Lecture | MI 70 years
Certainty in uncertain times
- Date
- Monday 12 May 2025
- Time
- Address
-
Gorlaeus Building
Einsteinweg 55
2333 CC Leiden - Room
- CM1.26
On 12 May we celebrate women in mathematics. The goal of the day is to inspire women everywhere to celebrate their achievements in mathematics, and to encourage an open, welcoming and inclusive work environment for everybody. This year, which is also the 70th birthday of the Leiden University Mathematical Institute, we mark this day with a public lecture by prof. dr. Eva Miranda on certainty in uncertain times.
Programme
17.00: Take a seat
17.15: Certainty in uncertain times
18.15: Drinks
All students and staff are invited and encouraged to join!
Abstract
Will the 2024 YR4 asteroid strike Earth? Science’s answer: highly unlikely. While there’s a faint chance it could make a dramatic arrival on Christmas Eve 2032, the probability remains extremely low. Despite our reliance on mathematics and physics for precise predictions, history warns us that certainty is elusive.
At the dawn of the 20th century, David Hilbert envisioned a world where uncertainty would be conquered by pure reason. But as the century unfolded, this dream unraveled. Alan Turing laid the foundations of modern computing and logic with his proof of the undecidability of the halting problem, revealing an uncomfortable truth: some questions are inherently unanswerable.
Chaos theory warns us that even the slightest imprecision in measurement can spiral into wildly unpredictable outcomes over time. This classical chaos appears in celestial mechanics, where we discover a universe far less predictable than Newton had imagined. Modern chaos theory, reveals that deterministic systems—such as planetary motion—can exhibit extreme sensitivity to initial conditions, making long-term predictions practically impossible.
But beyond classical chaos lies something even more unsettling—logical chaos. Some systems are not just sensitive to initial conditions but fundamentally undecidable. In 2021, in collaboration with Robert Cardona, Daniel Peralta-Salas, and Francisco Presas, I proved the existence of undecidable fluid paths—trajectories so complex that no logical framework can determine whether they will ever reach a given region. And what of the cosmos? Could similar undecidable phenomena exist in celestial mechanics? Are there cosmic events so complex that no theory, no supercomputer will ever decipher them?
About the speaker
Eva Miranda is a Full Professor at UPC and a leading expert in Differential Geometry, Mathematical Physics, and Dynamical Systems. Recognised with two consecutive ICREA Academia Awards (2016, 2021), she has also received prestigious honours such as the François Deruyts Prize from the Royal Academy of Belgium and the Bessel Prize from the Alexander von Humboldt Foundation. In 2023, she was named the London Mathematical Society Hardy Lecturer, delivering a nine-stop lecture tour across the UK.
Currently the director of the Laboratory of Geometry and Dynamical Systems and leader of the GEOMVAP research group, Prof. Miranda has recently co-founded the SYMCREA excellence unit. Her research spans Symplectic and Poisson Geometry, Hamiltonian Dynamics, and Geometric Quantization, with a focus on b-Poisson manifolds and their applications in Celestial Mechanics and Fluid Dynamics.
In 2025, Prof. Miranda will hold distinguished positions as the Gauss Professor at the University of Göttingen and Nachdiplom Lecturer at ETH Zurich.