Just as there is more to art than portraits and landscapes, there is more to mathematics than numbers and computation, geometrical figures and the calculus.
Consider, for example, fifth degree algebraic equations or the even more fascinating conceptual investigation of symmetries; or, exploration into abstract spaces; or the properties of a set of elements which are specified by certain internal rules. The last mentioned is at the basis of what mathematicians call group theory.
The seeds of group theory were sown in the field of mathematics by a young man of extraordinary genius by the name of Évariste Galois (born: 25 October 1811). Galois was a tragedy as human lives go. He started out as an average student, but when in his teens we was drawn quite by chance to the works of some master-mathematicians like Legendre and Lagrange which only those who have entered the higher realms of the discipline can even vaguely understand.
Galois’ teachers were unkind to him, his efforts to get into the best schools were thwarted because of his impatience with procedures appropriate perhaps for intelligent students, but intolerable to a genius. It is said that during an oral entrance exam, his unorthodox methods of solving the posed problems were incomprehensible and therefore unacceptable to the judges. Young Galois was so frustrated in the interchange, he threw the eraser at one of the examiners and walked out.
Young Galois mastered many branches of mathematics. He detected a serious error in an important paper by a famous mathematician on a fundamental theorem. He began writing papers and sent them to the great ones at the Académie des Sciences. The eminent Augustin Cauchy not only did not present it to his colleagues for consideration of publication, he misplaced and lost it to the world.
In the midst of his mind-elevating mathematics, Galois also got embroiled in the politics of the time. This got him into trouble. His name appeared in papers as a dangerous republican. He was thrown into prison for a brief six months, but enough to demoralize the young man. Upon coming out he was snared by the charms of a damsel who turned out to be no more than a passing pleasure, for she abandoned him all too soon. He got into an argument with a fellow political activist, and agreed to a duel. Whether it was for a political matter or because of “an infamous coquette,” we don’t know. But we do know that on 30 May 1832, the twenty-one year old mathematical genius was shot in the stomach in a ritual to defend his honor, left in pain in the field for a few hours before a passer-by took note of the writhing body and took it to the local hospital. There, the next morning, Évariste Galois, the teenage founder of Group Theory in mathematics, breathed his last.
Group theory, which had its genesis in the work of Galois, has evolved into of the most abstract branches of mathematics. Quite unexpectedly, it has also found numerous applications in science. It is used in crystallography and in spectroscopy. It is also a key ingredient quantum mechanics and in theoretical high energy physics. Through it we are able to classify the plethora of particles under-girding the material world, and also understand why they are there. It has enabled physicists to uncover the existence of entities of which they had never known before. Group theory is at the very basis of the physicist’s understanding of the origins of the universe. Without it there can be no string theory of current physics.