 Aug 2023

hub.jhu.edu hub.jhu.edu

"But there's a very famous theorem in topology called the Jordan curve theorem. You have a plane and on it a simple curve that doesn't intersect and closes—in other words, a loop. There's an inside and an outside to the loop." As Riehl draws this, it seems obvious enough, but here's the problem: No matter how much your intuition tells you that there must be an inside and an outside, it's very hard to prove mathematically that this holds true for any loop that can be drawn.
How does one concretely define "inside" and "outside"? This definition is part of the missing space between the intuition and the mathematical proof.

 Jul 2023


I'm using LaTeX to create my Zettel notes. .t3_158gy35._2FCtqQzlfuNSwVMUZMM3 { postTitleVisitedLinkColor: #9b9b9b; postTitleLinkVisitedLinkColor: #9b9b9b; postBodyLinkVisitedLinkColor: #989898; }
reply to u/AndreSanch at https://www.reddit.com/r/Zettelkasten/comments/158gy35/im_using_latex_to_create_my_zettel_notes/
This sort of thing has certainly been done before by many. Be careful of going overboard.
If you don't already have a list of most of the common LaTeX math symbols, here's a good starter list, but make sure that your assigned meaning to them from an argumentation perspective is either "standard" or you've written it down for later use/memory. (There's nothing worse than a 10 year old note whose symbols you no longer remember.)
If you haven't done a course in philosophy or logic (something along the lines of Elements of Logic), then that may also help you in terms of many of the common uses/meanings, though there are a variety of meanings to various symbols through time, so take care.
Scribes and scholars over time have used a variety of symbols and annotations to mean various things, some of which were standardized in various contexts. For more on this take a look at some of Evina Stein's work and research on historic texts. Some of this might include:
Steinová, Evina. “Nota and Require. The Oldest Western Annotation Symbols and Their Dissemination in the Early Middle Ages.” Scribes and the Presentation of Texts (from Antiquity to c. 1550). Proceedings of the 20th Colloquium of the Comité International de Paléographie Latine, 2021, 473–89. https://doi.org/10.1484/M.BIBEB.5.124987.<br /> ———. Notam Superponere Studui: The Use of Annotation Symbols in the Early Middle Ages. Brepols, 2019.<br /> Steinova, Evina. “Technical Signs in Early Medieval Manuscripts Copied in Irish Minuscule.” In The Annotated Book in the Early Middle Ages: Practices of Reading and Writing, edited by M. J. Teeuwen and I. Van Renswoude, 37–85. Brepols, 2017.
For those interested in scratching the surface of some possibilities and history, I might recommend:
Scheinerman, Edward R. Mathematical Notation: A Guide for Engineers and Scientists. CreateSpace, 2011.
Your note about Forte, while cute and clever doesn't necessarily mean that he's an old man, however, so take care about your propositions and what you draw from them or else your system won't hold up for long.

 Apr 2023

www.cube20.org www.cube20.org

God's number is 20. Proven by Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge

 Mar 2023

www.ams.org www.ams.org

Resources and inspiration for math instruction and learning
Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:  Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.  Items previously published in the Journal of InquiryBased Learning in Mathematics, a refereed journal  Refereed publications at the AMS
Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

 Feb 2023

personal.math.vt.edu personal.math.vt.edu

An Introduction to Proofs and the Mathematical Vernacular<br /> by Martin Day

My experience is that whatever students learn from that formalism is left by the wayside as soon as they move into a mathematical context of any substance.
I've experienced and seen this myself.


www.youtube.com www.youtube.com

One of the problems in approaching quantum gravity is the choice for how to best represent it mathematically. Most of quantum mechanics is algebraic in nature but gravity has a geometry component which is important. (restatement)
This is similar to the early 20th century problem of how to best represent quantum mechanics: as differential equations or using group theory/Lie algebras?
This prompts the question: what other potential representations might also work?
Could it be better understood/represented using Algebraic geometry or algebraic topology as perspectives?
[handwritten notes from 20230202]

 Jan 2023

inferencereview.com inferencereview.com

Woit does provide problems, but they are all at the back of the book. It would have been better to see them between chapters. That provides a natural break in the material and gives the student a quick check on his understanding.
Homework problems are pedagogical devices and many (most) authors place them in the text near where they would be profitably be done. They also provide a useful break in the text to prompt more novice students to actually perform them at the end of a section.
More advanced students, however, should have caught on eventually at the need to work out examples for themselves which are presented in a textbook, but they should also be seeking out additional problems where ever they appear in the text, not to mention seeing out any outside additional problems, making up their own, and exploring any additional questions these pose.
In mathematics textbooks this working of problems, expanding on them and seeking out new ones is often a large part of what is lurking behind the sometimes nebulous sounding idea of "mathematical sophistication". The rest of that equation typically includes experience with the various methods and means of proofs and some basic background in logic.

Woit does not, for the most part, follow the death march of proposition, lemma, proof. He writes in the style of a theoretical physicist.
"death march of proposition, lemma, proof"
This is a bit harsh n'cest pas?

 Dec 2022

math.stackexchange.com math.stackexchange.com

My freely downloadable Beginning Mathematical Logic is a Study Guide, suggesting introductory readings beginning at subMasters level. Take a look at the main introductory suggestions on FirstOrder Logic, Computability, Set Theory as useful preparation. Tackling midlevel books will help develop your appreciation of mathematical approaches to logic.
This is a reference to a great book "Beginning Mathematical Logic: A Study Guide [18 Feb 2022]" by Peter Smith on "Teach Yourself Logic A Study Guide (and other Book Notes)". The document itself is called "LogicStudyGuide.pdf".
It focuses on mathematical logic and can be a gateway into understanding Gödel's incompleteness theorems.
I found this some time ago when looking for a way to grasp the difference between firstorder and secondorder logics. I recall enjoying his style of writing and his commentary on the books he refers to. Both recollections still remain true after rereading some of it.
It both serves as an intro to and recommended reading list for the following:  classical logics  first & secondorder  modal logics  model theory<br />  nonclassical logics  intuitionistic  relevant  free  plural  arithmetic, computability, and incompleteness  set theory (naïve and less naïve)  proof theory  algebras for logic  Boolean  Heyting/pseudoBoolean  higherorder logics  type theory  homotopy type theory

 Nov 2022

github.com github.com

2 • 3 = 6


github.com github.com

Ideally we could use Unicode, 3 2 1 ~ 3 2 1 ≃

 Aug 2022

www.sciencedirect.com www.sciencedirect.com

Weiss, D. J., & Shanteau, J. (2021). The futility of decision making research. Studies in History and Philosophy of Science Part A, 90, 10–14. https://doi.org/10.1016/j.shpsa.2021.08.018

 Oct 2021

twitter.com twitter.com

Shematologist, MD on Twitter: “How it started. How it’s going. Https://t.co/il5DWFm11W” / Twitter. (n.d.). Retrieved October 10, 2021, from https://twitter.com/acweyand/status/1442304094945873922

 Sep 2021

blogs.lse.ac.uk blogs.lse.ac.uk

Impact of Social Sciences. “How Models Change the World – and What We Should Do about It,” August 20, 2021. https://blogs.lse.ac.uk/impactofsocialsciences/2021/08/20/howmodelschangetheworldandwhatweshoulddoaboutit/.

 Jul 2021

link.aps.org link.aps.org

Wang, B., Gou, M., Guo, Y., Tanaka, G., & Han, Y. (2020). Network structurebased interventions on spatial spread of epidemics in metapopulation networks. Physical Review E, 102(6), 062306. https://doi.org/10.1103/PhysRevE.102.062306

 May 2021

github.com github.com

twitter.com twitter.com

🔥 Kareem Carr 🔥 on Twitter. (n.d.). Twitter. Retrieved 1 May 2021, from https://twitter.com/kareem_carr/status/1383925269132582912

 Mar 2021

arxiv.org arxiv.org

Holme, Petter, and Jari Saramäki. ‘Temporal Networks as a Modeling Framework’. ArXiv:2103.13586 [Physics], 24 March 2021. http://arxiv.org/abs/2103.13586.


en.wikipedia.org en.wikipedia.org

Two of the predominant types of relationships in knowledgerepresentation systems are predication and the universally quantified conditional.


psyarxiv.com psyarxiv.com

Ryan, W., Baum, S., & Evers, E. (2021). People Behave as if they Anticipate Regret Conditional on Experiencing a Bad Outcome. PsyArXiv. https://doi.org/10.31234/osf.io/dcgpy


github.com github.comd3/d31

To the consternation of some users, 3.x employed Unicode variable names such as λ, φ, τ and π for a concise representation of mathematical operations. A downside of this approach was that a SyntaxError would occur if you loaded the nonminified D3 using ISO88591 instead of UTF8. 3.x also used Unicode string literals, such as the SIprefix µ for 1e6. 4.0 uses only ASCII variable names and ASCII string literals (see rolluppluginascii), avoiding encoding problems.

 Feb 2021

twitter.com twitter.com

Health Nerd. (2021, February 1). The story continues—After @ikashnitsky and I pointed out that this paper was mathematically impossible, and had numerous errors, it was partially corrected Now, the lead author is calling us ‘trolls’ [Tweet]. @GidMK. https://twitter.com/GidMK/status/1356085063998267398

 Jul 2020

amp.dev amp.dev

The above errors can be resolved by simply adding the ⚡attribute to the <html> tag like so: <html ⚡ lang="en">


en.wikipedia.org en.wikipedia.org

the overloaded operators ¬, =, ≠, and abs are defined


en.wikipedia.org en.wikipedia.org

Most of Algol's "special" characters (⊂, ≡, ␣, ×, ÷, ≤, ≥, ≠, ¬, ⊃, ≡, ∨, ∧, →, ↓, ↑, ⌊, ⌈, ⎩, ⎧, ⊥, ⏨, ¢, ○ and □) can be found on the IBM 2741 keyboard with the APL "golfball" print head inserted; these became available in the mid1960s while ALGOL 68 was being drafted. These characters are also part of the Unicode standard and most of them are available in several popular fonts.

 Jun 2020

www.thelancet.com www.thelancet.com

Kucharski, A. J., Klepac, P., Conlan, A. J. K., Kissler, S. M., Tang, M. L., Fry, H., Gog, J. R., Edmunds, W. J., Emery, J. C., Medley, G., Munday, J. D., Russell, T. W., Leclerc, Q. J., Diamond, C., Procter, S. R., Gimma, A., Sun, F. Y., Gibbs, H. P., Rosello, A., … Simons, D. (2020). Effectiveness of isolation, testing, contact tracing, and physical distancing on reducing transmission of SARSCoV2 in different settings: A mathematical modelling study. The Lancet Infectious Diseases, 0(0). https://doi.org/10.1016/S14733099(20)304576


arxiv.org arxiv.org

Velásquez, N., Leahy, R., Restrepo, N. J., Lupu, Y., Sear, R., Gabriel, N., Jha, O., Goldberg, B., & Johnson, N. F. (2020). Hate multiverse spreads malicious COVID19 content online beyond individual platform control. ArXiv:2004.00673 [Nlin, Physics:Physics]. http://arxiv.org/abs/2004.00673

 Jan 2014

onlinelibrary.wiley.com onlinelibrary.wiley.com

Once a searchable atlas has been constructed there are fundamentally two approaches that can be used to analyze the data: one visual, the other mathematical.
