Dr Ferrol - The Calculator
Type of Spiritual Experience
Dr. Ferrol (b. 1864) was a 'calculator' - a person capable of performing extraordianry mathematical calculations, often of considerable complexity, in their head. Ferrol had a sister about a year his elder, who shared his gift for mental calculation. His father was an architect and a 'good reckoner', and his 'mother's mind was occupied with architectural computations at the time of the birth of these two children; whether this prenatal influence had any effect on their mental powers cannot be determined'. Ferrol's gift showed itself at an early age, but as soon as he learned the elements of algebra, at the age of 10, he developed a preference for mental algebra instead of mental arithmetic. He was head of his class in mental arithmetic, but below the average in all other studies. He was a remarkably poor visualizer. His processes were entirely "intuitive";
"the answer to a problem, he tells us, comes "instantly," and is always correct".
His general memory was 'probably about normal'; his figure memory depended on mnemonics.
A description of the experience
J. Mobius, Die Anlage zur Mathemaiik, 1900, p. 73. The name is given simply as "Dr. Ferrol"; we are not told whether he is an M. D., or what are his initials.
As quoted in An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard
If I was asked any question, rather a difficult one by itself, the result immediately proceeded from my sensibility without my knowing at the first moment how I had obtained it; starting from the result, I then sought the way to be followed for this purpose. That intuitive conception which, curiously enough, has never been shaken by an error, has developed more and more as needs increased. Even now, I have often the sensation of somebody beside me whispering the right way to find the desired result; it concerns some ways where few people have entered before me and which I should certainly not have found if I had sought for them by myself.
If often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.