Were all great mathematicians great with mental calculations? Were they able to multiply large numbers within seconds?


This is a question i find rather ridiculous, because being mathematician does not guarantee rapid mental health calculations, although, i asked the same question while i was in school studying mathematics. I thought the great mathematicians were great mental calculators as we have seen in many movies about "gifted students" who perfomed large calculations within seconds.
The answer is No.
Vast majority of mathematicians pay very little attention to mental calculations, because most people who have been recorded in history to perform such calculations didn't just do it within seconds, it took them ages of practice to become perfect, which mathematicians don't have the time to pay attention to, they are rather busy trying to proposed ground breaking theorems, problems and solution.
Mathematicians such as Gauss was famously able to carry out highly intricate calculations by "hand"(computers were not quite around during his lifetime), but I’m not aware that he indulged in elaborate mental arithmetic tricks. Leonard Euler was known to perform mental arithmetic but that was after he lost his eyesight. Other mathematicians did indulge in calculatuns by hand or basic mental arithmetic but I have never heard that Riemann, or Poincaré, or Hilbert, or Fermat were able to multiply anything by anything within seconds, or extract cube roots to ten digits of precision in their head. This isn’t even remotely what they cared about.
So our great mathematical figures never pay much attention to performing tedious maths tricks Becuase to them it wasn't ground-breaking, they were rather focused on mathematical research that will change the world. 
I myself find it very dificult to multiply 2-digits or 3-digits numbers mentally, i did rather use calculator and sincerely, i have been used to doing this for over a decade. 
A Jewish Russian engineer during WW2, Jackow Trachtenberg who was held at the Nazi concentration camp was known to have developed one of the greatest systems for mental calculations. This process was later known as the Trachtenberg Systems, it is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. Although Jackow Trachtenberg was not a mathematician, but his breakthrough has lead mathematicians to write many papers that have lead to even simpler methods of the Trachtenberg.
The movie "Gifted" was based on a young elementary student who used Trachtenberg system to perform mental calculations of very large numbers. 
I will be writing on the Trachtenberg system in my next post.