mcmurmerings
@mcmurmer.bsky.social
Maths and Physics teacher: trader in Derivative thoughts.
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mcmurmerings
@mcmurmer.bsky.social
· Dec 12
Imagine the horror. The 23rd roots of unity, beautifully distributed around unit circle belies an ugly arithmetic imperfection within its cyclotomic field-the inability to uniquely decompose its elements. An imperfection discovered by Kumer scuppering Lamé’s proof of Fermat’s Last Theorem. #mathSky
Photons are indistinguishable and yet: we say we cannot tag or trace a specific photon as “belonging” to Sirius except by inference based on angle and wavelength. Observers differ: each human gets a different pencil of light photons from Sirius. That it is Sirius cannot be serious.
May 10, 2025 at 7:50 AM
Photons are indistinguishable and yet: we say we cannot tag or trace a specific photon as “belonging” to Sirius except by inference based on angle and wavelength. Observers differ: each human gets a different pencil of light photons from Sirius. That it is Sirius cannot be serious.
December 28, 2024 at 1:05 AM
Imagine the horror. The 23rd roots of unity, beautifully distributed around unit circle belies an ugly arithmetic imperfection within its cyclotomic field-the inability to uniquely decompose its elements. An imperfection discovered by Kumer scuppering Lamé’s proof of Fermat’s Last Theorem. #mathSky
December 12, 2024 at 10:03 PM
Imagine the horror. The 23rd roots of unity, beautifully distributed around unit circle belies an ugly arithmetic imperfection within its cyclotomic field-the inability to uniquely decompose its elements. An imperfection discovered by Kumer scuppering Lamé’s proof of Fermat’s Last Theorem. #mathSky
A superabundant number is a positive integer for which the sum of divisors (inclusive of the number itself) divided by the number is greater than that for any smaller positive integer.
#mathsky
#mathsky
December 12, 2024 at 7:22 PM
A superabundant number is a positive integer for which the sum of divisors (inclusive of the number itself) divided by the number is greater than that for any smaller positive integer.
#mathsky
#mathsky
A number m in a finite set S = {1, 2, . . . , n} is called a rough prime relative to a prime set P = {p1, p2, . . . , pk} if m is not divisible by any prime in P and m ≤ n. Rough primes naturally relate to residues and arithmetic progressions modulo the primes in $P$ #mathSky #iteachMath
December 11, 2024 at 8:01 PM
A number m in a finite set S = {1, 2, . . . , n} is called a rough prime relative to a prime set P = {p1, p2, . . . , pk} if m is not divisible by any prime in P and m ≤ n. Rough primes naturally relate to residues and arithmetic progressions modulo the primes in $P$ #mathSky #iteachMath
Reposted by mcmurmerings
"We have a duty to shareholders-"
I don't care about your duty.
"Well without it shareholders-"
I don't care about shareholders.
"You better because capitalism needs-"
I don't care about capitalism.
"Well what DO you care about?"
The harm we do to each other and the excuses we hide behind.
I don't care about your duty.
"Well without it shareholders-"
I don't care about shareholders.
"You better because capitalism needs-"
I don't care about capitalism.
"Well what DO you care about?"
The harm we do to each other and the excuses we hide behind.
December 10, 2024 at 3:14 AM
"We have a duty to shareholders-"
I don't care about your duty.
"Well without it shareholders-"
I don't care about shareholders.
"You better because capitalism needs-"
I don't care about capitalism.
"Well what DO you care about?"
The harm we do to each other and the excuses we hide behind.
I don't care about your duty.
"Well without it shareholders-"
I don't care about shareholders.
"You better because capitalism needs-"
I don't care about capitalism.
"Well what DO you care about?"
The harm we do to each other and the excuses we hide behind.
Physics is the disciplined pursuit for a description of an agreeable independent truth using increasingly less half-baked models. Seems a less futile pursuit than many these days given lack of consensus on most matters quotidian.
December 11, 2024 at 12:18 AM
Physics is the disciplined pursuit for a description of an agreeable independent truth using increasingly less half-baked models. Seems a less futile pursuit than many these days given lack of consensus on most matters quotidian.
42 is the smallest deficient number with radical of 3 possessing a non-zero Möbius function* whose prime basis cuboid^ has the smallest surface area to volume, 82/42. #mathSky #iteachMaths
December 9, 2024 at 7:42 PM
42 is the smallest deficient number with radical of 3 possessing a non-zero Möbius function* whose prime basis cuboid^ has the smallest surface area to volume, 82/42. #mathSky #iteachMaths
Reposted by mcmurmerings
Here's few more photons that I found in my driveway photon trap!
The Seagull Nebula in on the border of constellations Monoceros and Canis Major.
🔭🧪 #astrophotography
The Seagull Nebula in on the border of constellations Monoceros and Canis Major.
🔭🧪 #astrophotography
December 8, 2024 at 9:40 PM
Here's few more photons that I found in my driveway photon trap!
The Seagull Nebula in on the border of constellations Monoceros and Canis Major.
🔭🧪 #astrophotography
The Seagull Nebula in on the border of constellations Monoceros and Canis Major.
🔭🧪 #astrophotography
The rats in the bag model of the nucleon follows naturally from the liquid drop model of the nucleus
December 8, 2024 at 1:04 PM
The rats in the bag model of the nucleon follows naturally from the liquid drop model of the nucleus
Reposted by mcmurmerings
i'm no stephen hawking but i think what happens is that they cancel each other out
December 7, 2024 at 2:27 AM
i'm no stephen hawking but i think what happens is that they cancel each other out
Reposted by mcmurmerings
Renaissance Philanthropy and XTX Markets have launched a $9.2 million "AI for Math fund" to support the development of new AI tools as long-term building blocks to advance mathematics. (I have agreed to serve on the advisory board for this fund.) renaissancephilanthropy.org/news-and-ins...
Renaissance Philanthropy and XTX Markets Launch New $9 million AI for Math Fund – A brighter future for all through science, technology, and innovation
renaissancephilanthropy.org
December 5, 2024 at 4:05 PM
Renaissance Philanthropy and XTX Markets have launched a $9.2 million "AI for Math fund" to support the development of new AI tools as long-term building blocks to advance mathematics. (I have agreed to serve on the advisory board for this fund.) renaissancephilanthropy.org/news-and-ins...
The fraction of numbers less than n and not relatively prime to it can be expressed in terms of the fractions of numbers divisible by each of the prime factors of n. #mathsky
December 4, 2024 at 7:54 PM
The fraction of numbers less than n and not relatively prime to it can be expressed in terms of the fractions of numbers divisible by each of the prime factors of n. #mathsky
To speak freely: to speak your mind without leaving a trail that could potentially cost you later at the risk of saying something spontaneously your later self might wish you had edited away.
i am sorry to my gen x coworkers but you have to understand i am never, under any circumstances, going to answer a teams call without a message outlining why we need to talk first
December 4, 2024 at 8:04 AM
To speak freely: to speak your mind without leaving a trail that could potentially cost you later at the risk of saying something spontaneously your later self might wish you had edited away.
First 10,000,000 integers on a polar coordinate system, in which each point's radial distance from the origin is determined by its log and the incremental rotated angle is the golden angle. Each point corresponding to a Fibonacci number asymptotically aligns along a radial line at 222 degrees...?
December 3, 2024 at 11:17 PM
First 10,000,000 integers on a polar coordinate system, in which each point's radial distance from the origin is determined by its log and the incremental rotated angle is the golden angle. Each point corresponding to a Fibonacci number asymptotically aligns along a radial line at 222 degrees...?
Reposted by mcmurmerings
The FORmula TRANslating system is aging well.
Happy 70th birthday, Fortran! 🧪
Happy 70th birthday, Fortran! 🧪
December 2, 2024 at 6:19 AM
The FORmula TRANslating system is aging well.
Happy 70th birthday, Fortran! 🧪
Happy 70th birthday, Fortran! 🧪
There are 34 ways to load up a 60 kg knapsack via its divisor weights. Does such a semi-perfect number (equal to the sum of some its proper divisors) reveal more ways than a non semi perfect number? Define more ways here as a fraction of the number of ways with respect to the number itself. #mathSky
December 1, 2024 at 5:00 PM
There are 34 ways to load up a 60 kg knapsack via its divisor weights. Does such a semi-perfect number (equal to the sum of some its proper divisors) reveal more ways than a non semi perfect number? Define more ways here as a fraction of the number of ways with respect to the number itself. #mathSky
In the long run should the the 4n-1 primes 3,7,11,19,23,31,43,47,.. give rise to longer quadratic residue chains than 4n+1 primes? #mathsky www.jstor.org/stable/2004934
November 30, 2024 at 12:35 PM
In the long run should the the 4n-1 primes 3,7,11,19,23,31,43,47,.. give rise to longer quadratic residue chains than 4n+1 primes? #mathsky www.jstor.org/stable/2004934
Of the first 75 Bell numbers: 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ... the 2nd,3rd,7th,13th, 42nd and 55th (index) ordinal numbers are the only prime ones. What is the first prime Bell number whose ordinal number has a non zero mobius function? #mathSky
November 30, 2024 at 10:50 AM
Of the first 75 Bell numbers: 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ... the 2nd,3rd,7th,13th, 42nd and 55th (index) ordinal numbers are the only prime ones. What is the first prime Bell number whose ordinal number has a non zero mobius function? #mathSky
Put 41 at the center of an Ulam spiral and you can just about see -if you squint- some structure developing between 4n-1 and 4n+1 primes #mathSky
November 28, 2024 at 11:38 PM
Put 41 at the center of an Ulam spiral and you can just about see -if you squint- some structure developing between 4n-1 and 4n+1 primes #mathSky