- What controversy arose around Selberg's proof and Paul Erdős?
Famous Conjectures and Proofs
Landmark problems and their eventual proofs in mathematics.
- How is the Sierpiński triangle constructed, and why does it enclose zero area despite infinite perimeter?
- What areas of mathematics did Sierpiński contribute to across his prolific career?
- How did Sierpiński's career survive the destruction of Warsaw and two world wars?
- What is the 'large sieve' technique Enrico Bombieri used to study the distribution of prime numbers?
- What gap was discovered in Wiles's original proof, and how did he eventually fix it?
- How long is the complete proof of Fermat's Last Theorem, and what does that suggest about Fermat's original claim?
- What mathematical tools did Andrew Wiles combine to finally prove Fermat's Last Theorem?
- What was the gap discovered in Wiles's original 1993 proof, and how was it fixed?
- How did Paul Erdős live and work without a fixed home, and what did he mean by 'my brain is open'?
- How many papers and collaborators did Erdős accumulate over his career?
- What is the Erdős number, and how is it used to measure a mathematician's collaborative distance from him?
- Why did Andrew Wiles receive a special silver plaque rather than a Fields Medal at the 1998 ceremony?
- How did Grigori Perelman use Ricci flow and a surgery procedure to overcome the obstacle that had stopped Richard Hamilton?
- Why did Perelman decline both the Fields Medal and the Clay Millennium Prize money?
- Why is the Poincaré conjecture the only Millennium Prize Problem solved to date?
- What did Grigori Perelman prove using Richard Hamilton's Ricci flow technique?
- Why did Perelman decline both the Fields Medal and the Clay Millennium Prize?
- What is optimal transport theory, and how did Alessio Figalli advance it?
- How did Gerd Faltings's 1983 proof use tools from arithmetic geometry that number theorists hadn't previously combined?