Faraday's theoretical encyclopedia has no systematic mathematical system, which shows that his theory still lacks strict theoretical form. Maxwell decided to use his mathematical talent to make up for this defect. Enlightened and helped by his teacher william thomson, he expressed Faraday's intuitive mechanics with images in accurate mathematical form, and gave the differential relationship between current and magnetic field. 1855 published a paper on Faraday's magnetic field lines, which systematically summarized these achievements. This paper was quickly supported and praised by Faraday.