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Here's a simple game at which a human can out-fox even the cleverest algorithm.

The INI is celebrating its 30th birthday. What is it and what is it do for maths and mathematicians?

Here's our coverage from the International Congress of Mathematicians 2022, including the Fields Medals and other prizes.

The COVID-19 pandemic has amplified the differences between us. Understanding these inequalities is crucial for this and future pandemics.

There have been accusations that the modelling projecting the course of the pandemic was too pessimistic. Are they justified?

Consider the second equation, i.e. a^2 = ab. Subtracting ab from both sides gives you a^2 - ab = 0. If you look at the last equation (with the a's and b's in it) and substitute in 0 for the expression a^2 - ab as just obtained, on both sides, you have 2 x 0 = 1 x 0, i.e. 0 = 0 which is perfectly correct. The error is to cancel on both sides an expression that you've shown to be equal to zero, otherwise you can "prove" an infinite number of absurdities, e.g. if 1 x 0 = 100 x 0, then cancelling the zeros on each side would "prove" that 1 = 100, etc.