エバリステ・ガロワがそのような若い頃に亡くなったのは確かに大きな悲劇です。彼は素晴らしい数学者であり、代数と数の理論の分野に多大な貢献をしました。

ガロアが長生きしていた場合、彼が数学でさらに画期的な発見をすることができたはずです。しかし、彼が何を成し遂げたのかを確実に知ることは不可能です。彼が彼の短い人生で完了した仕事と、それが数学に与えた永続的な影響を理解することが重要です。

18歳で発展したグループ理論に関するガロアの研究は、代数の研究に革命をもたらし、抽象代数の開発の基礎を築きました。彼のアイデアは今日も数学者によって研究され、適用され続けており、彼の遺産は数学者の世代に新しいアイデアと発見を追求するように促しています。
It is indeed a great tragedy that Évariste Galois died at such a young age. He was a brilliant mathematician who made significant contributions to the fields of algebra and number theory.

If Galois had lived longer, it is certainly possible that he could have made even more groundbreaking discoveries in mathematics. However, it is impossible to know for sure what he might have accomplished. It is important to appreciate the work that he did manage to complete in his short life and the lasting impact that it has had on mathematics.

Galois' work on group theory, which he developed at the age of 18, revolutionized the study of algebra and laid the foundation for the development of abstract algebra. His ideas continue to be studied and applied by mathematicians today, and his legacy has inspired generations of mathematicians to pursue new ideas and discoveries.