#riemann — Public Fediverse posts

Мы с женой нашли один запрет за 7 нерешаемыми задачами и первым делом построили машину, которая не даёт нам соврать

Ну всё, я это сказал. «Один запрет за проблемами тысячелетия». Половина из вас уже тянется к минусу и слову на букву «к». И правильно тянется, потому что почти каждый, кто пишет такое, несёт чушь. Решили задачу тысячелетия или пробили столетнюю гипотезу, которую не смогли сотни умнейших математиков планеты до вас. Ну точно кранки! Поэтому договоримся сразу. Первым делом не пафос, а признание! Где мы могли соврать

https://habr.com/ru/articles/1057330/

#lean #collatz_conjecture #Twins_conjecture #riemann #navierstokes_equation #fractal #prime_numbers #доказательства #формальная_верификация #простые_близнецы

“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?” – David Hilbert

#RiemannHypothesis #DavidHilbert #RiemannZetaFunction #ZetaFunction #UnsolvedProblem #MathHistory #Hilbert #Riemann

The #Riemann Hypothesis – interactive explanation

https://riemann.adilmoujahid.com

The #Riemann Hypothesis – interactive explanation

https://riemann.adilmoujahid.com

It's #math 🧌 time!

proof of the #riemann #hypothesis (simplified):
-2 -1 -0 +0 +1 +2
two zeros:
+0 = 00. nothing was ever here.
-0 = 11. something was. it isn't.
work in F₅.
i = 2, so ±i = ±2 ✓
1/2 = 3 = -2 = -i
the critical line Re(s) = 1/2 is Re(s) = -i.
the #real part of s on the critical line is #imaginary.
the critical strip lives between vacuum and one.
the #zeta zeros are not #vacuum. they're #annihilation.
#integers have a winding number.
you're welcome ∎🍑

It's #math 🧌 time!

proof of the #riemann #hypothesis (simplified):
-2 -1 -0 +0 +1 +2
two zeros:
+0 = 00. nothing was ever here.
-0 = 11. something was. it isn't.
work in F₅.
i = 2, so ±i = ±2 ✓
1/2 = 3 = -2 = -i
the critical line Re(s) = 1/2 is Re(s) = -i.
the #real part of s on the critical line is #imaginary.
the critical strip lives between vacuum and one.
the #zeta zeros are not #vacuum. they're #annihilation.
#integers have a winding number.
you're welcome ∎🍑

#Riemann is the room temperature #Superconductivity of #Mathematics. She is beautiful enough to make one cry as she tempts at a glance,then vanishes.The link between harmonic analysis , #Fourier , and pretty much all of #Physics takes a sledgehammer to the idea that mathematics and #Physics are twin sons of different mothers.This video is a not bad , very good introduction for newcomers. Timely and up to date

Via #NewScientist:
PrimeNumbers Might Not Be Random After All
https://youtu.be/59I84mWLK_c?si=zrm6TiKV_oD0LIxy

#Riemann is the room temperature #Superconductivity of #Mathematics. She is beautiful enough to make one cry as she tempts at a glance,then vanishes.The link between harmonic analysis , #Fourier , and pretty much all of #Physics takes a sledgehammer to the idea that mathematics and #Physics are twin sons of different mothers.This video is a not bad , very good introduction for newcomers. Timely and up to date

Via #NewScientist:
PrimeNumbers Might Not Be Random After All
https://youtu.be/59I84mWLK_c?si=zrm6TiKV_oD0LIxy

1/6

I'm investigating a regression that appeared after upgrading #OpenJDK in a setup where #syslog_ng communicates with a #Riemann server (a Java application).

My investigation led me to a C library (riemann-c-client, used by syslog-ng) that uses #GnuTLS to establish a mutually authenticated TLS connection to the Java service. The library provides a CLI utility that allows me to reproduce the problem, which suggests that the issue lies in this library rather than in syslog-ng itself.

1/6

I'm investigating a regression that appeared after upgrading #OpenJDK in a setup where #syslog_ng communicates with a #Riemann server (a Java application).

My investigation led me to a C library (riemann-c-client, used by syslog-ng) that uses #GnuTLS to establish a mutually authenticated TLS connection to the Java service. The library provides a CLI utility that allows me to reproduce the problem, which suggests that the issue lies in this library rather than in syslog-ng itself.

#paperOfTheDay for Friday was "The Riemann Hypothesis: Past, Present and a Letter Through Time" from Thursday. The #Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function have real part 1/2. Stated as a remark in Riemann's legendary paper 165years ago, it is by now one of the most well-known open problems in #mathematics. In the first half of the present paper, Connes gives a well-structured overview of several of the many relations, equivalent formulations, and consequences of the Riemann hypothesis. Very informative for the general (mathematically educated) reader! The second half describes one of the ongoing proof attempts in greater technical detail. #dailyPaperChallenge https://arxiv.org/abs/2602.04022

#paperOfTheDay for Friday was "The Riemann Hypothesis: Past, Present and a Letter Through Time" from Thursday. The #Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function have real part 1/2. Stated as a remark in Riemann's legendary paper 165years ago, it is by now one of the most well-known open problems in #mathematics. In the first half of the present paper, Connes gives a well-structured overview of several of the many relations, equivalent formulations, and consequences of the Riemann hypothesis. Very informative for the general (mathematically educated) reader! The second half describes one of the ongoing proof attempts in greater technical detail. #dailyPaperChallenge https://arxiv.org/abs/2602.04022

The Riemann Hypothesis: Past, Present and a Letter Through Time
https://arxiv.org/abs/2602.04022

#RiemannHypothesis #Riemann #Conjecture #Hypothesis #ZetaFunction #RiemanZetaFunction #RH #MillenniumPrizeProblems #PrimeNumbers

"In the mid-19th century, Bernhard #Riemann conceived of a new way to think about #mathematical spaces, providing the foundation for modern #geometry and #physics."

Cool article on #manifolds on wired.com:

🌍 https://www.wired.com/story/behold-the-manifold-the-concept-that-changed-how-mathematicians-view-space/

#manifolds

"In the mid-19th century, Bernhard #Riemann conceived of a new way to think about #mathematical spaces, providing the foundation for modern #geometry and #physics."

Cool article on #manifolds on wired.com:

🌍 https://www.wired.com/story/behold-the-manifold-the-concept-that-changed-how-mathematicians-view-space/

#manifolds

-->3:
Ja: der Fritz #Riemann, der auch das bekannte Buch “Grundformen der Angst” schrieb, ein wichtiges Werk aus dem Bereich Psychologie. Wissenschaft kann im Sinne einer guten #Deutungskunst zu Rate gezogen werden. Aber #Astrologie ist keine Wissenschaft.
Leider gibt es immer wieder Negativ-Beispiele für unzutreffende Beschreibung von Astrologie, die Vorurteile und Falschannahmen verstärkt. Sowohl in Artikeln als auch von selbsternannten "Astrologen".

https://feddit.org/post/506740

-->2: Jahrhunderte alte #Deutungskunst (s. Das astrologische Luftzeitalter, Buch, https://www.buecher.de/shop/horoskop/das-astrologische-luftzeitalter-eine-neue-aera-der-verbindung/schlieffen-alexander-von/products_products/detail/prod_id/61390871/). Diese Deutungskunst ist nicht wissenschaftlich. Astrologie und Wissenschaft haben nichts gemeinsam. Die #Planeten stehen in der #Astrologie für #Archetypen und die Aspekte für Beziehungen zwischen diesen Archetypen usw. Ein gutes Buch über astrologische Archetypen gibt es von Fritz #Riemann “Lebenshilfe Astrologie” (https://www.klett-cotta.de/produkt/fritz-riemann-lebenshilfe-astrologie-9783608946574-t-4101). -->3

One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅

#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals

Can You Visualize the Riemann-Stieltjes INTEGRAL?
https://youtube.com/watch?v=D5bbIxbsNqE

#Mathematics #Integral #Rates_ofChange #Partition #Sum #Supremum #SetRefinement #Riemann #Stieltjes #RiemannStieltjes #youtubevideo

#StableDiffusion #aiart #digitalart #abstract #riemann #visualized_mathematics

Will the toughest problem in #math ever be solved? David Whitehouse about the Riemann hypothesis
https://www.spectator.co.uk/article/will-the-toughest-problem-in-maths-ever-be-solved/

Recently there has been some progress - a proof creates stricter limits on potential exceptions to the famous #Riemann hypothesis
https://www.quantamagazine.org/sensational-proof-delivers-new-insights-into-prime-numbers-20240715/

Will the toughest problem in #math ever be solved? David Whitehouse about the Riemann hypothesis
https://www.spectator.co.uk/article/will-the-toughest-problem-in-maths-ever-be-solved/

Recently there has been some progress - a proof creates stricter limits on potential exceptions to the famous #Riemann hypothesis
https://www.quantamagazine.org/sensational-proof-delivers-new-insights-into-prime-numbers-20240715/

#Riemann’s Novel Lecture that Changed the Course of #Geometry : Medium

What is #Air #Pollution and how to protect your #Family from it. : UNICEF

A Clean, Green Way to #Recycle #SolarPanels : IEEE

Check our latest #KnowledgeLinks

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

#Riemann’s Novel Lecture that Changed the Course of #Geometry : Medium

What is #Air #Pollution and how to protect your #Family from it. : UNICEF

A Clean, Green Way to #Recycle #SolarPanels : IEEE

Check our latest #KnowledgeLinks

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

Une avancée notable vers la résolution de l' #hypothèse de #Riemann .

Poir cela, #LarryGuth et #JamesMaynard utilisent des #polynômes de #Dirichlet et une meilleure borne de leurs zéros.

Référence : https://arxiv.org/abs/2405.20552

https://www.mundodeportivo.com/urbantecno/ciencia/los-matematicos-estan-a-punto-de-resolver-uno-de-los-7-problemas-mas-dificiles-que-existen

Une avancée notable vers la résolution de l' #hypothèse de #Riemann .

Poir cela, #LarryGuth et #JamesMaynard utilisent des #polynômes de #Dirichlet et une meilleure borne de leurs zéros.

Référence : https://arxiv.org/abs/2405.20552

https://www.mundodeportivo.com/urbantecno/ciencia/los-matematicos-estan-a-punto-de-resolver-uno-de-los-7-problemas-mas-dificiles-que-existen

@zvavybir
It does diverge. It has no sum.
However, the uniquely valued #Riemann #ZetaFunction can be analytically continued into the left half-plane where we find zeta(-1)=-1/12 (which 'looks like' 1+2+...). #Cesàro #summation will get you part of the way there also, and, as you say, yields the same result; presumably due to some ultimate cosmic logical rightness :-)
I very strongly recommend BP's superb exposition of this issue
https://www.youtube.com/watch?v=YuIIjLr6vUA
#maths #AnalyticContinuation #Ramanujan

`Two years later, in 1849, he returned to Göttingen to pursue his PhD with Gauss, completing his thesis in 1851 on the theory of complex variables, the basis for what we now call Riemann surfaces. Gauss described Riemann as having “a gloriously fertile originality” in his report on the thesis, and two years later, when #Riemann was required to give a lecture to land a faculty position at Göttingen, Gauss assigned his star pupil the topic of the foundations of #geometry`

https://www.aps.org/archives/publications/apsnews/201306/physicshistory.cfm

`Two years later, in 1849, he returned to Göttingen to pursue his PhD with Gauss, completing his thesis in 1851 on the theory of complex variables, the basis for what we now call Riemann surfaces. Gauss described Riemann as having “a gloriously fertile originality” in his report on the thesis, and two years later, when #Riemann was required to give a lecture to land a faculty position at Göttingen, Gauss assigned his star pupil the topic of the foundations of #geometry`

https://www.aps.org/archives/publications/apsnews/201306/physicshistory.cfm

DOMINATED CONVERGENCE THEOREM
Lebesgue's dominated convergence theorem provides sufficient conditions under which pointwise convergence of a sequence of functions implies convergence of the integrals. It's one of the reasons that makes #Lebesgue integration more powerful than #Riemann integration. The theorem an be stated as follows:

Let \((f_n)\) be a sequence of measurable functions on a measure space \((\mathcal{S},\Sigma,\mu)\). Suppose that \((f_n)\) converges pointwise to a function \(f\) and is dominated by some Lebesgue integrable function \(g\), i.e. \(|f_n(x)|\leq g(x)\ \forall n\) and \(\forall x\in\mathcal{S}\). Then, \(f\) is Lebesgue integrable, and

\[\displaystyle\lim_{n\to\infty}\int_\mathcal{S}f_n\ \mathrm{d}\mu=\int_\mathcal{S}f\ \mathrm{d}\mu\]
#ConvergenceTheorem #Convergence #DominatedConvergenceTheorem #Lebesgue #MeasurableFunction #LebesgueFunction #LebesgueIntegration #RiemannIntegration #MeasureSpace

@jcamos I used to rely on #collectd (with the #Riemann writter) but switched to riemann-tools (which happens to be more hackable for me and has saner defaults) to collect metrics.

Downstream, Riemann does some processing and alerting (it is also used to ingest logs from #syslog_ng), and then persist information in #OpenSearch.

For visualization, I currently use #Grafana which really get on my nerves and plan to switch to using OpenSearch Dashboards, the tool I use to browse logs.

@jcamos I used to rely on #collectd (with the #Riemann writter) but switched to riemann-tools (which happens to be more hackable for me and has saner defaults) to collect metrics.

Downstream, Riemann does some processing and alerting (it is also used to ingest logs from #syslog_ng), and then persist information in #OpenSearch.

For visualization, I currently use #Grafana which really get on my nerves and plan to switch to using OpenSearch Dashboards, the tool I use to browse logs.

My unofficial syslog-ng 4.4.0 packages for @opensuse / #SLES are now available:

https://www.syslog-ng.com/community/b/blog/posts/installing-latest-syslog-ng-on-rhel-and-other-rpm-distributions

New features include:

- #Grafana #Loki and #S3 destinations (only in Tumbleweed)
- http() compression

Support for #Riemann temporarily disabled due to compile problems.

My unofficial syslog-ng 4.4.0 packages for @opensuse / #SLES are now available:

https://www.syslog-ng.com/community/b/blog/posts/installing-latest-syslog-ng-on-rhel-and-other-rpm-distributions

New features include:

- #Grafana #Loki and #S3 destinations (only in Tumbleweed)
- http() compression

Support for #Riemann temporarily disabled due to compile problems.

The unproved Riemann hypothesis states that the nontrivial zeros of the Riemann zeta function occur only on the critical line \( z = \frac12 + i y \). While it is not difficult to understand why these zeros can only occur inside the critical strip \( 0 < \operatorname{Im} z < 1 \), the restriction to the critical line is spooky cool.

With an implementation of the zeta function in #JavaScript one has a proof near the origin via #visualization. The real part is blue, imaginary red:

https://mathcell.org/www/riemann-zeta-zeros.htm

Manipulating the imaginary part of the argument along the critical strip shows immediately that zeros only occur on the critical line for an imaginary part of approximately

±14.13, ±21.02, ±25.01, ±30.42, ±32.94, ±37.59, ±40.92, ±43.33, ±48.01, ±49.77

For more context and the relation to the Riemann xi function, visit

https://analyticphysics.com/Special%20Functions/Visualizing%20Riemann%20Zeta%20Function%20Zeros.htm

#SpecialFunctions #Riemann #zeta

Next week, the school of our thematic programme on #Geometry beyond #Riemann: #Curvature and #Rigidity is coming. 🤓 Hope everyone is registered who is into #Riemannian and #Lorentzian #conemanifolds, #Hilbert and #Finsler #metrics!

Find out more about the schedule here. 📝
https://www.esi.ac.at/events/e477/

@univienna

Click for the video here: https://twitter.com/ESIVienna/status/1702317593401651693

Il paraît que ça bouge autour de la #conjecture de #Riemann ! .. #mathematiques #maths

https://www.sciencesetavenir.fr/fondamental/mathematiques/nombres-premiers-le-mystere-de-leur-repartition-bientot-resolu_172276

There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction

There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction

Do you use #syslog_ng to send data to #Riemann? There was a bug in riemann-c-client, which was fixed by @smortex . Client packages are now updated with the fix in all my syslog-ng RPM repos for @fedora / #RHEL & @opensuse / #SLES:

https://www.syslog-ng.com/community/b/blog/posts/overview-of-syslog-ng-rpm-repositories

Official #Fedora & #EPEL packages will follow soon.

#AlexKontorovich - The #RiemannHypothesis Explained

https://www.youtube.com/watch?v=zlm1aajH6gY&ab_channel=QuantaMagazine

#PhilosophyOfMathematics #Math #Maths #Mathematics #BernhardRiemann #Riemann #Prime #Primes #PrimeNumbers #ComplexNumbers #ImaginaryNumbers #ComplexPlane #QuantaMagazine