One of the most famous and touted claims of computing is Moore’s Law: the number of components in an electronic circuit (and therefore its computational performance) doubles every two years. The “law” was formulated in 1965 by the American engineer Gordon Moore, co-founder and former president of the company Intel, with a prediction that it would be valid for a decade. But it proved to be much longer lasting, remaining valid to this day.
The phenomenon described by Moore’s law is part of the explanation for the dizzying development of electronic computing in recent decades. But there is another explanation, more significant but much less well known. That it is less well known is simply a result of the fact that we mathematicians are much worse at propaganda than our computing colleagues. A regrettable fact, which urgently needs to be corrected!
Because the truth is that advances in mathematical methods of calculation are even more spectacular than improvements in machines. Take the case of linear programming, one of the most important areas of scientific computing. According to the specialized magazine Operations Research, between 1988 and 2004, computers were 1,600 times faster. But in that same period, mathematical algorithms have become 3,300 times faster!
The combination of the two factors made linear programming 5.3 million times more efficient in just 16 years: a calculation that took two months at the beginning of the period dropped to one second at the end.
In other areas, like optimization, the comparison is even more spectacular: between 1990 and 2014, machines improved 6,500 times, but mathematical methods got 870,000 times faster. The total progress in the speed of calculation is breathtaking: 5.6 billion times, which means that 180 years has dropped to just one second of calculation.
Philippe Toint, professor at the University of Namur and speaker at the 2018 International Congress of Mathematicians, in Rio de Janeiro, does not hesitate: “I would rather have today’s mathematical algorithms on yesterday’s computers than the other way around.”
And there are those who argue that, going beyond the famous “Intel inside” propaganda, computers should come with the phrase “Mathematics inside!” (“Contains math!”) which better reflects where the power of the machine comes from.
