Coding classes in Nottinghamshire

Ada's last note sets out a formula that gives each Bernoulli number from the ones before it, and describes the engine's steps for her B7, "B 1 , B 3 , B 5 being supposed given". The learner writes it as a loop in Python, using the fractions module so every value is exact. Out come 1/6, −1/30, 1/42 and −1/30 for Ada's B1, B3, B5 and B7. Mathematicians today number these B2, B4, B6 and B8: the values match, but the labels are shifted, a classic source of confusion when two programs use different conventions. We then checked the first 30 against a modern formula, and all 30 agree.

Ordinary computer decimals, called floating point, keep about sixteen significant figures. Ada's formula adds large numbers of opposite sign that nearly cancel, and each step loses a little accuracy that the next step inherits. The error passes one part in a thousand million at her B25 and reaches 2.6 per cent at B49; by B59 the answer is about 26 times the size it should be. With exact fractions the same loop never goes wrong, because nothing is rounded. Choosing the right kind of number is part of writing a correct program.

Our own first attempt had a bug, and it is worth confessing. One factor in the loop was off by one, and the program printed 1/6 and −1/30 correctly, then 4/21 instead of 1/42 for B5. The first two answers looked right, so a quick glance would have passed it. Only checking every result against known values caught the slip, which is exactly the kind of care Babbage says Ada showed when she sent his working back to be corrected.

That is why learning to code in 2026 matters for a Nottinghamshire teenager: it lets you check what a machine was really told to do. The longer argument is in why teenagers should still learn to code in 2026.