International Maths Challenge

  Whether it’s physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to stochastics—an area of mathematics which deals with probabilities—this is even possible when randomness plays a role in these processes. Something researchers have been working on for some decades now are so-called stochastic partial differential equations. Working together with other researchers, Dr. Markus Tempelmayr at the Cluster of Excellence Mathematics Münster at the University of Münster has found a method which helps to solve a certain class of such equations. The results have been published in the journal  Inventiones mathematicae . The basis for their work is a theory by Prof. Martin Hairer, recipient of the Fields Medal, developed in 2014 with international colleagues. It is seen as a great breakthrough in the research field of singular stochastic partial differential equ...

  What does “equals” mean? For mathematicians, this simple question has more than one answer, which is causing issues when it comes to using computers to check proofs. The solution might be to tear up the foundations of maths. When you see “2 + 2 = 4”, what does “=” mean? It turns out that’s a complicated question, because mathematicians can’t agree on the definition of what makes two things equal. While this argument has been quietly simmering for decades, a recent push to make mathematical proofs checkable by computer programs, called formalisation, has given the argument new significance. “Mathematicians use equality to mean two different things, and I was fine with that,” says Kevin Buzzard at Imperial College London. “Then I started doing maths on a computer.” Working with computer proof assistants made him realise that mathematicians must now confront what was, until recently, a useful ambiguity, he says – and it could force them to completely redefine the foun...

  Researchers at The University of Western Australia’s ARC Industrial Transformation Research Hub for Transforming Energy Infrastructure through Digital Engineering (TIDE) have made a significant mathematical breakthrough that could help transform ocean research and technology. Research Fellow Dr. Lachlan Astfalck, from UWA’s School of Physics, Mathematics and Computing, and his team developed a new method for spectral density estimation, addressing long-standing biases and paving the way for more accurate oceanographic studies. The study was published in the journal Biometrika, known for its emphasis on original methodological and theoretical contributions of direct or potential value in applications. “Understanding the ocean is crucial for numerous fields, including offshore engineering, climate assessment and modeling, renewable technologies, defense and transport,” Dr. Astfalck said. “Our new method allows researchers and industry professionals to advance ocean t...