Sophia Gilman was born in Paris, the capital of France, on April 1, 1776. She was an outstanding female mathematician. Her father was a businessman who loved to learn. The rich collection of books at home enabled Gilman to live in a good learning environment since childhood. At the age of 13, a biography of the mathematician Archimedes made her intoxicated and planted the seeds of love for science in her young mind. This earliest excitement for science determined her lifelong mathematical career. With her tenacious perseverance, she taught herself calculus. At the age of 18, Gilman, who was receiving correspondence education at the Paris Polytechnic School, had the honor to listen to classes from Lagrange, a famous mathematics master. The master's profound thoughts greatly inspired her. Gilman wrote a paper under a pseudonym and sent it to Lagrange. After reading it, Lagrange applauded the table and notified the author for an interview. Unexpectedly, the person who came was a female student in her prime, which surprised Lagrange. Lagrange made an exception and became Gilman's godfather, often guiding Gilman in his studies.

During the Franco-Prussian War of 1807, French troops occupied the German city of Hanover. Gauss, the world-famous "Prince of Mathematics", lives there. At this time, a young girl recalled the tragedy of the ancient Greek mathematician Archimedes being killed by Roman soldiers and became extremely anxious. After reading the biography of Archimedes at the age of thirteen, she was deeply indignant at the barbaric act of destroying human civilization. Gilman's father was a French businessman and was friends with the commander of the French army at the time. Gilman used her father's connections to visit the French commander-in-chief and insisted that he ensure the personal safety of the German mathematician. Therefore, she gained Gauss's trust and found herself another erudite teacher.

Under the careful guidance of mathematicians such as Lagrange and Gauss, Gilman's research work progressed rapidly. In addition to making great achievements in number theory, he has also achieved fruitful results in the field of applied mathematics. In 1811, she won the gold medal set by the French Academy of Sciences for establishing a mathematical theory of elastic surfaces that conforms to actual engineering data for three outstanding papers, which caused a huge sensation. Unfortunately, due to the prejudice of society at that time, although Gilman had made great achievements, she was a woman and was discriminated against. Therefore, she did not obtain any degree in her life, did not hold any scientific position, let alone enter a university. As a professor.

In 1831, Gilman, an outstanding woman, the first female mathematician in modern history to make great achievements and deserve to have made great achievements, closed her eyes in Paris with lifelong regret due to breast cancer.