Winning the Fields Medal can make a mathematician part of the establishment, leading to increased expectations and responsibilities, which can constrain their freedom to explore and innovate.

While the Fields Medal can inspire young mathematicians, it's important to respect those like Grigori Perelman, who prioritize their principles over recognition and awards.

The mathematical community is a collective intelligence that surpasses any individual mathematician, as seen in collaborative platforms like MathOverflow, where diverse expertise contributes to solving complex problems.

Alan Turing and Kurt Gödel are connected through their groundbreaking work in mathematics and computer science, both exploring the limits of what can be proven or computed.

Mathematics is about finding connections between different fields, and this process has been ongoing throughout history, such as the unification of geometry and number theory.

When physicists need mathematics, they often rely on precursors developed by mathematicians, as seen when Einstein sought help from mathematicians for curved space.

The theories that explain the universe often involve the same mathematical objects that solve mathematical problems, indicating a deep connection between the two fields.

The beauty of mathematics often lies in its simplicity, as seen in elegant equations like Euler's identity, which connects fundamental constants.

I started my research in mathematics in Vienna, focusing on partial differential equations, which model various natural phenomena in physics and biology.