Mathlete Alexis Lemaire, 27, found the answer to the 13th root to a random 200-digit number using nothing but brain power in 70.2 seconds, beating his own previous record of 72.4.
Alexis correctly calculated an answer of 2,407,899,893,032,210 from the possibility of 393 trillion answers.
Lemaire used a computer to generate a massive 200-digit number before working out its 13th root
Lemaire set the world record at London's Science Museum using a computer package to randomly generate a 200-digit number before calculating the correct answer.
Jane Wess, curator of mathematics at the London Science Museum said: "He sat down and it was all very quiet - and all of a sudden he amazingly just cracked it.
"He seems to have a large memory and he's made this his life's ambition. It's quite remarkable to see it happen. A very small number of people have this extraordinary ability; nowadays there is only a handful.
"I believe that it is the highest sum calculated mentally."
Deep in concentration, Lemaire beat his own mental arithmetic world record
Lemaire, who attends the University of Reims, began demonstrating his mental calculation prowess by finding the 13th root of a random 100 digit number.
This feat soon became too easy for him and he abandoned trying to improve his time when he calculated an answer in less than four seconds in 2004.
He trains daily for the much harder task of finding the 13th root of a random 200-digit number in an attempt to sharpen his brain - much like other athletes.
Lemaire broke the record in the Science Museum's History of Computing galley, against the backdrop of Charles Babbage's Difference Engine No.2, the world's first successful mechanical calculator, designed in the 1840s.