
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
Model of human nuclear pore complex, built using AlphaFold2; credit: Agnieszka ObarskaKosinska, Nature
AlphaFold 2: A breakthrough in computational protein folding
The 2024 Nobel Prize in Chemistry has been awarded to David Baker of the University of Washington and to Demis Hassabis and John Jumper of Google DeepMind. Hassabis and Jumper, now at the Google DeepMind Research Center in the U.K. (a subsidiary of Alphabet, Google’s parent company), developed an artificial intelligencebased software package that predicts with remarkable accuracy the structure of proteins. Baker, now at the University of Washington in Seattle, was recognized for his work on designing
Continue reading 2024 Nobel Prize in Chemistry awarded to computational protein folding pioneers
Credit: Valentin Tkach for Quanta Magazine
Computerassisted 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. Customwritten code, often
Continue reading Terence Tao’s vision of AI assistants in research mathematics
Updated 24 September 2024 (c) 2024
Credit: Walker, Packer, Cody, “Reconceptualizing the origins of life,” https://royalsocietypublishing.org/doi/10.1098/rsta.2016.0337
Introduction
In the past few decades, modern science has uncovered a universe that is far vaster and more aweinspiring than ever imagined before, together with a set of elegant natural laws that deeply resonate with the idea of a cosmic lawgiver. In spite of these exhilarating developments, some writers, principally of the creationist and intelligent design communities, prefer a highly combative approach to science, particularly to geology and evolution.
In addition to citing deeply flawed probabilitybased arguments (see Probability), these evolution skeptics
Continue reading New developments in the origin of life on Earth
Credit: Mykal McEldowney, The Indianapolis Star/ USA TODAY Network
What do American Olympic swimmers Kate Douglass, Gretchen Walsh and Paige Madden, French goldmedalist Leon Marchand, and Australian Olympian Kyle Chambers have in common? In their training, these five leading swimmers and numerous others have employed (and, in the case of Douglass, personally helped develop) advanced data science and physics techniques to finetune their athletic performance.
Many of these top swimmers, who have traditionally relied on their “feel” in the water, now employ accelerometers strapped to their bodies, measuring movements in 3D up to 512 times per second, thus capturing
Continue reading Data science and physics give Olympic swimmers the edge
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Optimal stacking of oranges.
Computer tools in mathematics: From foot dragging to full embrace
The present author recalls, while in graduate school at Stanford nearly 50 years ago, hearing two senior mathematicians (including the present author’s advisor) briefly discuss some other researcher’s usage of computation in a mathematical investigation. Their comments and body language clearly indicated a profound disdain for such efforts. Indeed, the prevailing mindset at the time was “real mathematicians don’t compute.”
Some researchers at the time attempted to draw more attention to the potential of computer tools in mathematics. In the
Continue reading Computation, AI and the future of mathematics
Yes, Pi Day (March 14), that day of mathematical trivia and pieeating, is almost here again.
As is the custom on this site, we present below a crossword puzzle constructed on a theme of mathematics, computing and the digits of pi. Enjoy!
This puzzle has been constructed in conformance with New York Times crossword puzzle standards. In terms of overall difficulty, my mathematician daughter and my genealogist spouse agreed that it would likely rate as a Tuesday (the New York Times grades its puzzles, with Monday puzzles being the easiest and Saturday puzzles being the most challenging).
Continue reading Pi Day 2024 crossword puzzle
Johann Sebastian Bach; credit Wikimedia
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Bach as “mathematician”
Johan Sebastian Bach (16851750) regularly garners the top spot in listings of the greatest Western classical composers, typically followed by Mozart and Beethoven. Certainly in terms of sheer volume of compositions, Bach reigns supreme. The BachWerkeVerzeichnis (BWV) catalogue lists 1128 compositions, from short solo pieces to the magnificent Mass in B Minor (BWV 232) and Christmas Oratorio (BWV 248), far more than any other classical composer. Further, Bach’s clever, syncopated style led the way to twentieth century musical innovations, notably jazz.
There does seem to be a
Continue reading Using network theory to analyze Bach’s music
History of measurements of the speed of light; from Henrion and Fischloff, “Assessing uncertainty in physical constants,” American Journal of Physics, September 1986
Reproducibility in modern science
Reproducibility has emerged as a major issue in numerous fields of scientific research, ranging from psychology, sociology, economics and finance to biomedicine, scientific computing and physics. Many of these difficulties arise from experimenter bias (also known as “selection bias”): consciously or unconsciously excluding, ignoring or adjusting certain data that do not seem to be in agreement with one’s preconceived hypothesis; or devising statistical tests posthoc, namely AFTER data has already been
Continue reading Overcoming experimenter bias in scientific research
The CRISPRCas9 editing system (artistâ€™s impression) for experimental treatments. Credit: Biolution GmbH/Science Photo Library; see https://www.nature.com/articles/d41586023037977
In today’s world, there is certainly no shortage of troubling news: fullscale war in Ukraine and Gaza; simmering conflicts in Sudan, Myanmar, Niger, Afghanistan, Colombia and Somalia; wildfires, droughts and floods connected to humaninduced climate change, which world governments have been deplorably slow to address; outbreaks of Covid19, malaria, RSV and other diseases; hunger and poverty afflicting millions worldwide; a troubling receptiveness for autocracy; continuing sexism, racism and xenophobia; and large numbers of people embracing utterly discredited pseudoscientific conspiracy theories (“your Zodiac sign holds
Continue reading Progress in troubled times: Good news in science, medicine and society

