19 questions · 12 sources · 0 syntheses
Number Theory
The study of integers and their properties.
Source-derived questions
Questions extracted from the papers in this topic, excluding the curated questions above.
- How did Alan Baker's bounds on linear forms in logarithms help decide which Diophantine equations have integer solutions?
- How did Andrew Wiles use the Taniyama-Shimura conjecture to prove Fermat's Last Theorem?
- How did Atle Selberg's elementary proof of the prime number theorem differ from earlier proofs?
- How did Gerd Faltings's 1983 proof use tools from arithmetic geometry that number theorists hadn't previously combined?
- How did Manjul Bhargava apply the geometry of numbers to questions about elliptic curves?
- How long is the complete proof of Fermat's Last Theorem, and what does that suggest about Fermat's original claim?
- What areas of mathematics did Sierpiński contribute to across his prolific career?
- What controversy arose around Selberg's proof and Paul Erdős?
- What did Fermat actually claim in his famous marginal note, and why did it go unproven for 358 years?
- What did Fermat's marginal note claim about the equation a^n + b^n = c^n?
- What did James Maynard and Maryna Viazovska each prove about prime gaps and sphere packing respectively?
- What does the Mordell conjecture claim about rational points on curves of genus greater than one?
Show 7 more questions
- What gap was discovered in Wiles's original proof, and how did he eventually fix it?
- What is a Diophantine equation, and why did Faltings's techniques become standard for studying them?
- What is higher algebraic K-theory, and how does it connect topology, algebra, and number theory?
- What is the 'large sieve' technique Enrico Bombieri used to study the distribution of prime numbers?
- What is the Langlands program, and what fields of mathematics does it try to unify?
- What question about approximating algebraic irrational numbers by fractions had been open since Liouville in 1844, and how did Roth resolve it?
- What was the gap discovered in Wiles's original 1993 proof, and how was it fixed?