What will happen when the last bitcoin will be find I have read there is a mathematical limitation of bitcoin count.
What will happen when a miner will find the last bitcoin ? I have read nobody will do mining anymore.
But, we will need miners in order to compute proof of work of transactions ?
They will earn bitcoin with transaction fees ? So mining won't stop ?

Thanks
The Mining process uses the proof-of-work algorithm to generate new bitcoins and protect the network from attack by attackers, such as the publication of an invalid block or the modification of a transaction within a block. .
Bitcoin performs the validation of transactions on average every 10 minutes and they are considered "valid" only when the block containing them is appended to the official chain; each transaction can include within it a bitcoin value which is equivalent to a fee addressed to the miner for reward of the work done, which can choose to give precedence to transactions with a higher commission than a quantity of bitcoins of their choice.
Bitcoin establishes a process of creating a new decreasing and limited currency, in fact it imposes a maximum upper limit of twenty-one thousand bitcoins; the value created by the miners halves every 210,000 blocks, on average every 4 years.
The creation of bitcoin began with an amount equal to 50 bitcoins per block in January 2009 and halved to 25 bitcoins in November 2012 thus estimating the complete issuance of all the bitcoins available in 2140; at the end of the issue, the gain of each miner will be exclusively the value of the commission.

So, the mining will not stop, only the miner's gain will decrease (it is not said because there could be many transactions)