27/04/2022

In Folha, Viana comments on computational and mathematical advances.

Reproduction of Marcelo Viana's column in Folha de S.Paulo

One of the most famous and widely publicized claims in 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 Intel, with the prediction that it would last for a decade. But it has proven to be much more long-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, more significant, but much less known explanation. The fact that it is less known is simply a result of the fact that we mathematicians are much worse at marketing than our colleagues in computing. A regrettable fact that urgently needs to be corrected!

Because the truth is that advances in mathematical calculation methods are even more spectacular than the improvement of machines. Take the case of linear programming, one of the most important areas of scientific computing. According to the specialized journal Operations Research, between 1988 and 2004, computers became 1,600 times faster. But, in that same period, mathematical algorithms became 3,300 times faster!

The combination of these two factors meant that, in just 16 years, linear programming became 5.3 million times more efficient: a calculation that took two months at the beginning of the period was reduced to one second by the end.

In other areas, such as optimization, the comparison is even more spectacular: between 1990 and 2014, machines improved 6,500 times, but mathematical methods became 870,000 times faster. The total progress in calculation speed is breathtaking: 5.6 billion times, meaning that 180 years of calculation time has been reduced to just one second.

Philippe Toint, professor at the University of Namur and speaker at the 2018 International Congress of Mathematicians in Rio de Janeiro, doesn't hesitate: "I would prefer to have today's mathematical algorithms on yesterday's computers, rather than the other way around."

To read the full text, visit the newspaper's website.