But Laszlo had other ideas - prompted by a chance observation at a printworks, where he noticed that the thicker ink they used dried almost as soon as it came into contact with the paper.
This more viscous ink would not flow from a conventional pen. But by incorporating a single ball bearing instead of a nib, he found the ink could be drawn from its reservoir as the pen moved across the page.
In 1940, he emigrated to Argentina and began to market his invention, which was spotted by a British consul and promptly enlisted in the war effort. Unlike fountain pens, the Biro (as it was now called) worked at altitude and thousads of them were issued to RAF navigators.
When the war ended, the battle to market the new pen began. The Reynold's Rocket, an American version of the Biro, claimed to last for two years without a refill and to write underwater. But on land it leaked or simply wouldn't work, and sales dried up as fast as a pen left without its cap on. Suddenly it seemed the ballpoint pen would never live to write another day.
Then, in 1949, Frenchman Marcel Bich dropped his H and started making precision tooled pens that were reliable and would write for miles. Literally. His company - which would later branch out into other low-cost, disposable, plastic and metal products such as lighters and razors - took over the Biro name in the 1950s and now sells almost 20 million pens every day.
The Biro is a design classic - virtually unchanged in 60 years. Its creator is one of a select band of people whose names have become generic terms for the products they invented. So is Monsieur Bic - un Bic is French for a Biro. But whatever happened to the publicity shy Mr Ball-Point remains a mystery.