In 1890, Russell was admitted to Trinity College, Cambridge University, where he studied mathematics, philosophy and economics. His mathematics teacher Whitehead appreciated his talent very much and introduced him to MacTagor, then a philosophy lecturer at Cambridge University, and Moore, who later became a great philosopher. Russell graduated with a bachelor's degree in mathematics in 1893, before switching to philosophy in his fourth year and graduating with a bachelor's degree in ethical sciences. He hesitated to choose philosophy or economics as a career but ultimately chose the former, writing a fellowship thesis on non-Euclidean geometry, a successful thesis that earned him a six-year fellowship at Trinity College. researcher qualifications. He endeavored to track the development of the new physics until at least the early 1930s.

In 1894, despite the opposition of his family, Russell married the American girl Alose Polsas Smith, who was five years older than him. In the third year after his marriage, he and his wife went to Berlin, where they studied economics and political science, carefully read Marx's "Das Kapital", interacted with German labor movement leaders such as Bebel and Liebknecht, and participated in Workers' rally. The results of Russell's activities were reflected in the book "Social Democracy in Germany" published in 1896. The following year he published On the Foundations of Geometry, based on his fellowship thesis.

In July 1900, Russell met the Italian logician Peano at the International Philosophical Conference in Paris, and found in Peano's mathematical logic system the "idea for logical analysis" that he had been seeking for many years. "Tools", thus opening his eyes to the technical possibility of reducing mathematics to logic. Russell improved Peano's technique and then turned to work on basic concepts in analytic mathematics. For several months, he was at his intellectual peak, with inspiration flowing like a fountain, and new discoveries and gains every day. Russell completed the first draft of "The Principies of Mathematics" at the end of that year. After careful revision, it was published in 1903. This work is still a milestone in the history of the development of basic mathematics research. After this, Russell and Whitehead collaborated on Principia Mathematica. Russell was mainly responsible for the philosophical content, and Whitehead was mainly responsible for the mathematical content. They exchanged drafts with each other and revised them together. The great results of his work were divided into three volumes and published in 1910, 1912 and 1913 respectively. This work is a major achievement of science in the 20th century. It is hailed as "one of the highest achievements of the human mind" and won Russell a high academic status and honor.

During this period, Russell did not neglect other aspects of philosophy. He published the title "On Denotation" in the magazine "Mind" in 1905. This article indeed came from his research on logic and laid the foundation for his famous description theory. He first clarified the important difference between these two kinds of knowledge in his 1911 book "Knowledge by Knowledge and Knowledge by Descriptor". In 1912, he published "Philosophical Questions" in the "Home University Series". He was satisfied with this small work because it contained many of his basic philosophical views. In March 1914, Russell went to the United States to start classes at Harvard University and gave a series of lectures for the Nowell Lectures. His lecture was warmly received, and the text of it was published in August 1914 under the title "Our Knowledge of the External World". The book takes a thoroughly empiricist stance, placing Russell among the heirs of John Locke, Berkeley, David Hume, and John Mill.

With the outbreak of World War I, Russell's interest in philosophy was overwhelmed by his fear of the huge threat facing European civilization, and he devoted himself to writing, speaking, and organizing activities as an anti-war activist. In early 1915, he wrote an anti-war pamphlet, "The Source of Terror of War," which was quite influential. In 1916, he published an important political book, "Principles of Social Reconstruction," which put forward views that were contrary to popular views on major issues such as marriage, education, and church, and attracted widespread attention from people from all walks of life in the United Kingdom. From Britain's entry into the war in 1914 to the end of 1917, he continued to campaign for anti-war activities. He organized the Objection Committee and was found guilty by a court of law over a leaflet, for which he was dismissed from Trinity College. In 1918, he was sentenced to prison for writing an anti-war article. In prison, he completed "Introduction to Mathematical Philosophy" and began to write "Analysis of the Heart". After 1916, Russell had only a relatively short-term university career, relying mainly on writing to make a living. This was part of the reason for his prolific writings later on. In May 1920, Russell visited the Soviet Union as an informal member with the Labor Party delegation to inspect the work of the Bolshevik government. He was disappointed and even frightened by the rule of the Soviet Russian government. His views were elaborated in the book "The Theory and Practice of Bolshevism". In August of the same year, Russell was invited to give lectures in China. In October, he delivered a lecture "On Philosophy" at Nanjing University (then known as National Southeast University), advocating the use of logical reasoning and scientific methods to seek knowledge. He has great admiration for the ancient Chinese culture and appreciates the Chinese people's education and sense of humor. While in China, Russell suffered from severe malaria, so much so that the Japanese rumored that he had died. Later, these speeches of his were published under the title "Analysis of Objects".

Russell returned to England in 1921 and married Dora Black. There was a boy and a girl. His father's role made him interested in education, and he and his wife founded an experimental school. In Russell's opinion, the school was not successful and expensive to run, making it necessary for him to go to the United States to give lectures and raise money. In 1932, he divorced Dora and no longer participated in school affairs. Dora ran it alone until 1943.

From the 1920s to the 1930s, Russell wrote a large number of works on Russia, China, relativity, history, education, sexual ethics, international relations, religion and future society, the more important of which are "The Heart" Analysis" (1921), "On Education, Especially the Education of Young Children" (1926), "Analysis of Things" (1927), "Outline of Philosophy" (1927), "Collected Essays on Doubt" (1928), "Morality and Marriage" "(1929), "Education and Social Order" (1932), "Liberty and Organization" (1934), "Religion and Science" (1935), "Power: A New Social Analysis" (1938).

Although many of these activities were in part an effort to earn a living, Russell remained a tireless supporter of various political activities until, in the mid-1930s, he was tired of this life and needed to support two families (he returned in 1936). Marrying and having a child the following year), he hoped to return to university life, which was not easy because university positions were scarce and Russell was a controversial figure. In 1938, he lectured at Oxford University and then at the University of Chicago. He gained visiting positions at Los Angeles State University, and finally the City College of New York offered him a permanent position. At this time, World War II broke out, and he was trapped in the United States due to Russell's concerns about abortion, divorce, and homosexuality. Viewed as "not sufficiently orthodox," the appointment aroused opposition from the Catholic community in New York and was overturned in a famous lawsuit. Fortunately, Harvard University still insisted on the original invitation, allowing Russell to deliver the James Lecture for a year. The manuscript was published in 1940 under the title "Inquiry into Meaning and Truth"

Due to the rampant conservative forces, Russell's other lectures and travel plans fell through, and newspapers did not dare to ask him for manuscripts. This left Russell almost completely deprived of his means of livelihood and in an isolated and helpless situation. At this time, Dr. Barnes, a millionaire in Philadelphia, rescued Russell from the predicament and invited Russell to teach Western studies at the Barnes Art Foundation in Philadelphia. History of Philosophy (5 years) Although Barnes fired Russell in 1942, he solved Russell's financial problems for good, as Russell received a substantial liquidated damages and his lectures became the basis for his The basis of the hugely successful History of Western Philosophy (1945), this work was one of the main sources of his later international fame, and its royalties were the main source of income. In 1944, Russell returned to England and accepted three scholarships. His return marked not only an improvement in his relations with Trinity College, but also with the British administration. improvement. His sustained denunciation of communism in general and Soviet-style communism in particular was well suited to the Cold War era, and Russell enjoyed an unusual reputation (although he also criticized the American nuclear bomb). and censorship). In 1949 he was elected an honorary fellow of the British Academy, and in 1950 King George VI awarded him the Order of Merit, Britain's highest honor.

In 1950, Russell was invited to give a lecture tour in Australia. In addition to giving lectures in various places, he also gave speeches on television, gave courses at universities, and wrote articles for newspapers. His lectures were later compiled into the book New Hopes for a Changing World. Then, he was invited to teach philosophy in the United States. On the way to give a lecture at Princeton University, news came that the Nobel Prize Committee had awarded him the Literature Prize (the winning work was "Marriage and Morality"). The reason for awarding the prize was that Russell's "philosophical works have made a great contribution to human moral culture." contribute". Russell flew to Sweden to receive the award and delivered the award-winning speech "Political Important Aspirations". He used this important forum to call for world peace. Around the same time, he married his fourth wife.

After Stalin's death, Russell's attitude toward the Soviet government softened, and the threat of nuclear war began to dominate his thinking. What he was most concerned about in his later years was the future of mankind in a world with nuclear weapons. During the 1950s he wrote extensively about the dangers of war and increasingly felt the need for action. In 1955, he won the support of Einstein (Einstein died shortly before the letter of consent was sent) and issued the famous "Russell-Einstein Declaration" (or "Einstein-Russell Declaration") ). He also collected signatures from famous scientists from various countries and convened a world conference to discuss practical steps to take to deal with the crisis faced by the emergence of atomic weapons. Since many of the famous scientists who signed it were Nobel Prize winners, the declaration had a great impact. Later, the conference gradually evolved into the famous "Vienna Declaration".

Russell founded the Committee of 100 for Civil Disobedience in 1958 to promote nuclear disarmament. In 1961, he was imprisoned again for inciting civil disobedience.

The 1960s were a politically fraught time for Russell, who supported many causes, opposed the Vietnam War, and founded the Russell-Sartre Tribunal with Jean-Paul Sartre. In 1964, he established the Russell Peace Foundation and auctioned off part of his archives to raise funds. He published his last book, War Crimes in Vietnam, in 1967. His last political statement was on the Middle East, condemning Israeli attacks on Egypt and Palestinian refugee camps. This statement was written two days before his death (February 2, 1970), which shows that Russell was still working for the cause of world peace and the future of mankind at the end of his life.