lost tells us the same thing twice. IOAA has moved marks out of visual observation and into quantitative data analysis.
| Topic | 2007 to 2012 | 2019 to 2025 | Change |
|---|
One caveat sits under all of this. The syllabus changed while we were studying it. The current version adds a Mathematical Methods and Tools section that includes basic calculus, where the older text ruled calculus out, so we read early papers against a document written later.
We took the problems and solutions from the IOAA problem book, which is all rights reserved. We reproduce none of them here. This page carries syllabus topic names, mark shares and layout positions and nothing else. We are not affiliated with the IOAA and they have not endorsed this work.