The second mathematical crisis refers to 17 and 18 century, when calculus was born, a debate about the basic definition of calculus. This crisis finally perfected the definition of calculus and the theoretical system related to real numbers, basically solved the continuity problem of infinite calculation in the first mathematical crisis, and pushed the application of calculus to all disciplines related to mathematics.
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The origin of that third mathematic crisis
After the first and second mathematical crises, people attributed the non-contradiction of the basic theory of mathematics to the non-contradiction of set theory, which has become the logical basis of the whole modern mathematics, even though the grand building of mathematics has been built. Set theory does not seem to be contradictory, and the goal of strict mathematics is about to be realized.
The famous French mathematician Poincare (1854- 19 12) boasted at the international congress of mathematicians held in Paris in 1900: "Now it can be said that it has reached the absolute rigor."
However, less than two years later, the famous British mathematical logician and philosopher Russell (1872- 1970) announced an amazing news: set theory is self-contradictory and has no absolute rigor! History is called "Russell Paradox".
19 18, Russell extended this paradox and called it "barber paradox". The discovery of Russell's paradox is tantamount to breaking the fog in a sunny day and waking people up from their dreams. Russell paradox and other paradoxes in set theory go deep into the theoretical basis of set theory, thus fundamentally endangering the certainty and rigor of the whole mathematical system. So it caused an uproar in the fields of mathematics and logic, and formed the third crisis in the history of mathematics.
Baidu Encyclopedia-The First Mathematical Crisis
Baidu Encyclopedia-The Second Mathematical Crisis
Baidu Encyclopedia-Mathematical Crisis