Constance Reid’s Hilbert is an outstanding biography of David Hilbert, widely regarded as the greatest mathematician of his era, second only to his senior, Henri Poincaré. Reid blends historical depth with clear chronological narration, making the story engaging and easy to follow, though the mathematical ideas are still tough to grasp and hard to picture for anyone without a specialist background.
Born in 1862 in East Prussia, David Hilbert pursued a distinguished academic career. After earning his PhD, he moved between various German institutions, as was customary in his field, before establishing himself in Göttingen, where he spent the majority of his professional life. At the time, Europe stood at the heart of scientific and philosophical progress, with countries such as Germany, England and France, and cities like Göttingen, Copenhagen and Cambridge leading the way in academic development.
Early in his career, David Hilbert resolved the Invariant Problem, also known as Gordon’s Problem, and soon after produced a new proof of the transcendence of the numbers e and π. These achievements quickly established his reputation among his peers as a mathematician of great promise. Further breakthroughs followed across diverse areas of mathematics, including his work on the Dirichlet Principle and Euclidean Geometry.
Highly respected within the academic community, David Hilbert was invited to deliver a keynote address at the International Congress of Mathematicians in Paris in 1900. In this historic lecture, he not only gave an inspiring speech but also presented a list of 23 problems that would shape the course of mathematics in the century to come. His aim was to propose challenges that were both difficult and meaningful, capable of driving scientific progress as they were solved. Many of the problems from his famous list, such as the proof of the Riemann Hypothesis, remain unsolved even today, more than a century later, despite tremendous scientific and technological progress.
This period was likely the height of Hilbert’s career. In his personal life, he enjoyed close friendships with brilliant contemporaries such as Hermann Minkowski, but he also endured difficulties in his relationship with his only son, who suffered from mental illness.
Minkowski’s family escaped anti-Semitism in the Russian Empire and settled in Germany during his childhood. A prodigy, he won international recognition at just 18, receiving a Grand Prix in Paris for his solution to the problem of expressing an integer as the sum of five squares. His curiosity extended beyond mathematics into experimental physics: he collaborated with Heinrich Hertz on problems of electricity and later taught a young Albert Einstein in Zurich. Moving freely between mathematics and physics, Minkowski introduced a geometric approach to number theory and played a pivotal role in the early development of relativity, when the theory was still taking shape. His brilliant career was cut short when he died of appendicitis in his mid-forties.
A few years after the death of his close friend, Germany became embroiled in the First World War and was left devastated afterward by inflation and economic hardship. The interwar period saw the rise of Nazism and a decline in Hilbert’s health. During this time, he lost many close friends and collaborators, some of whom fled to the United States, while others were captured or killed. Hilbert himself passed away in the midst of the Second World War.
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