Born: 1 July 1646 · Leipzig, Electorate of Saxony, Holy Roman Empire

Died: 14 November 1716 (aged 70) · Hanover, Electorate of Hanover, Holy Roman Empire

Education: Alte Nikolaischule · Leipzig University (BA, 1662; MA, 1664; LLB, 1665; Dr. phil. hab., 1666) · University of Jena (1663) · University of Altdorf (Dr. jur., 1666)

Era17th-/18th-century philosophy

Region: Western philosophy

School: Rationalism · Pluralistic idealism · Foundationalism · Conceptualism · Optimism · Indirect realism · Correspondence theory of truth · Relationalism

Theses De Arte Combinatoria (On the Combinatorial Art) (March 1666) · Disputatio Inauguralis de Casibus Perplexis in Jure (Inaugural Disputation on Ambiguous Legal Cases) (November 1666)

Doctoral advisor: Bartholomäus Leonhard von Schwendendörffer (Dr. jur. thesis advisor)

Major contributions of Gottfried Wilhelm Leibniz  include:

• Developed differential and integral calculus independently of Sir Isaac Newton.

• Introduced the Transcendental Law of Homogeneity and the Law of Continuity.

• Invented binary arithmetic, the representational basis for today's digital computing.

• Developed a system of infinitesimal calculus.

Problem/events that influence Gottfried Wilhelm Leibniz's mathematical ideas:

Gottfried Wilhelm Leibniz’s mathematical ideas were shaped by a blend of intellectual pursuits, personal experiences, and the broader intellectual climate of the 17th century. Growing up in a scholarly environment, Leibniz had access to a vast library of works that introduced him to mathematics, philosophy, and science at an early age. His fascination with logic and metaphysics, influenced by the works of ancient Greek philosophers like Aristotle, laid the foundation for his later efforts to formalize mathematical reasoning.

Leibniz’s travels and interactions with prominent scientists and mathematicians of his time were pivotal in shaping his ideas. During a visit to Paris, he studied under the mathematician Christiaan Huygens, who encouraged him to delve deeper into advanced mathematics. This mentorship sparked Leibniz’s interest in the study of infinitesimals, leading him to independently develop calculus—a monumental achievement in mathematics. The challenges of solving problems in physics, mechanics, and geometry further drove Leibniz to innovate.

The intellectual rivalry between Leibniz and Isaac Newton, particularly regarding the development of calculus, also influenced his work. While both mathematicians arrived at calculus independently, their different notational systems and methods became a lasting influence on mathematics, with Leibniz’s notation proving to be more widely adopted due to its clarity and practicality.

Leibniz was also deeply inspired by his vision of a universal mathematical language, or "characteristica universalis," which he believed could unify all fields of knowledge. This ambition guided his exploration of combinatorics, binary arithmetic, and symbolic logic, laying the groundwork for modern computational mathematics. The interplay between philosophical ideals, academic mentorship, and the scientific challenges of his era significantly shaped Leibniz’s mathematical legacy.

His Impact on the modern mathematics: 

Gottfried Wilhelm Leibniz made a lasting impact on modern mathematics, particularly through his independent development of calculus. His clear and practical notation, such as ∫\int for integration and dd for differentiation, remains widely used today, simplifying complex calculations in fields like physics, engineering, economics, and biology. These tools are essential for analyzing change and optimizing systems across various disciplines.

Beyond calculus, Leibniz’s work in symbolic logic and combinatorics helped lay the groundwork for modern computer science, influencing the development of algorithms, programming, and artificial intelligence. His early exploration of binary arithmetic—using only 0s and 1s—was ahead of its time and became a fundamental concept in digital computing.

Leibniz’s vision of a universal mathematical language inspired efforts to formalize mathematics and integrate scientific disciplines. This idea significantly influenced later advancements in mathematical logic and computation, including the work of George Boole and Alan Turing. Leibniz’s belief in using mathematics to solve practical problems and connect fields of knowledge continues to shape the way mathematics is applied today, securing his place as a key figure in its evolution.