Castelldefels & Barcelona · Small groups
Williams
Maths Circle
— taught in English
“Studying mathematics can generate the same enthusiasm as playing a team sport, without necessarily being competitive.”
Mark Saul · Mathematical Circles (Russian Experience), AMS 1996
in the tradition ofBudapest & St Petersburg
Joseph Williams leads the circle · Stanford Engineering · Harvard MBA
Passionate about inspiring children to go further than they normally would.
You can see more in your child than school asks of them. So do we.
A maths circle for children whose parents can see what they could become. Not extra homework — harder problems, and a room where working at them is normal.
- Do you feel your child is actually being pushed in maths at school?
- What does your child say when you ask what they did in maths today?
- Is your child surrounded by children who make working hard at maths normal?
If those questions landed, this is for your child.
Already flying — and bored.
Finishes the worksheet in five minutes, then waits. Needs a harder problem, not more of the same.
Not yet there — but you can see it.
Capable, uninspired, or not yet reached their true potential. Needs a reason to care, a peer group, and a coach who expects more.
Where a child starts is a question of placement, not admission.
We believe that ability is built — by hours on problems that don't crack straight away, by a coach who refuses to hand over the answer, and by a room where every other child is doing the same.
So a class isn't a lesson and then exercises. Children meet a problem nobody has shown them how to do, fight it and solve the problem in a small group, then defend the reasoning out loud. The answer alone earns nothing.
A child's opponent is the problem, never another child.
The class is not only where it happens.
Learning does not only happen in the Maths Circle. It happens afterwards, sometimes alone, on the homework — so we support the week in between with WhatsApp video messages and animations of problems.
The tradition is older than any border. In 1894 Budapest began a problem journal for schoolchildren and a competition whose winners included John von Neumann and Paul Erdős; in 1934 the mathematicians of St Petersburg, then Leningrad, opened their university to children in weekly circles. We teach the same way, in English.
| Age | UK · UKMT | USA · MAA |
|---|---|---|
| 11–13 | Junior Challenge → Junior Mathematical Olympiad | AMC 8 |
| 13–16 | Intermediate Challenge → Cayley · Hamilton · Maclaurin | AMC 10 → AIME |
| 16–18 | Senior Challenge → BMO 1 → BMO 2 | AMC 12 → AIME → USA Mathematical Olympiad |
The competitions British and American universities recognise. We promise the same problems, and the same standard, as the children who reach the top — not the top itself.
most are 9–14
the same faces
Saturday 90 min, to be confirmed
& Barcelona
to place your child
For the child who is ready for more than a circle can give.
One child, one coach, and a fixed path through three courses: from the first book of Olympiad problems to the classic olympiad problem sets and the British challenges. What is being bought is mastery — a chapter is done when the child can do it alone, not when it has been read.
Joseph only teaches the chapters a child cannot get through by themselves. Everything else is worked at home, and the family follows progress in our app, chapter by chapter, problem by problem. Very few places open each year.
Placement
A short assessment with Joseph, in person or online. It answers one question: where does this child actually start?
A path, not a timetable
The next class is the next chapter the child cannot do alone — never simply the next page in the book.
Work between classes
The child logs their own answers in the app and marks what was hard. Parents see where to help next; the answers stay with the book and with Joseph.
Competitions, together
MOEMS, the UK challenges, AMC. Sat when the child is ready, never before.
Online and in person are the same class at the same standard.
Ask about a place
Joseph Williams
Competition Maths Coach. Stanford engineering, Harvard MBA. Joseph teaches every class himself — no rotating assistants, no substitute teacher.
He founded and coaches a Math Olympics club at a British international school near Barcelona, and coaches his own children the same way. The method is the one he was taught: a hard problem, a small group, and the expectation that the reasoning be defended out loud.
He is a father of four and lives between Castelldefels and Barcelona.
“There aren't many inflection points in a human life. Meeting an inspiring teacher is one of them.”
A parent, 2026
My daughter used to detest maths, and for a very long time, we did not know why. This was until one day Joseph came to BCG, and, after an exciting speech about mathematics, inspired my daughter and many more to join Math Olympics.
My daughter had never been so excited about maths, and once she started this extracurricular activity, we understood why she was enjoying it now, and not before. It was because she never had a teacher who taught it in the right way before Joseph.
For us, the right way is by the teacher explaining clearly, pushing students to their maximum potential and also by motivating them to keep going forward, because without determination and the correct way of looking at challenges, one would not get anywhere.
We are very lucky and grateful to have Joseph teaching our daughter mathematics in that enthusiastic and motivational way.
Until last year, my daughter and I were stuck in the “I don’t understand maths” loop. I could clearly see that we had to find a way out of this toxic cycle. We finished every study session angry or in tears.
While searching a way out, at the beginning of Year 8, she started attending Maths Olympics at school twice a week. With consistent work—not even particularly hard work—she finished the year with her best maths score.
But for me, the most important achievement is not the grade. It is the confidence and understanding she has gained, and the feeling that she is perfectly capable of understanding maths and achieving good results.
I could not have got her here without Joseph’s work. The depth of understanding she is building day after day will make her journey through her learning years so much easier, and even after that.
I can only recommend Joseph and thank him for helping my daughter discover that she really can do maths.
One open workshop. Free.
Bring your child and watch them work on a problem with others. Saturday time slots in Barcelona are still to be confirmed — ask for those, or for a place in a weekly circle, and Joseph will come back to you. What we ask is weekly attendance and the work in between.
+34 661 342 183WhatsApp · Joseph info@williamsmaths.comEmail- Who it is for. Children 8 and up who can already do school maths and are not being stretched.
- What happens. One problem, forty minutes, the children do the talking.
- Then. A short assessment places your child in a circle of up to six.
- Cost of the workshop. None.