Two high school students present new proof for 2,000-year-old math theorem

Ne'Kiya Jackson and Calcea Johnson, both 17 years old, two high school students from New Orleans (USA), made 'history' when they found new evidence for the Pythagorean theorem that has existed for more than 2,000 years.

Ne'Kiya Jackson (left) and Calcea Johnson - two students who found more evidence of the Pythagorean theorem - Photo: CNN

The work of two students on the Pythagorean theorem was recently published in The American Mathematical Monthly , one of the most prestigious mathematics journals in the US, in the issue dated October 28, 2024.

A year ago, in March 2023, two students presented these proofs at a meeting of the American Mathematical Society.

Jackson and Johnson's discovery attracted national attention and was recognized as one of the most remarkable mathematical achievements in recent times. The success was shared on the program "60 Minutes".

According to CNN, the new proof of the Pythagorean theorem by Ne'Kiya Jackson and Calcea Johnson is a combination of trigonometric principles to prove something that was once thought impossible. As mathematician Elisha Loomis once argued, there can be no trigonometric proof of the Pythagorean theorem because the basic formulas of trigonometry such as (sin^2 x + cos^2 x = 1) are inherently based on the Pythagorean theorem.

However, Jackson and Johnson found a way to use the law of sines without falling into a logical loop to prove the Pythagorean theorem.

This law states that the ratio between the length of a side and the sine of the angle opposite that side is constant in any triangle. Students used this law to create a logical chain of proof of the Pythagorean theorem without relying on formulas derived from the Pythagorean theorem itself.

The Pythagorean Theorem is one of the basic and popular theorems in mathematics programs - Photo: EuroSchool

The new proof methods of Ne'Kiya Jackson and Calcea Johnson have been tested and accepted by the mathematical community, with many professional mathematicians participating in discussions about their validity.

Scott Turner, communications director for the American Mathematical Society (AMS), said it is rare for high school students to present at a mathematics conference of the size of the AMS.

Meanwhile, Catherine Roberts - executive director of AMS - said the mathematics community is very encouraging of the contributions of young mathematicians and encourages the two to continue their research as well as submit their papers to scientific journals so that experts can review the correctness of this proof.

Some other experts said that although this research needs to be further verified in specialized scientific journals, the fact that two high school students achieved this is very impressive and has the potential to open up new approaches to teaching mathematics.

Della Dumbaugh, editor-in-chief of The American Mathematical Monthly , emphasized that Jackson and Johnson's work brought a fresh perspective to the field of mathematics, while also reflecting the important role of teachers in developing the next generation of mathematicians.

Starting from... curiosity

Two students Ne'Kiya Jackson and Calcea Johnson with their families - Photo: NEWS!

Ne'Kiya Jackson and Calcea Johnson are both students at St. Mary's Academy in New Orleans (USA). They are excellent math students and regularly participate in math competitions, creating a foundation for approaching complex mathematical concepts from a very early age.

The turning point came when Jackson and Johnson read Elisha Loomis's book, The Pythagorean Proposition, in which Loomis asserted that it was impossible to prove the Pythagorean theorem using trigonometry without running into a logical loop.

Loomis's reasoning inadvertently piqued the two boys' curiosity, and they began experimenting with methods of using the Law of Sines to create an independent logical chain.

It took them many months of testing, calculating, and tweaking before achieving the initial successes they have today.

Source: https://tuoitre.vn/hai-hoc-sinh-trung-hoc-dua-ra-bang-chung-moi-cho-dinh-ly-toan-hoc-2-000-nam-20241030151712845.htm