Quicksort algorithm; credit: Abhilash Kakumanu
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Introduction
The operation of sorting a dataset is one of the most fundamental of all operations studied in computer science. Literally trillions of sort operations are performed each day worldwide, more if one counts operations where a relatively small set of elements are merged into a larger set.
Many sorting algorithms are in use, including special routines for datasets of a certain size, and other routines optimized for specific hardware platforms and types of data.
One relatively simple algorithm, which is actually quite efficient, is the “quicksort” algorithm. It
Continue reading DeepMind program discovers new sorting algorithms
Is modern science socially constructed and forever tentative? Updated 20 April 2023
Introduction
Writers from the discipline known variously as “postmodern science studies” or “sociology of scientific knowledge” are often cited in discussions of science, philosophy and religion. Some of these writers, notably Karl Popper and Thomas Kuhn, have had significant impact on the field of scientific research.
Issues such as ensuring proper credit for the scientific contributions of nonWestern societies (such as the ancient mathematics of India and China — see, for example, [Bailey2012]), as well as dealing with the chronic underrepresentation of women, racial minorities and indigenous
Continue reading Is modern science socially constructed and forever tentative?
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Peter Borwein
Peter Borwein, former professor of mathematics at Simon Fraser University and director of the university’s Centre for Interdisciplinary Research in the Mathematical and Computational Sciences (IRMACS), died on August 23, 2020, at the age of 67, of pneumonia, after courageously battling multiple sclerosis for over 20 years.
The Notices of the American Mathematical Society has just published a memorial tribute, written by the present author, that summarizes Peter’s life and career. Here are a few highlights:
Peter Borwein is perhaps best known for discovering (often but not always with his brother Jonathan) new
Continue reading Peter Borwein: A visionary mathematician
So soon? Yes, it is that time of year again — PiDay (March 14) is just a few days away. In honor of this mathematical holy day, we present once again a crossword puzzle with an appropriate pirelated theme.
This year’s puzzle implements a new design for a mathematical crossword, which to the present author’s knowledge has never before been employed. See, for example, clue 40 Across below. In all respects, though, the puzzle conforms to the standards of New York Times crosswords. In terms of overall difficulty (Monday = easiest; Saturday = most difficult), this puzzle most likely would
Continue reading PiDay 2023 crossword puzzle
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ChatGPT: A milestone in artificial intelligencebased language models
Many readers have doubtless heard of ChatGPT, the latest instance of a language generation tool developed by the technology startup OpenAI. This tool, which is now available for public experimental use, takes as input a request or other statement from the user, then responds. It employs a dialogue format, which makes it possible for ChatGPT to answer followup questions, and even admit its mistakes.
It is clear, even from a cursory examination, that ChatGPT represents a rather dramatic advance in artificial intelligence. Some of the results are rather
Continue reading Can ChatGPT prove math theorems?
Credit: Wikimedia
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Introduction
Most of us learn the basic scheme for matrix multiplication in high school. What could be more simple and straightforward? Thus it may come as a surprise to some the basic scheme is not the most efficient.
German mathematician Volker Strassen was the first to show this, in 1969, by exhibiting a scheme that yields practical speedups even for moderately sized matrices. In the years since Strassen’s discovery, numerous other researchers have found even better schemes for certain specific matrix size classes. For a good overview of these methods, together with some
Continue reading Machine learning program finds new matrix multiplication algorithms
Highlevel diagram of Shor’s algorithm for factoring integers. Credit: ResearchGate; Archimedes Pavlidis
The Breakthrough Prizes
The Breakthrough Prizes are awarded annually for scientists who do groundbreaking work addressing fundamental questions in physics, mathematics, computer science and life sciences. The prizes include a stipend of US$3 million (some earlycareer awards have smaller stipends, typically US$50,000). The Breakthrough Prizes were founded by Sergey Brin (cofounder of Google, now Alphabet), Pricilla Chan, Mark Zuckerberg (cofounder of Facebook, now Meta), Yuri Milner (founder of DST Global, a global technology investor), Julia Milner, and Anne Wojcicki (founder of 23andMe, a genomics firm).
The latest
Continue reading Breakthrough Prizes honor AlphaFold and quantum computing pioneers
The 2022 recipients of the Fields Medal, arguably the highest honor in the field of research mathematics, have been announced by the International Mathematical Union, as part of the quadrennial International Congress of Mathematicians, which this year is being held in Helsinki, Finland.
This year’s award recipients are interestingly diverse. One was raised in Ukraine, and grieves over her childhood city being bombed in the current military activity; one is known for his passionately independent approach to both life and mathematics; one is very active athletically, and has often found key insights while engaged in these activities; and one
Continue reading 2022 Fields Medalists: Diverse backgrounds, breakthrough mathematics
Artificial intelligence in technology; credit: iStockmetamorworks
A brief history
The modern field of artificial intelligence (AI) arguably dates to 1950, when Alan Turing outlined the basics of AI in his paper “Computing machinery and intelligence” [Paper]. He even proposed a test, now known as the Turing test, for establishing whether true AI had been achieved. Early computer scientists were confident that true AI system would soon be a reality. In 1965 Herbert Simon wrote that “machines will be capable, within twenty years, of doing any work a man can do.” In 1970 Marvin Minsky declared, “In from three to
Continue reading Advances in artificial intelligence raise major questions
Delicate Arch at night; credit: Astronomy.com
Updated 12 June 2023 (c) 2023
Introduction
In 1950, while having lunch with colleagues Edward Teller and Herbert York, who were chatting about a recent cartoon in the New Yorker depicting aliens, physicist Enrico Fermi suddenly blurted out, “Where is everybody?,” a question now known as Fermi’s paradox. This article presents background on Fermi’s paradox, explains why many of the proposed solutions are not viable, and mentions a few promising new results and directions.
Behind Fermi’s question was this line of reasoning: (a) Given the vast number of stars in the Milky
Continue reading Where are the extraterrestrials? Fermi’s paradox, diversity and the origin of life

