Leopold Kronecker (1823-1891) was a German mathematician who made significant contributions to number theory and algebraic geometry. He is known for developing Kronecker’s theorem, which states that any algebraic number is a root of a polynomial equation with integer coefficients. Kronecker also worked on elliptic functions, group theory, and the theory of algebraic equations.
John Wallis (1616-1703) was an English mathematician who made significant contributions to algebra, geometry, and calculus. He is known for his work on infinite series, including the famous Wallis product for pi, which he derived in 1655. Wallis also worked on the development of calculus, and his work on the subject included the first systematic use of symbols for differentiation and integration.
In addition to his mathematical work, Wallis was also a prominent theologian and served as Savilian Professor of Geometry at Oxford University. Kronecker, on the other hand, was a contemporary of mathematicians like Karl Weierstrass and Ernst Kummer, and was a member of the Berlin Academy of Sciences.
Both Kronecker and Wallis made significant contributions to the field of mathematics and are remembered today for their important work in the subject.
Leopold Kronecker and John Wallis had different views on the concept of infinity, which reflected their different approaches to mathematics.
Kronecker was known for his constructivist view of mathematics, which held that mathematical objects should be constructed from basic concepts and operations rather than simply assumed to exist. In the case of infinity, Kronecker was skeptical of its use in mathematics, arguing that it was only a useful concept if it could be explicitly constructed in terms of finite operations. He famously stated that “God created the integers, all else is the work of man”, suggesting that the infinite was not a natural concept in mathematics.
On the other hand, Wallis was known for his more classical view of mathematics, which held that mathematical objects existed independently of human constructions. In the case of infinity, Wallis argued that it was a legitimate concept that could be used to describe actual mathematical objects such as infinite series and curves. He believed that infinity was a natural and necessary concept in mathematics and that it played an important role in the development of calculus.
The different views of Kronecker and Wallis on the concept of infinity reflect a broader debate in the philosophy of mathematics between constructivists and classical mathematicians. While Kronecker’s constructivist approach has gained some traction in modern mathematics, Wallis’ classical approach remains dominant and the concept of infinity continues to be an important tool in mathematical research.
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