Date and time: 30 June 2025, 19:00
Location: Residencia de Estudiantes (Calle de Pinar, 21-23, 28006 Madrid)
Summary:
There are several well-known—and extremely difficult—conjectures about prime numbers in mathematics: Can every even number greater than two be written as the sum of two primes? (Goldbach’s conjecture); Is there an infinite number of ‘twin’ primes, such as 5 and 7, 11 and 13, or 2027 and 2029? (the twin prime conjecture); If a number has an even or odd number of prime factors, does that affect how many prime factors the two following numbers have? Far from being mere curiosities, these conjectures allow us to explore deep questions about the integers—and about their “atoms,” the prime numbers. What lies beneath these conjectures is the idea that primes and integers seem to follow relatively simple random models, but proving this is extremely difficult.
About the speaker
Harald Helfgott is one of the world’s leading experts on Goldbach’s conjecture. In 2013, he proved the weak version of the conjecture (which states that every odd number can be written as the sum of three primes), a problem open since the 18th century, first approached by G. H. Hardy and J. E. Littlewood, and later by Ivan Vinogradov in the early 20th century. Helfgott is a principal researcher at the CNRS, affiliated with the Institut de Mathématiques de Jussieu (at the University of Paris VI/VII). His research interests include number theory, group theory, discrete mathematics, and other topics.