A “cursed” equation since 1832 finally resolved by two Australian researchers

For almost two centuriesa complex polynomial equation resisted all efforts. Furthermore, Todaytwo Australian researchers have just resolved it thanks to a daring approach mixing geometry et Catalan names. For example, A breakthrough that could transform much more than mathematics.

A polynomial equation blocked since 1832 finally broken – "cursed" equation since 1832 finally

THE polynomial equations constitute one of the pillars of algebra. For example, Everyone has already resolved a simple ax² + bx + c = 0. Howeverfrom degree 5, the complexity explodes. Similarly, Since 1832, it was admitted that no general formula could resolve these higher equations, “cursed” equation since 1832 finally which even discouraged the most brilliant minds.

It is. For example, in this context that come Norman Wildberger et Dean rubytwo Australian researchers. Therefore, Their discovery, published in June 2024 in The American Mathematical Monthlydoes not just offer a solution.

In factit opens a new field in understanding mathematical structures and could influence other disciplines.

« We have chosen to go off the beaten trackexplains Wildberger. Rather than forcing classic methods, we have explored another mathematical universe. »

From Catalan numbers to a revolutionary method

Their approach takes root in Catalan namesusually used to count simple geometric configurations. such as the cuttings of polygons. At first glanceno obvious link with high “cursed” equation since 1832 finally degree polynomials.

Yetby looking for structural analogies and connecting different concepts, researchers have developed complex equivalents to these numbers.

Sothis detour by the geometry allowed them to completely rephrase the problem. They combined geometric structures, extensions des Catalan names et Advanced IT tools. Thanks to this hybrid approacha 192 -year -old impasse ended up yielding.

« This unexpected connection perfectly illustrates how ideas from elsewhere can resolve historical blockages “, Underlines Rubine. What’s moreit demonstrates the interest of exploring distant a priori areas.

The discovery of “La Géode”. a new mathematical paradigm

By continuing their research, the two scientists identified a fundamental structure that they baptized “La Géode”. This entity seems to underlie the numbers of Catalan and could well be even more important than the initial resolution.

For Rubine, “cursed” equation since 1832 finally ” Structures and geode are rare. They change our way of seeing problems apparently unrelated. » Thereforetheir discovery is not limited to a simple technical feat: it opens the way to new theories.

Potential applications largely exceed pure mathematics. Indeedthis method could be useful:

• In Molecular biologyto model the RNA and predict the folding of proteins.
• In cryptographyto create more resistant encryption algorithms.
• In artificial intelligenceto optimize the architecture of neural networks.
• In Quantum physicsto solve complex equations linked to the subatomic world.

This advance proves that an idea born in an area can revolutionize several others. Soa “cursed” equation since 1832 could well become the key to unexpected innovations.