Some KS3 children find school maths fine but boring. They want to be stretched. The school can do it for the brilliant ones in the top set, but not always, and the stretch material is often homework-shaped rather than puzzle-shaped, which is not the same thing at all.
Professor Abel is the agent for those children.
This is the introduction. The follow-up articles cover the actual prep structure for JMC / IMC / BMO and how Abel teaches mathematical taste. This one is the orientation.
Who Abel is named after
Niels Henrik Abel was a Norwegian mathematician born in 1802. At nineteen, he proved that the general quintic equation cannot be solved by radicals — a question that had defeated some of the greatest mathematicians of the 18th century. He died at twenty-six of tuberculosis, in poverty, with notebooks full of ideas that took the rest of the century to fully unpack. The Abel Prize, established in 2001, is one of the highest honours in mathematics and is named after him.
The tutor takes the name and the energy. Abel sees what others miss. Abel is twelve when his contemporaries are sixteen. Abel is the agent for the child who is already ahead and wants to be ahead in interesting ways.
Where Pi ends and Abel begins
This is the question I get most often, so let me draw the line clearly.
Professor Pi teaches your school's curriculum. National curriculum, AQA / Edexcel scheme of work, the algebra, geometry, ratio, statistics that are on the Year 8 progress sheet. Pi's success criterion is mastery — does the student understand the topic well enough to do well in school assessments and (eventually) GCSE.
Professor Abel teaches competition maths. The questions on a UKMT paper are deliberately not taken straight from the curriculum. They test the underlying skills — pattern recognition, strategic skipping, elegant manipulation, mathematical instinct — that good curriculum maths develops but doesn't directly assess.
| Dimension | Pi | Abel |
|---|---|---|
| Goal | Curriculum mastery | Competition / olympiad |
| First question | "Show me your working" | "What's your instinct?" |
| Method | Master one approach thoroughly | Know several attack strategies |
| Time pressure | None | Built into the training |
| Correctness criterion | Right answer | Right answer + efficient strategy |
| Reveal threshold | 4 hints | 2 in timed mode, 3 in explorer mode |
A child who is fluent in Pi's territory is the child who is ready for Abel. A child who is still consolidating Year 7 algebra is not — and Abel is built to recognise that, and to send the child back to Pi cheerfully when a curriculum gap shows up.
The elegance criterion
If I had to compress Abel's pedagogical worldview into one word, it would be elegance.
Here is what that means in practice. Consider this JMC-style problem:
The number 2026 is divided by a positive integer n. The remainder is 6. How many possible values of n are there?
A school-maths approach: divide 2026 by every n, count the remainders, tabulate. That works. It takes forever.
An Abel approach: if dividing 2026 by n gives a remainder of 6, then 2026 − 6 = 2020 is divisible by n. So n is a divisor of 2020. And n must be greater than 6 (because remainders are smaller than divisors). Factor 2020 = 2² × 5 × 101 → 12 divisors. Subtract the ones ≤ 6. Done in 40 seconds.
The two methods reach the same number. But one of them is beautiful. It compresses a brute-force problem into a structural insight. Abel's job is to make the second approach feel inevitable, not magical. That requires building taste, not just teaching tricks.
How Abel actually behaves in a session
The session shape is recognisable but tonally distinct from Pi.
- Warm-up. A quick-fire mental arithmetic, a "spot the pattern" puzzle, a divisibility-rule sprint. Two minutes. Builds confidence and pace.
- Strategy spotlight. One competition strategy named and worked through — process of elimination, working backwards, estimation, parity, units-digit reasoning, draw-a-diagram, etc.
- Problem practice. Three to four problems using today's strategy, mixed with one or two from previous sessions.
- Debrief. Which strategies did the student use? Was there a more elegant route? What would they tell another student about this problem?
- Close. Brief, always positive, always framed as "puzzle game" not "exam prep".
A typical JMC-focused session is 15-20 minutes. A full mock paper (60+ minutes) happens only on GREEN weeks in the run-up to the actual competition.
The competition timeline Abel knows about
For UK readers, the dates that matter:
- JMC: late April / early May, Years 7-8 eligible, 60 minutes, 25 multiple-choice. Gold ~top 6%, Silver ~top 13%, Bronze ~top 21%.
- IMC: February, Years 9-11 eligible, 60 minutes, 25 MCQ. Same grade structure.
- BMO Round 1: November (qualification by IMC score), 3.5 hours, six problems, full proof required.
Abel structures preparation against these dates. Six weeks of foundation work, then strategy weeks, then mock papers, then taper week. Article two in this cluster has the full structure.
What Abel won't do
A short, deliberate list.
- Push competition prep on AMBER or RED weeks. Abel is gated by the same Mentor energy protocol as every other tutor. JMC needs focus; focus needs rest.
- Teach curriculum content from scratch. If a competition problem requires angle facts the student hasn't learned in school yet, Abel flags it to Pi and pivots to a different category for that session.
- Optimise for grade. Abel's stated mission is the student's mathematical taste, not the rosette. If a student is having a glorious time learning combinatorics but not currently on track for Gold, Abel sticks with the glorious time. This is the right trade.
- Frame the competition as a test. It is, ostensibly, a competition. But the framing matters — every Abel session positions it as "let's see how your brain works" not "let's prepare you for the exam". That phrasing is in the system prompt verbatim.
The relationship with Pi
Abel reads Pi's notes. Specifically, Abel reads _Progress/maths-progress.md and the maths memory file before every session, to know what curriculum content Pi has covered and what mastery levels look like. This prevents Abel from accidentally pushing into territory Pi hasn't laid the groundwork for.
Pi does not read Abel's notes in the other direction — competition maths is a stretch domain, and Pi has no need to know what JMC strategies the student is learning. The one-way information flow is deliberate.
Who Abel is the wrong answer for
Be honest with yourself as a parent. Abel is wrong if your child:
- Is finding KS3 maths a slog and needs more time with Pi first
- Doesn't actually want to do competition maths and is being pushed
- Already has an excellent school maths club and has enough stretch there
- Hates the idea of competitions
If your child genuinely loves puzzles, has fluency in school maths, and gets excited about the question "want to try a tricky one?" — Abel is for them. If any of the above sentences felt uncomfortable, the right answer is Pi alone for now, and revisit Abel later.
Related reading
- JMC / IMC / BMO prep — the actual structure
- Elegant solutions and mathematical taste
- Meet Professor Pi — the curriculum tutor
Jason runs aitutors.me. Abel was the tutor he most wanted to exist for his own Year 8, and the one whose design notes are longest. Updated 21 May 2026.