Teacher · PhD student · Barcelona
Àlex Reyes
Manuel Alejandro Reyes Jiménez
Maths teacher at Col·legi Maristes Sants—Les Corts and PhD student at UPC, working on the Collatz conjecture and symbolic dynamics. This is my workspace — where the classroom and research meet.
Teaching
- School
- Maristes Sants—Les Corts
- At this school since
- 2018
- Teaching since
- 2011
- Position
- Mathematics teacher (ESO, BTL & IB)
- Form tutor
- 2nd ESO
PhD
- Institution
- FME — UPC
- PhD started
- 2026
- Research line
- Symbolic dynamics — Collatz
About
Since I was a kid, I've been fascinated by problem solving. I never cared whether the solution had a practical application — I just enjoyed thinking, analysing, getting to the bottom of things. I graduated from the FME at UPC in Mathematics, and also completed an MSc in Applied Mathematics and an MSc in Teacher Training.
I spent 7 years at Escola Meritxell in Mataró as a mathematics teacher for ESO and Bachillerato — the last two as Head of Studies for Bachillerato. For the last 8 years I've been teaching at Col·legi Maristes Sants—Les Corts — the same school where I did all of my primary and secondary education.
Fifteen years in the classroom brought me back to something I had long set aside: the drive to solve real problems. One day I came across the Collatz conjecture — a problem that captures everything I love about mathematics. And thanks to that, I'm currently doing a PhD under Dr. Jaume Franch at UPC.
Right now
Working on Paper 2, focused on fibers, strong couplings and the $h_m=4$ conjecture.
Wrapping up the 2025–2026 school year and preparing 2026–2027.
Latest updates
Teaching
Copa Cangur9
- Jun 12, 2026 Historical archive begins: 11th Copa Cangur Final · Júnior (La Garriga, May 2025), 14 problems solved in three languages.
- Jun 12, 2026 Round 1, morning · 12th Copa Cangur · Cadet (Jan 28, 2026): 12 problems solved and explained in three languages.
- Jun 12, 2026 Round 1, morning · 12th Copa Cangur · Júnior (Jan 28, 2026): 12 problems solved and explained in three languages.
- Jun 12, 2026 Round 1, afternoon · 12th Copa Cangur · Cadet (Jan 28, 2026): 12 problems solved and explained in three languages.
- Jun 12, 2026 Round 1, afternoon · 12th Copa Cangur · Júnior (Jan 28, 2026): 12 problems solved and explained in three languages.
- Jun 12, 2026 Semifinal A · 12th Copa Cangur · Cadet (La Garriga, May 5, 2026): 10 problems solved and explained in three languages.
- Jun 12, 2026 Final · 12th Copa Cangur · Cadet (La Garriga, May 5, 2026): 14 problems solved and explained in three languages.
- Jun 12, 2026 Semifinal A · 12th Copa Cangur · Júnior (La Garriga, May 5, 2026): 10 problems solved, with the original figures.
- Jun 11, 2026 New Cangur section: final of the 12th Copa Cangur · Júnior (La Garriga, May 5, 2026), 14 problems solved one by one.
Applied Maths · CCSS22
- May 28, 2026 New Applied Maths CCSS (1st BTL) exam: Comprehensive — 3rd term (May 28, 2026), with step-by-step solutions.
- May 19, 2026 New Applied Maths CCSS (1st BTL) exam: Partial 2 · 3rd term — Probability (May 19, 2026), with step-by-step solutions.
- May 14, 2026 Applied Maths CCSS (1st BTL) notes: Binomial distribution (Unit 10) — Bernoulli, B(n,p), a worked example and 6 exercises.
- 28 Apr 2026 Probability notes (U9): Types of events — compatible/incompatible, dependent/independent, with diagrams and 4 exercises.
- 27 Apr 2026 Real functions notes (U5): Images and preimages — definitions, several examples and 4 solved exercises.
- 27 Apr 2026 Real functions notes (U5): Functions and domain — definition, 5 examples by type and 21 exercises.
- 27 Apr 2026 Inequalities notes (U4): first-degree inequalities — rules, 4 examples and the solution on the number line.
- 27 Apr 2026 Applied Maths CCSS (1st BTL) sheet: exponential and logarithmic equations and systems — 59 solved exercises, with PDF.
- 27 Apr 2026 Equations and systems notes: non-linear systems — substitution as the engine, an intro example and 8 cases.
- 27 Apr 2026 Equations and systems notes: absolute-value equations — the critical-points method and examples.
- 27 Apr 2026 Equations and systems notes: radical equations — strategy, a worked example and 10 solved exercises.
- 27 Apr 2026 Equations and systems notes: logarithmic equations — the two key identities and 11 solved exercises.
- 27 Apr 2026 Equations and systems notes: exponential equations — four types, one example per type and exercises.
- 27 Apr 2026 Equations and systems notes: review session — 17 solved equations (polynomial, biquadratic and rational).
- 27 Apr 2026 Equations and systems notes: rational equations — a five-step strategy and two solved exercises.
- 27 Apr 2026 Equations and systems notes (U3): biquadratic equations — the substitution xⁿ=z, three examples and exercise 30.
- 27 Apr 2026 Polynomials notes: GCD and LCM — the property P·Q=GCD·LCM, two examples and three exercises.
- 27 Apr 2026 Polynomials notes: Homework — five exercises (numeric value, Ruffini, factorisation) solved.
- 27 Apr 2026 Polynomials notes: Factorisation — common factor, quadratics, Ruffini and 8 worked examples.
- 27 Apr 2026 Polynomials notes (U2): monomial, polynomial, degree, numeric value, roots and factors.
- 26 Apr 2026 Full Probability unit, Applied Maths CCSS (1st BTL): sets (Morgan app), total probability, Bayes and 6 exercises.
- 26 Apr 2026 Published the full subject information for Applied Maths CCSS (1st BTL): schedule, criteria, calendar and syllabus.
2nd ESO3
PhD
Publications2
- 28 May 2026 Preprint published on arXiv: “A Fibonacci theorem for Collatz trajectories via modular graph structure” (arXiv:2606.02621 [math.NT]).
- Mar 2026 First draft of the paper “A Fibonacci theorem for Collatz trajectories via modular graph structure”.
Notes & outreach2
Conferences
Coming soon.
Milestones2
- Apr 2026 Started the PhD at UPC with Dr. Jaume Franch.
- Feb 2026 Progress on the formalisation of fractal modular dynamics over the Collatz conjecture.