Jean baptiste joseph fourier (1768 ~ 1830) was born in a tailor's family in Oszer, central France. He became an orphan at the age of 8, studied in the local military academy, 1795 served as an assistant professor at the Paris Polytechnic University, and 1798 went on an expedition to Egypt with Napoleon's army, which was highly valued by Napoleon. After returning to China, he was appointed as the governor of Grenoble Province. 18 17 was elected as an academician of the Paris Academy of Sciences, and 1822 became a lifelong secretary of the Academy of Sciences. Fourier Drought wrote a basic paper on heat conduction in 1807, but it was rejected by the Academy of Sciences after being reviewed by Lagrange, Laplace and Legendre. 18 1 1 submitted a revised paper and won the Academy Award, but it was not officially published. 1822, Fourier finally published the monograph "thermal analysis theory" (Paris, 1822). This classic book developed the trigonometric series method applied by Euler and Bernoulli in some special cases into a rich general theory, and trigonometric series was later named after Fourier. Fourier uses trigonometric series to solve the heat conduction equation, and in order to deal with the heat conduction problem in infinite region, the so-called "Fourier integral" is derived, which greatly promotes the study of boundary value problems of partial differential equations. But the significance of Fourier work goes far beyond this, which forces people to revise and popularize the concept of function, especially the discussion of discontinuous function; The convergence of trigonometric series stimulated the birth of set theory. Therefore, "thermal analysis theory" has influenced the process of analytical rigor in the whole19th century.