David Hilbert’s Contribution to Mathematics and Biography

David Hilbert’s biography includes his early life, education, career, personal life and ending days. He first started as a lecturer at the University of Königsberg at the beginning of his career. He taught for nine years as a professor and then moved to the University of Göttingen, where he was a professor till he retired. David Hilbert’s contribution to mathematics began with the Finite Basis theorem, which he proved for any number of variables. From there, he went on to prove the algebraic number theory which is one of David Hilbert’s inventions in an illustrious career in mathematics and physics. The motivating words to all the scientists after him, ‘We must know, we will know,’ were the famous words spoken by David Hilbert. David Hilbert’s contribution to mathematics includes the 21 axioms in geometry, the Basis Theorem, The Algebraic Number Theory and the Hilbert Space Theory.

David Hilbert’s Biography

The Biography of David Hilbert begins with his birth on January 23, 1862, in a place called Königsberg, Prussia. He was a son of a legal Judge, Otto and Maria, a mathematician cum astronomer. He began his studies at the high school called Friedrichskollegium Gymnasium at the age of eight. He then enrolled for his doctorate degree and received his PhD at the University of Königsberg. He began his career by beginning to teach mathematics there in 1886. From 1895 he went on to teach at the University of Göttingen. He married Kathe Jerosch in 1892, and they had a son named Franz Hilbert. He then had the opportunity in 1902 to be the co-editor of the Mathematische Annalen journal. David Hilbert’s contribution to mathematics was vast and is written in books like Grundlagen der Mathematik and Principles of Mathematical Logic. Though most of David Hilbert’s inventions were in Mathematics, some physics-related work like gravitational field equations was also done by him. 

List of David Hilbert’s Contributions to Mathematics

Some of David Hilbert’s contribution to mathematics is listed as follows. 

• Proving the Basis Theorem
• 2D and 3D geometrical axioms
• 23 mathematical problems
• Algebraic number theory
• Epsilon calculus

Hilbert’s Finiteness Theorem 

The Basis Theorem is one of David Hilbert’s inventions, in which he proved that a finite generator set existed. He invented a completely new strategy to prove that the basis theorem was true for any number of variables. Even though there was a method of splitting equations into a number of finite possible equations, they could be used again to make up the original equations.  

Hilbert’s 2D and 3D Geometrical Axioms

In the narration of David Hilbert’s biography, the combination of the 2D and 3D geometrical axioms into a single system is worth mentioning. 21 axioms were proposed by Hilbert and well explained in the book Grundlagen der Geometrie. This was written in the year 1899, in which a geometrical setting was formed for the axioms. It led to the inculcation of the axiomatic perspective to mathematics in the entire next century. The traditional Euclid’s axioms were replaced by Hilbert’s axioms, followed by the completeness axiom, which was added later by Hilbert. The conformity of angles, line segments or parallelism between pairs of points and congruence between points, planes and lines interchangeably is discussed in detail. Hilbert brings together Euclid’s plane and solid geometry into one system. 

Hilbert’s list of 23 Mathematical Problems 

The 23 mathematical problems enlisted by Hilbert were the challenges faced in the field. The open problems were compiled by Hilbert and are some of the best well-thought problems ever. Even though most of the problems have been solved since then, some problems like the Riemann Hypothesis, the theorem extension problem by Kronecker-Weber and the geometry of curves and other algebraic surfaces remain to be deciphered. 

The Hilbert Space Concept

Amongst David Hilbert’s inventions, the Hilbert Space concept cannot go missing as it is used extensively in various physics-related fields. Quantum mechanics, functional analysis, and mathematical analysis are some of the areas which use the Hilbert space concept. The number of dimensions in finite or infinite spaces could be explained by using calculus and vector algebra. 

The use of pre-logical symbols explains another concept known as Hilbert’s formalism. This is a system that can be brought together in the form of strings or forms of axioms and changed by the set of interference rules. 

Conclusion

The David Hilbert biography accounts how he retired in the year 1930 in the absence of his beloved friends who fled Göttingen. He openly refuted the ‘Ignoramibus principle’ of that age, which meant that humans would never fully know some truths. He later died in 1943 at the age of 81. His famous words have been etched on his tombstone ‘We must know, we will know. Even though David Hilbert was one of the best mathematicians of his time and beyond, he could not prove some of the 23 mathematical problems he himself had formulated.