The father and son named Andrey Andreyevich Markov both became famous as what?

Andrey Andreyevich Markov (1856–1922) was a Russian mathematician known for his work on stochastic processes. His son, also called Andrey Andreyevich Markov (1903–1979), also became a noted mathematician.

Andrey Markov senior attended St. Petersburg Grammar School -- where he did badly in most subjects other than mathematics -- and Saint Petersburg Imperial University, where he was invited to stay on to have a career as a mathematician. He later taught at high schools and continued his own mathematical studies.

The principal topic of Markov senior’s research was the mathematics of processes through time. A so-called “Markov process” is special in that it is memoryless: predictions can be made regarding future outcomes of the process based solely on where the process has reached right now. These predictions are just as good as the predictions that could be made knowing the process's full history. Watching a frog in a pond jumping from lily pad to lily pad, you do not need to know about the previous jumps to model the probability of where the frog will jump next.

In case this seems absurdly abstract, note that such ideas underpin the logic of everyday apps on the device you are using right now. Page ranks by Google, predictive text and other learning algorithms all use Markov’s insights. Markov processes are also applied in finance and economics to model phenomena such as consumer brand-switching, the behaviour of asset prices and stock market crashes.