“I Prefer Pi” is appropriate title for Pi Day (3/14, i.e., March 14), as it is one of the few palindromes involving Pi = 3.141592653589793… (a palindrome is a phrase that reads the same forwards or backwards).
Pi Day is particularly memorable this year, since only once a century can one celebrate this event in a year where the longer version 3/14/15 continues two more correct digits of Pi. The Museum of Mathematics in New York City, among others, is taking Pi Day 2015 one step further, by celebrating at 9:26am, i.e., 3/14/15/926, adding three more digits. See MoMath’s website
Continue reading I Prefer Pi: Background for Big Pi Day (3/14/15)
Prime numbers
In the field of mathematics, prime numbers are whole numbers that cannot be evenly divided by any integer other than itself and one. The first 12 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37. Although the study of prime numbers is a very old field of mathematics, numerous intriguing questions remain. “Number theory,” as this field is known, is also increasingly indispensable in modern technology, as it underlies techniques for compressing and encrypting digital data.
One of the as-yet-unsolved questions in number theory is the twin prime conjecture, which asks if
Continue reading Is the nature of mathematical proof changing?
New Pew Research Center poll on scientists’ views versus public views
A new poll by the Pew Research Center has highlighted some stark differences between views of leading scientists, in particular members of the American Association for the Advancement of Science (AAAS), and those of the general U.S. public. The results are summarized in this NPR report, while the full results are available from the Pew website.
Here are some of the poll’s findings:
98% of AAAS scientists agree that humans have evolved over time, versus only 65% of the U.S. public. 88% of AAAS scientists agree that it is
Continue reading Does public opinion always agree with scientific fact?
Amir Aczel, mathematician and author of a number of semi-popular books on mathematics and science (see, for example, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem), has just published Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers.
Aczel’s Finding Zero addresses a very significant historical question: What is the origin of positional decimal notation with zero, and the associated schemes we learn in grade school for doing basic arithmetic? We concur with Aczel that this discovery is clearly one of the most important scientific discoveries of the ancient world, although his characterization “the greatest
Continue reading Amir Aczel’s Finding Zero
The twin prime and prime gap conjectures
Paul Erdos, one of the 20th century’s most famed mathematicians (1913-1996) was well-known for offering prizes for the solution of various mathematical problems. Although most of these prizes were a token USD$25 or the like, he did offer a UDS$10,000 prize for the solution to a certain conjecture of his on prime gaps. Until very recently, it had not been solved.
The twin prime conjecture is that the gap between successive primes, namely gn = pn+1 – pn, is two for infinitely many n. This has not been proven, and is one of
Continue reading New results on the prime gap conjecture
Introduction
The world community is truly at a crossroads like never before faced in the history of our civilization. If we continue business-as-usual with the consumption of fossil fuels, then, according to the 2014 edition of the Intergovernmental Panel on Climate Change (IPCC)’s climate change report, grave consequences will almost surely ensue, including rising sea levels, extreme temperatures, flooding, drought, agricultural losses and, quite likely, violent conflicts among human societies. Delays may have already cost the world society USD$8 trillion.
Some who distrust the scientific consensus on climate change have taken heart at an apparent leveling off of world temperatures
Continue reading Low energy nuclear reactions: Papers and patents
On 17 November 2014, research groups at Google and Stanford University jointly announced significant advances in image recognition software.
Image recognition has been pursued for many years. One of the first and still most widely deployed applications is to recognize faces. Indeed, facial recognition systems have been employed in numerous settings:
In numerous U.S. locations, such as airports; in fact, many presume that such cameras are ubiquitous, as in TV police dramas, although this is not the case. In London, as part of their closed-circuit TV camera crime monitoring system. In various casinos, to recognize “card counters” and other unwanted
Continue reading Big brother is watching, with new image-recognition techniques
June 23, 2014 was a very nice day for five mathematicians: Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor. They were informed that they would be receiving the inaugural Breakthrough Prizes in Mathematics, each with a cash award of USD$3,000,000. They plan to share their good fortune.
The international, if still Euro-centric, nature of mathematics is obvious when we list where the five were born, educated and currently work:
Name Born Educated Current appointment(s) Donaldson Cambridge, UK Cambridge, UK; Oxford, UK Stony Brook, USA; Imperial College, UK Kontsevich Khimki, Russia Moscow State, Russia; Univ. Bonn, Germany IHES,
Continue reading Big Bucks for Big Breakthroughs: Prize recipients give three million dollar maths talks
When numbers of any sort are presented, whether in mathematics, science, business, government or finance, the default assumption is that the data presented are reasonably reliable to the last digit presented. Thus, if a light bulb is listed as using 3.14 watts, then its actual usage is presumably between 3.13 and 3.15 watts, and certainly not 2.8 or 4.2 watts. Or if the average interest rate paid on a set of securities is listed as 2.718 percent, then a reasonable reader presumes that the actual figure is between 2.717 and 2.719 percent.
The total number of significant digits can vary
Continue reading Dubious digits: Is this data really that accurate?
The IPCC report’s warning
The latest draft edition of the UN’s Intergovernmental Panel on Climate Change (IPCC) bluntly warns that business-as-usual increases in greenhouse gas emissions will cause “further warming and long-lasting changes” in the earth’s the climate system, with increasing likelihood of “severe, pervasive and irreversible impacts for people and ecosystems.” Specific dangers include rising sea levels, more frequent extreme temperatures, flooding, drought, harm to marine life and violent conflicts among human societies in the wake of agricultural changes. Delays may have already cost the world society US$8 trillion.
So what can be done? As we argued in a
Continue reading Fusion energy: Hope or hype?
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