Meaning: This quote by Benoit Mandelbrot, a renowned mathematician, reflects the evolution of scientific and academic trends over time. In the field of mathematics, as in many other disciplines, certain topics and theories may experience fluctuations in popularity and relevance. Mandelbrot's observation that his Ph.D. topics, once deemed unfashionable, have now become popular highlights the dynamic nature of academic pursuits and the ever-changing landscape of knowledge and research.

Benoit Mandelbrot was a visionary mathematician known for his work in fractal geometry and the concept of self-similarity in nature. He is often regarded as the father of fractal geometry, a field that explores complex and irregular shapes and patterns found in nature and art. Mandelbrot's quote likely refers to the initial reception of his ideas and research, which may have been considered unconventional or niche at the time of his Ph.D. studies.

The quote also speaks to the concept of intellectual trends and paradigms within the academic community. Throughout history, certain areas of study or specific theories have experienced fluctuations in interest and acclaim. This phenomenon is often influenced by factors such as technological advancements, cultural shifts, and the emergence of new research methodologies.

In the context of mathematics, the evolution of popular topics and areas of focus can be attributed to various factors. Advances in computing technology, for example, have enabled mathematicians to explore and visualize complex geometric patterns and structures in ways that were previously inaccessible. This has contributed to a renewed interest in fields such as fractal geometry and chaos theory, which were once considered on the fringes of mathematical research.

Moreover, the interdisciplinary nature of modern science has also played a role in reshaping the landscape of mathematical research. Concepts and theories that were once confined to specific mathematical subfields have found applications in diverse areas such as physics, biology, and finance, leading to a broader appreciation and relevance of previously "unfashionable" topics.

Mandelbrot's own contributions to the study of fractals and self-similarity have had a lasting impact on various fields, demonstrating the enduring value of pursuing unconventional or overlooked areas of research. His quote serves as a reminder that the trajectory of academic inquiry is not fixed, and that ideas once considered ahead of their time may eventually find widespread acceptance and significance.

In conclusion, Benoit Mandelbrot's quote encapsulates the dynamic nature of academic pursuits and the changing fortunes of scientific ideas. It underscores the importance of perseverance and open-mindedness in exploring diverse and unconventional areas of research, as well as the enduring relevance of ideas that may have been initially dismissed as "unfashionable." The quote also prompts reflection on the ever-shifting currents of intellectual trends and paradigms within the academic community, highlighting the need for continued adaptation and innovation in the pursuit of knowledge.