Ocean Waves: Unstable Islands of Mathematical Complexity

Resources

Resources & Recommendations

Books

• "Computer-Assisted Proofs" by Doron Zeilberger - A book on computer proofs, referenced as a resource for solving a complex mathematical problem.

Research & Studies

• "The hidden math of ocean waves crashes into view" by Joe Howlett (Quanta Magazine) - This article explores the mathematical challenges in understanding wave dynamics, even for the simplest wave patterns.
• Paper by Bernard Deconinck and Katie Oliveras - This paper was the first to identify and plot the full structure of instabilities on Stokes waves through numerical simulations.
• Paper by Massimiliano Berti, Alberto Maspero, Paolo Ventura, and Livia Corsi - This paper provided a rigorous mathematical proof for the instabilities observed in Stokes waves, building on the numerical simulations.

People Mentioned

• Joe Howlett (Math writer for Quanta Magazine) - Discussed his article on the hidden math of ocean waves.
• Leonhard Euler (Swiss mathematician, 1700s) - Developed the Euler equations that describe the motion of fluids.
• Sir George Stokes (Mathematician) - Proposed the concept of Stokes waves as a simple type of wave solution to Euler's equations.
• T. Brooke Benjamin (Applied Mathematician) - Advised his student Jim Feir to observe waves in a wave tank, leading to the discovery of wave instabilities.
• Jim Feir (Student of T. Brooke Benjamin) - His laboratory experiments first revealed the instability of Stokes waves.
• Bernard Deconinck (Applied Mathematician at the University of Washington) - Conducted computer simulations of wave instabilities with Katie Oliveras and later approached Massimiliano Berti about the problem.
• Katie Oliveras (Applied Mathematician, Seattle University) - Noticed the unusual pattern of instabilities in Stokes waves during her PhD research with Bernard Deconinck.
• Massimiliano Berti (Pure Mathematician, Italian) - Led a group of Italian mathematicians to rigorously prove the observed wave instabilities.
• Alberto Maspero (Italian Mathematician) - Collaborated with Massimiliano Berti on the rigorous proof of wave instabilities.
• Paolo Ventura (Italian Mathematician) - Collaborated with Massimiliano Berti on the rigorous proof of wave instabilities.
• Livia Corsi (Italian Mathematician) - Collaborated with Massimiliano Berti on the rigorous proof of wave instabilities.
• Doron Zeilberger (Author, Rutgers) - Helped with the computational aspect of the proof for wave instabilities, offering a reward for its completion.
• Christoph Koutschan (Expert in computer algebra) - Helped complete the computational aspect of the proof.
• Marc van Hoeij (Expert in computer algebra) - Helped complete the computational aspect of the proof.
• Alberto Boffa (Researcher) - Observes waves from his window in Trieste, Italy, and connects them to the instability of Stokes waves.

Organizations & Institutions

• Quanta Magazine - The publication that hosts the podcast and publishes articles on fundamental science and math.
• University of Washington - Affiliation of Bernard Deconinck.
• Seattle University - Affiliation of Katie Oliveras.
• Rutgers - Affiliation of Doron Zeilberger.
• Online Encyclopedia of Integer Sequences - A non-profit math website to which Doron Zeilberger offered a donation for solving a mathematical problem.

Websites & Online Resources

• Online Encyclopedia of Integer Sequences - A non-profit math website mentioned by Doron Zeilberger.
• Doron Zeilberger's website - Where he posted about his challenge regarding the infinite sum problem.

Other Resources

• "The Mary Golden Tree" by The Shovel Dance Collective - An old English sea shanty, recommended for its rhythmic and beautiful nature, reminiscent of ocean waves.
• The Shovel Dance Collective's record - The entire record is recommended for its traditional music.