Math Scholar

Credit: NASA Goddard Space Flight Center

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The standard model of mathematical physics

The standard model, namely the framework of laws at the foundation of modern mathematical physics, has reigned supreme since the 1970s, having been confirmed to great precision in a vast array of experimental tests. Among other things, the standard model predicted the existence of the Higgs boson, which was experimentally discovered in 2012, nearly 50 years after it was first predicted.

Yet physicists have recognized for many years that the standard model cannot be the final answer. For example, quantum theory and

Continue reading The “Hubble tension”: A growing crisis in cosmology

Credit: Valentin Tkach for Quanta Magazine

Computer-assisted tools for research mathematics

In a previous Math Scholar article, we highlighted some recent developments in sophisticated computer tools being applied to the enterprise of research mathematics. These tools include:

Typesetting tools (usually LaTeX), combined with tools such as MathJax for embedding typeset mathematics into web pages. Collaboration tools such as blogs, FaceTime, Skype, Zoom, Slack and Microsoft Teams to facilitate communication and collaboration between researchers. Symbolic mathematical software such as Mathematica, Maple and Sage to perform increasingly powerful symbolic manipulations and derivations, and to generate graphics illustrating results. Custom-written code, often

Continue reading Terence Tao’s vision of AI assistants in research mathematics