Viswanathan "Vishy" Anand (born 11 December 1969) is an Indian chess grandmaster, a former World Chess Champion, and the current World Rapid Chess Champion.Read about Viswanathan Anand in Wikipedia
It's important, according to me, to train in small doses so as to not lose the joy of playing chess. I personally think too many coaching and training classes may take away a child's interest in the game itself. The essential thing to do is practise often and, in case of a doubt, to consult a trainer.
Grandmasters decline with age. That's a given. There is nothing special about the age of 40, but age eventually takes its toll. That much is clear. Beyond that it's about how long you can put off the effects and compensate for them. Mistakes will crop in but you try to compensate for them with experience and hard work.
The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.