Globally, “We use mathematics every day. For weather forecast, to know what time it is, to manage money. Mathematics is much more than formulas or equations, it is logic, it is rationale, it is using one’s mind to solve the biggest mysteries in the world”.

This is the opening of the American series Numb3rs, played on CBS between 2005 and 2010, with the idea that mathematics could deal with the most difficult police plots. To follow this assumption, let’s say that a lot of our everyday gestures need calculation: count money or lambs for sleeping, estimate the duration of a trip, evaluate the discount obtained on clothes on sale, cut a cake in equal slices... 

Since ages, facing the increasing complexity of its needs, humankind has improved its computing resources because calculation is helpful.

Humankind has always needed to count… livestock, goods, trading. In primitive societies, our ten fingers provided an obvious and natural means; with history recording that this practice was at the origin of the decimal system. Subsequently in a more refined approach in Antiquity, piles of pebbles, or stick with notches were used.

 

 

 

The Ishango bone, a form of tally stick, is believed to be the oldest mathematical tool ever unearthed. It was found in an archaeological dig in the former Belgian Congo (now the Democratic Republic of Congo), dates back some 20,000 years and has several columns of tally marks.

 

In Abyssinia (today’s Ethiopia), there was a practice of warriors placing a stone on a pile when leaving to fight, which they then picked up on their return from war. The number of stones remaining then told them how many had been lost in combat. Shepherds also counted their sheep using stones placed in a jar, at the entrance and the exit to the sheep pen. 

  

Stones and sticks are the oldest means of calculation we have so far discovered and made it possible to add and subtract using whole numbers: number of animals in a herd, number of soldiers in an army, number of days in a calendar, the price to be paid during a trade or as a tax. 
These objects can also be shaped from clay as, for instance, hemispheres or spheres. During digs in 1977 in Susa, archaeologists discovered sealed fired clay vessels containing unfired earth balls, dating from 3300 BC and that were used by Sumerian accountants for their trading records.
 

Natural, or manmade, stones and sticks were the origins of tablets and abacus that were used for many centuries and constantly refined for use in ever more complex calculations: lengths, time, proportions, etc.

  

The origin of “calculation”? A small Roman stone!

It is because our ancestors counted using (small) pebbles (“calculus” in Latin) that we are now used to talk about calculations.
Calculus continues to be used in its original sense in medicine where it still describes a stone, i.e. a mineral mass that can be formed in the urinary tract (kidney stone) or gall bladder (gall stones).
 

With Pascal’s calculating machine presented in 1645, certain operations were automated: direct addition and subtraction of two numbers, multiplication and division by repetition. 
What was the mathematician-philosopher trying to do? To help his father, appointed as Superintendent of Finances in Haute-Normandie, to calculate (correctly) the province’s tax revenues. The "Pascaline" launched the development of mechanical calculations, first in Europe, and then around the world.
 

A main step is achieved in the middle of the XIXth century thanks to two British people, Charles Babbage and Ada Lovelace. The mathematician Charles Babbage is one of the main pioneers in the field of computer science and the first to state the principle of a computer. Looking at getting reliable mathematic, astronomic and nautical tables, Babbage intended to implement a programmable machine, called analytic machine that could works without errors.

With the help of Ada Lovelace, also a mathematician, he developed the “diagrams” for operating the machine. It is agreed today that Ada Lovelace has published the first algorithm for operating a machine.

The following centuries would see the perfection of mechanical, electromechanical and then electronic calculators, with the invention of the microprocessor by Intel in 1971. Calculators and cash registers are still in use today in sometimes extremely advanced forms.
 

In science and in industry, the development of numerical simulation, and the possibility of carrying out experiments that cannot be performed in a laboratory, especially when these are dangerous (simulation of an industrial incident), expensive (aircraft design), lengthy (climatology) or inaccessible on a human scale (astrophysics), has led to the concept of another type of “calculating machine”: the supercomputer.
Numerical simulation involves running a program on a computer in order to analyse the functioning and properties of a system or a phenomenon.
Third pillar of science along with theory and experience, numerical simulation is also a strategic tool for industry by reducing development and validation time and by boosting innovation.
 

The concepts of a computer, programing and program have been expressed by the British Alan Turing, in 1937. That same year, Howard Aiken presented to IBM a project of programmable calculation machine which will be developed two years later and tested in 1943. At the same time in Germany, Konrad Zuse designed a computing system able to perform an operation per second... 

At the end of the war, pursuant to Turing’s concepts, John Von Neumann built the architecture used even today in most of computers. And, in the 60’s, Seymour Cray manufactured the first supercomputers for Control Data Corporation.

 

TODAY, the most powerful machines can perform several million billion operations within that same time frame! 

And thus the terms HPC or supercomputing which also describe, by extension, the science that has grown up around this equipment (hardware, software, etc.).

The supercomputer: a silicon tiger

 

A supercomputer is a very big computer formed by several thousand servers all interconnected by very high-speed networks and consisting of tens of arithmetic units. Currently, a supercomputer such as Curie work as fast as a set of 100,000 laptops.

Supercomputers are useful to study the functioning and properties of a system or a phenomenonas well as to predict how it will develop, for instance how an oil platform reacts to the sea swell or fatigue in a material subject to vibrations.