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Are old mathematicians useless? - mklabgr - 09-15-2026
Albrecht Pietsch’s article “Are old mathematicians useless?” challenges G. H. Hardy’s famous claim that mathematics is essentially a “young man’s game” and that major original advances rarely come after age 50. Pietsch argues that such an age limit is unjustified. He gives numerous counterexamples of mathematicians who produced important work well after 50, including Poincaré, Cartan, Schwartz, Calabi, Atiyah, Erdős, and others. Particularly striking is the range of achievements he lists: major results were produced at ages 58, 62, 69, 72, 78 and beyond, while Louis Vietoris published a paper at 103. The evidence therefore suggests that although mathematical productivity may peak relatively early for many researchers, exceptional creativity and substantial contributions can continue throughout old age.
Pietsch then makes the argument personal, describing his own “second mathematical life.” He continued developing new mathematics decades after beginning his career, including work submitted at ages 82 and 89. His broader message is that mathematical research should not be viewed solely as a competition for youthful breakthroughs: curiosity, enjoyment, experience, and love of mathematics can remain valuable throughout life.
At the same time, he acknowledges that some older mathematicians may lose enthusiasm or mental energy and should decide individually whether to continue. Even when active research becomes difficult, however, senior mathematicians have an important role in transmitting knowledge, ideas, open problems, and experience to younger generations. His final appeal is therefore not to impose an age-based notion of usefulness, but to respect and appreciate the contributions of mathematicians at every stage of their careers.
ARTICLE [PDF]