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For SpaceNut .... no topic existed with the word mathematics in the title ....
https://getpocket.com/explore/item/this … ket-newtab
This article is about what is reported to be a way of multiplying integers that is said to be faster than traditional methods.
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This Guy Found a Faster Way to MultiplyBecause the method you learned in middle school is ridiculously slow.
Popular MechanicsDavid Grossman
Read when you’ve got time to spare.
Popular Mechanics
More from Popular Mechanicsperson speaking in front of a whiteboard filled with math figures
Photo by YouTube/UNSW
From grade school onward, complex multiplication has been a headache. But an assistant professor from the University of New South Wales Sydney in Australia has developed a new method for multiplying giant numbers together that's more efficient than the "long multiplication" so many are taught at an early age.
“More technically, we have proved a 1971 conjecture of Schönhage and Strassen about the complexity of integer multiplication,” associate professor David Harvey says in the video below.
The Schönhage–Strassen algorithm, developed by two German mathematicians, was actually the fastest method of multiplication from 1971 through 2007. Although a faster method was developed in 2007, it's rarely used today.
Schönhage and Strassen predicted that an algorithm multiplying n-digit numbers using n * log( n) basic operations should exist, Harvey says. His paper is the first known proof that it does.
Harvey picks the example of 314 multiplied by 159—a large equation, sure, but much larger ones are used every day in real-life scenarios. To solve the problem, most people are taught to multiply each individual number together, and then add up the sums:
9 is multiplied by 4, 1, and 3; then 5 is multiplied by 4, 1, and 3, and so on. The result ends up with 9 digit-by-digit products.
For some, seeing a word in the middle of a math problem might be enough to make their eyes glaze over like they did in algebra class. As a refresher: log is short for logarithm, which helps people decipher exponents that make numbers squared or cubed or even something higher. So 2⁵ is 32, but expressed logarithmically, it would look like log₂(32)=5. While it may seem like a mouthful, logarithms are crucial when numbers get much larger.
The Schönhage-Strassen method is very fast, Harvey says. If a computer were to use the squared method taught in school on a problem where two numbers had a billion digits each, it would take months. A computer using the Schönhage-Strassen method could do so in 30 seconds.
But if the numbers keep rising into the trillions and beyond, the algorithm developed by Harvey and collaborator Joris van der Hoeven at École Polytechnique in France could find solutions faster than the 1971 Schönhage-Strassen algorithm.
“It means you can do all sorts of arithmetic more efficiently, for example division and square roots," he says. "You could also calculate digits of pi more efficiently than before. It even has applications to problems involving huge prime numbers.
“People have been hunting for such an algorithm for almost 50 years," he continues. It was not a forgone conclusion that someone would eventually be successful. It might have turned out that Schönhage and Strassen were wrong, and that no such algorithm is possible.
“But now we know better,” he says.
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Logo for Popular MechanicsThis post originally appeared on Popular Mechanics and was published October 18, 2019. This article is republished here with permission.
This topic is available for NewMars members to post tips about mathematics required for the Mars Settlement problem, or news about mathematics discoveries or advances in general.
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For Mars_B4_Moon in particular .... Because you've been searching the Internet in so many topic areas, I am hoping you will keep this topic in mind as you review new items you find. Success in settling Mars will require successful execution of vast sets of numerical calculations.
We already have several project ideas that have the potential to be developed further with applied mathematics:
1) Large Ship - a Unitary Rotation space vessel design
2) Practical Ship - A dual counter rotating habitat design using a single axle
3) Inline habitat ship - a dual counter rotating habitat design using parallel axles held in place by an exterior frame
4) Solar energy powered plant to manufacture hydrocarbon fuels from air and water inputs
5) Nuclear fission powered plant to manufacture hydrocarbon fuels from air and water inputs
For all ... New Mars forum now offers the option to store completed work in Dropbox folders. This insures your work is readily available for access when it is needed. Please contact one of the Admins for details.
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The article at the link below is about research into the factorability of equations...
https://getpocket.com/explore/item/in-t … ket-newtab
The work increases the number of "prime" equations (recognized by mathematicians) and while practical applications may be few, they are not zero ... It appears that choosing equations that cannot be factored for encryption algorithms is a good idea.
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The local Linux group met this evening, via Zoom, as usual.
The group includes a mathematician.
We were looking at some software running on a Canadian machine, and I noticed that libreOffice 7.3 (and later) includes a Math package. I asked the mathematician to bring up that package on his machine, and we spent the next half hour exploring how LibreOffice allows the operator to format equations for display in a document (for publication or just for homework presentation). Somewhere along the line, someone suggested putting the ASCII translation of the equations into wolfram.com, which has an equation evaluation feature.
At that point, I really got to see a collaboration at work in real time ... the mathematician lead the process, by making selections from the examples provided by LibreOffice, or by composing his own equations, and submitting them to Wolfram.
The result was a realtime display of the equations as understood by the Wolfram math engine, including graphical displays showing the results over the span of integration specified by the mathematician.
For the first time in decades, I felt a sense of recognition of the processes of calculus.
If there is someone in the NewMars readership whose knowledge of calculus is a bit rusty, this is a way to restore some of the original gleam.
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The story at the link below is about a part of the history of mathematics that is new to me, and perhaps it will be interesting to NewMars readers.
https://www.quantamagazine.org/the-jagg … -20250123/
The article is about the discovery of a function that defeated the calculus of the time.
Since then, calculus has been improved so that it handles the problem of fractals better than it had previously.
The gent who pulled this off didn't start working seriously with math until he was 40.
Perhaps there is hope for other late bloomers in that example.
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Adding logarithms is literally multiplication, by definition, in mathematics. That is quite literally how a slide rule works, and has worked, for over 300 years.
GW
GW Johnson
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"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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This post is inspired by work on robotics in mid-2026. Measurement of angles is performed in radians for calculations, but for historical reasons, humans developed the compass points and specifically the 360 degree circle.
I asked Google Search why we humans use 360 degrees for a circle, and wondered if it had to do with the number of days in a year. That idea turned out to be correct, but there is much more to the story that I thought one or two NewMars readers might find interesting...
Yes, the choice of 360 degrees for a circle is directly connected to the number of days in a year. Ancient astronomers noticed that the sun takes roughly 365 days to complete its full orbital cycle through the constellations. Since 365 is a clumsy number for mathematics, they rounded it down to 360 to create a highly practical system.
I had to regenerate the search so this opening is slightly different from the above.
Ancient astronomers—primarily the Babylonians and Sumerians—observed that the Sun takes approximately 365 days to complete its path through the sky and return to the same starting position. Because they did not have modern precise instruments, they rounded this solar cycle to a much cleaner 360 days to create an "ideal" calendar consisting of 12 months of 30 days each. As a result, the Sun appeared to move through the sky at a rate of roughly 1 degree per day.
Here is a breakdown of why 360 remained the permanent standard:1. The Babylonian Base-60 Number SystemUnlike our modern base-10 system, the ancient Babylonians used a sexagesimal (base-60) system.They highly valued the equilateral triangle as a perfect geometric shape.Following their base-60 logic, they divided the angle of an equilateral triangle into 60 parts.Exactly six equilateral triangles fit perfectly inside a circle.
Multiplying 6 triangles by 60 parts yielded exactly 360 degrees.
2. High Divisibility (Superior Highly Composite Number)The choice to stay with 360 is reinforced by its incredible mathematical utility. If the circle were divided into 100 degrees or exactly 365 degrees, basic geometry would involve messy decimals.360 has 24 divisors.It can be divided perfectly by 1, 2, 3, 4, 5, 6, 8, 9, 10, and 12.This allows people to cleanly split a circle into halves (\(180^{\circ }\)), thirds (\(120^{\circ }\)), quarters (\(90^{\circ }\)), or fifths (\(72^{\circ }\)) without dealing with fractions.This historical intersection of sky tracking and math utility also explains why we still have 60 seconds in a minute and 60 minutes in an hour today.
The Google Search results included references for the citations quoted above.
Radians are a "natural" angle measurement. The 360 degree convention is clearly a human artifact imposed upon the circle for perfectly good reasons, but the two are clearly not related.
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This post is a follow up to #7 ... we have seen that the 360 degree system was invented millennia ago. Radians were "discovered" very recently.
Per Google Search:
English mathematician Roger Cotes developed the concept of the radian (originally called "circular measure") in 1714. He defined the unit using the ratio of an arc length to the radius of a circle.The actual word "radian" was coined much later, in 1871, by physicist James Thomson (brother of Lord Kelvin) and adopted in 1874 by mathematician Thomas Muir.
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This post is about how advanced AI systems are performing in the field of mathematics, and about how humans react.
https://www.theverge.com/podcast/982434 … ial-crisis
This is a long article so I won't try to paste it here.
It appears that OpenAI is claiming that one of it's advanced models solved 10 problems that have perplexed humans.
One of the points raised in the article is that we have no way of knowing how many math puzzles the AI failed to solve.
However, I get the impression that the 10 problems ** were ** solved, in that the proofs work, as tested by human mathematicians.
The interviewer and the interviewee spent a lot of time in serious discussion of the impact of such advanced AI on the field of mathematics.
It takes years for a human to develop the ability to contribute to the field, and that's assuming they have the talent to begin with.
One section of the article considered the benefits of having AI assistants for average persons. I think that the massive investment in AI by industry around the world is a reflection of the expectation of increased productivity for average persons.
Is something like that amplification possible with the smartest people on Earth?
I read the entire article, and didn't see that particular question.
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