For a half century, #mathematicians have tried to define the exact circumstances under which a #blackhole is destined to exist. A new #proof shows how a #cube can help answer the question.

https://www.quantamagazine.org/math-proof-draws-new-boundaries-around-black-hole-formation-20230816/?utm_source=Quanta+Magazine&utm_campaign=d0d9a84a9b-RSS_Daily_Physics&utm_medium=email&utm_term=0_f0cb61321c-d0d9a84a9b-389940605&mc_cid=d0d9a84a9b&mc_eid=ecf74dd79a

"For many people, the word mathematics evokes bad memories from their school years. Some develop an aversion that lasts a lifetime. Eugenia Cheng is on a mission to rectify that — to rid the world of what she calls ‘maths phobia’. Nature spoke to the mathematician, concert pianist, acclaimed author and passionate educator about her latest book, Is Maths Real?"

https://www.nature.com/articles/d41586-023-02555-z

@johncarlosbaez

#Mathematics #Mathematicians

#Dopamine, #Serotonin, #Endorphins, #Oxytocin: Your happy #Hormones, explained : Nat Geo

#Graphene ‘#Tattoo’ treats #Cardiac #Arrhythmia with light : Misc

#Mathematicians make even better never-repeating #Tile #Discovery($) : New Scientist

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

I think maybe #pschopaths and other #predators are innate #mathematicians of #socialrisk and #socialcontrol.

They learn at some #developmental stage that they can #hurt or #abuse people and get away with it through #language and other modalities of #lying.

The #power excites them or comforts them somehow and so they repeat. They can’t stop because their #evil success is #addicting to them.

Or that’s been my observation.

@BlackAzizAnansi
Okay. But just remember... You asked for it.

#Mathematicians #FoodFights #Pi #MathJoke #MathJokes #FunnyMeme #Humor #FarSide #Cartoon #MathFun

#HiddenFigures
"…is a 2016 American biographical #drama #film directed by Theodore Melfi and written by Melfi and Allison Schroeder. It is loosely based on the 2016 #nonfiction #book of the same name by Margot Lee Shetterly about three #female #AfricanAmerican #mathematicians: Katherine Goble Johnson (Taraji P. Henson), Dorothy Vaughan (Octavia Spencer), and Mary Jackson (Janelle Monáe), who worked at #NASA during the #SpaceRace…"

🔗https://Wikipedia.org/wiki/Hidden_Figures
🔗 https://en.wikipedia.org/wiki/Hidden_Figures_(book)

Mathematicians Christian Jäkel and Lennart Van Hirtum et al. simultaneously discover the 42-digit Dedekind number after 32 years of trying.

The exact values of the Dedekind numbers are known for \(0\leq n\leq9\):
\(2,3,6,20,168,7581,7828354,2414682040998,\)
\(56130437228687557907788,\)
\(286386577668298411128469151667598498812366\)
(sequence A000372 in the OEIS)

🔗 https://scitechdaily.com/elusive-ninth-dedekind-number-discovered-unlocking-a-decades-old-mystery-of-mathematics/?expand_article=1

🔗 https://www.sciencealert.com/mathematicians-discover-the-ninth-dedekind-number-after-32-years-of-searching

Summation formula👇
Kisielewicz (1988) rewrote the logical definition of antichains into the following arithmetic formula for the Dedekind numbers:
\[\displaystyle M(n)=\sum_{k=1}^{2^{2^n}} \prod_{j=1}^{2^n-1} \prod_{i=0}^{j-1} \left(1-b_i^k b_j^k\prod_{m=0}^{\log_2 i} (1-b_m^i+b_m^i b_m^j)\right)\]

where \(b_i^k\) is the \(i\)th bit of the number \(k\), which can be written using the floor function as
\[\displaystyle b_i^k=\left\lfloor\frac{k}{2^i}\right\rfloor - 2\left\lfloor\frac{k}{2^{i+1}}\right\rfloor.\]

However, this formula is not helpful for computing the values of \(M(n)\) for large \(n\) due to the large number of terms in the summation.

Asymptotics:
The logarithm of the Dedekind numbers can be estimated accurately via the bounds
\[\displaystyle{n\choose \lfloor n/2\rfloor}\le \log_2 M(n)\le {n\choose \lfloor n/2\rfloor}\left(1+O\left(\frac{\log n}{n}\right)\right).\]

Here the left inequality counts the number of antichains in which each set has exactly \(\lfloor n/2\rfloor\) elements, and the right inequality was proven by Kleitman & Markowsky (1975).

#DedekindNumber #Dedekind #NumberTheory #Mathematics #Sequence #Discovery #Mathematicians #Challenging #RichardDedekind #DifficultProblem #MathHistory #Pustam #ChallengingProblem #EGR #PustamRaut

Mathematicians Christian Jäkel and Lennart Van Hirtum et al. simultaneously discover the 42-digit Dedekind number after 32 years of trying.

The exact values of the Dedekind numbers are known for \(0\leq n\leq9\):
\(2,3,6,20,168,7581,7828354,2414682040998,56130437228687557907788,286386577668298411128469151667598498812366\)
(sequence A000372 in the OEIS)

🔗 https://scitechdaily.com/elusive-ninth-dedekind-number-discovered-unlocking-a-decades-old-mystery-of-mathematics/?expand_article=1

🔗 https://www.sciencealert.com/mathematicians-discover-the-ninth-dedekind-number-after-32-years-of-searching

Summation formula👇
Kisielewicz (1988) rewrote the logical definition of antichains into the following arithmetic formula for the Dedekind numbers:
\[\displaystyle M(n)=\sum_{k=1}^{2^{2^n}} \prod_{j=1}^{2^n-1} \prod_{i=0}^{j-1} \left(1-b_i^k b_j^k\prod_{m=0}^{\log_2 i} (1-b_m^i+b_m^i b_m^j)\right)\]

where \(b_i^k\) is the \(i\)th bit of the number \(k\), which can be written using the floor function as
\[\displaystyle b_i^k=\left\lfloor\frac{k}{2^i}\right\rfloor - 2\left\lfloor\frac{k}{2^{i+1}}\right\rfloor.\]

However, this formula is not helpful for computing the values of \(M(n)\) for large \(n\) due to the large number of terms in the summation.

Asymptotics:
The logarithm of the Dedekind numbers can be estimated accurately via the bounds
\[\displaystyle{n\choose \lfloor n/2\rfloor}\le \log_2 M(n)\le {n\choose \lfloor n/2\rfloor}\left(1+O\left(\frac{\log n}{n}\right)\right).\]

Here the left inequality counts the number of antichains in which each set has exactly \(\lfloor n/2\rfloor\) elements, and the right inequality was proven by Kleitman & Markowsky (1975).

#DedekindNumber #Dedekind #NumberTheory #Mathematics #Sequence #Discovery #Mathematicians #Challenging #RichardDedekind #DifficultProblem #MathHistory #Pustam #ChallengingProblem #EGR #PustamRaut

New #Model offers a way to speed up #Drug #Discovery : MIT

Why #Mathematicians Re-Prove What They Already Know : Quanta Mag

Linking #Modular #Architecture to #Development Teams : MartinFowler.com

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

#Mathematicians Discover The Ninth Dedekind Number, After 32 Years of Searching

https://www.sciencealert.com/mathematicians-discover-the-ninth-dedekind-number-after-32-years-of-searching

#MIT #Engineers develop a soft, #Printable, metal-free #Electrode : MIT

Do #Insects Feel #Joy and #Pain? : Sci Am

Flow #Proof Helps #Mathematicians Find #Stability in #Chaos : Quanta Mag

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

The Royal Society's new freely accessible "Science in the Making" #digital #archive includes profiles of 92 #mathematicians (https://makingscience.royalsociety.org/search?q=mathematics&filters[Record%20Type][0]=Person) and nearly 3,000 digitised documents related to #mathematics (https://makingscience.royalsociety.org/search?q=mathematics&filters[Record%20Type][0]=Archive+Item)

Have at it, folks!

#STEM #history

The @royalsociety 's new freely accessible "Science in the Making" #digital #archive includes profiles of 92 #mathematicians (https://makingscience.royalsociety.org/search?q=mathematics&filters[Record%20Type][0]=Person) and nearly 3,000 digitised documents related to #mathematics (https://makingscience.royalsociety.org/search?q=mathematics&filters[Record%20Type][0]=Archive+Item)

Have at it, folks!

#STEM #history

I asked #maths #teachers if they think they're #mathematicians: https://tommaths.blogspot.com/2023/06/do-maths-teachers-think-theyre.html

#Mathematicians Find Hidden Structure in a Common Type of #Space
https://www.wired.com/story/mathematicians-find-hidden-structure-in-a-common-type-of-space/
In 50 years of searching, mathematicians found only one example of a “#subspace design” that fit their criteria. A new proof reveals that there are #infinitely more.

How many requests did you get to assess an #Australian #Research Council grant application this year? I’d particularly like to hear from #mathematicians – FWIW I didn’t get any requests, which is a bit unusual … cc @ARC_Tracker

Mathstodon.xyz is a server for people who love maths. We have LaTeX rendering in the web interface!

:Fediverse: https://mathstodon.xyz

We hope there’ll be lots of maths chat, but any topic of conversation following the code of conduct and the principle of getting along together is OK.

If you have any questions, contact the admin at @christianp

#FeaturedServer #Maths #Math #Mathematics #Mathematical #Mathematicians #Mathematician #LaTeX #Science #Mastodon #Fediverse

Semiotics, Semiosis, Sign Relations • Comment 4
• https://inquiryintoinquiry.com/2021/08/23/semiotics-semiosis-sign-relations-comment-4/

ah, what do mathematicians know of life’s exigency?
proof is our rock and our soul necessity.
we don’t just make abstractions, we are abstractions.
it’s coffee and doughnuts all the way down …
no one disturbs our vain diagrams
till human voices wake us, and we drown.

🙞 also sprach 0*
— 23 august 2021

#Peirce #Logic #Semiotics #Semiosis #Sign Relations
#Mathematicians #Prufrock #TSEliot #Verse #ZeroAster

Hi there, #mathematicians and #math lovers on the #Fediverse.

Recently a new #delightful list was created by @mskf1383 that maintains a nice curated collection of #FOSS software for your field.

The list is still small, but I'm sure you have more to add to it. Don't hesitate and PR to the #Codeberg repository or create an issue in the tracker.

https://delightful.club/delightful-mathematics-softwares

I welcome questions and critical discussion but there are ways in which #mathematicians express disdain about areas other than their own, which convey more about the ignorance of the speaker than truth about any field. I wish everyone spoke up about these snarky attempts …