Jean-François COLONNA

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(CMAP28 WWW site: this page was created on 06/10/2023 and last updated on 11/14/2023 17:55:11 -CET-)

Mathematics are everywhere!

Thus, in everyday life, without them, there would be no GPS. Let's take a moment to focus on what is now indispensable to many of us. The GPS [01] was developed about forty years ago at the initiative of the

The situation is the same in the most fundamental research to such an extent that one can (and must!) consider Mathematics as a virtual optical instrument that reveals new perspectives on Reality every day. We will remember, for example, the gravitational waves [04] predicted by Albert Einstein in 1915. A mathematical prediction, but their actual detection required a century of efforts (

Unfortunately, this omnipresence seems to be ignored by many people, especially our government officials. Just remember the recent and unfortunate reforms of the baccalaureate, particularly concerning Mathematics, to be convinced of this. And that is a great pity because, indeed, pursuing Mathematics (especially Applied Mathematics) guarantees an exciting life, employment, and also being useful in these times when reindustrialization, energy efficiency, nuclear power, and other related areas are gaining momentum!

But despite these successes and ubiquity, their profound nature is still unknown to us. We still do not know whether our mathematicians are "inventors" or "explorers." I am certain that the answer to this question is beyond our reach without "external" assistance, as is the case with many other transcendent aspects [06]!

Under these circumstances, could "Martians" help us answer this question? The question may seem absurd, considering the uncertainty surrounding their existence. In 1950, during a lunch with several colleagues from the Los Alamos laboratories (USA), Enrico Fermi (Nobel laureate in Physics in 1938) expressed surprise that, given the age of the Universe, Earth had not yet been visited by extraterrestrials (assuming they possess curiosity and a drive for expansion, like us). This inquiry is now known as the

Even though I am convinced that our Earth is not the only cradle of life in the Universe, the encounter with "Martians" seems both highly improbable and undesirable due to the associated risks. However, if one of those spacecraft, which science fiction has familiarized us with, were to arrive on Earth and its occupants were benevolent, allowing for dialogue to be established, it would present a magnificent opportunity to question them, particularly about their understanding and "mastery" of the Universe: "Do you, like us, engage in Mathematics?" [07]. In the case of a positive response, our mathematicians would most likely be explorers, and the debate might be settled [08], even though the "Martians" themselves might not truly know what Mathematics truly are. But what if the answer is negative? What a disruption it would be to learn that such understanding and mastery (given that they have reached us) could be achieved without our sets, without our numbers, without our beloved equations... How could one imagine, for example, not relying on counting and yet identifying, say, the laws of invariance and then reaching the stars? Would we be capable of comprehending these truths, with our minds inevitably limited and conditioned by our terrestrial environment? The answer is certainly negative.

But unfortunately (or fortunately?), there is little chance that we will witness such an encounter and finally have the profound nature of Mathematics revealed to us.

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