Wrestling with Infinity, at Cambridge.

After spending the the week at School 21, KS and I took the remaining students (large rate of attrition in the buyer’s market of sixth forms) to Cambridge, to present what they have thought about to professional mathematicians (or, my friends and brother all who studied Part 3 and mostly are in the middle of PHDs). Tabitha, from Underground Maths, then led a problem-solving session, on this problem about the difference of two squares.

The students presented on:

  1. A problem I grappled with
  2. A story that resonated with me
  3. A question for my audience

Key Reflections



Tabitha would carefully listen to a group, before adding optional questions – “I have an idea. You don’t need to follow it, but you could”

Look before you leap. Too often I jump straight in, possibly repeating thoughts the students have already have, or derailing their thought process.

Nina did not know how to use a calculator, one of the students (much to their amazement), had to teach her.

Professional mathematics is not about calculation. Constantly remind students about this

Several of the PHD students had to struggle to understand the ideas being spoken about. “Wait, what even is an infinite fraction?” one asked.

Everyone, when meeting new Maths for the first time, struggles.

“It feels like it will be finite, because it is not very wiggly” said Tom.

Professional mathematicians use intuition much more than students. Nurture intuition more explicitly.

The session was the highlight of the week, because the professional Mathematicians were instinctively and continually asking excellent questions and providing incredible explanations. All students were hooked.

A reinforcement in the belief that content knowledge should never be underestimated…

One student had never eaten a raspberry. Another had never seen a tennis court. Several spoke about Hogwarts.

Do not forget the “side”-effects of trips to contrasting places.

Last minute preparation on the train. (The iphone is being used to learn about Hilbert’s Hotel, not to play games…)
Harry (16 yrs old) teaches Hugh (Masters in Maths) a proof he has never seen before (Banach-Tarski Paradox)



Examples of work

Lecture notes
Briefly mentioned once, and this student went away and researched it
Banach-Tarski. Deep thinking here!
She taught herself integration…
She has internalised the sniffing dog and the wise elephant

Brains worked so hard that sleep was necessary…

In John’s…
On the train…

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