πŸ“š Agora node [[math]] β˜†
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πŸ“œ File pages/math.org by @jakeisnt β˜† πŸ“Ž β›Ά

Notes and resources for mathematics.

Links

https://mathenchant.wordpress.com/2020/10/17/when-11-equals-0/amp/?__twitter_impression=true the philosophy of math, from oxford https://github.com/jaintj95/Math_by_Richard_Feynman https://github.com/fastai/numerical-linear-algebra computational linear algebra course https://github.com/chubin/pyphoon ascii art phase of the moon

https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/index.htm The radix 2^51 trick https://blog.plover.com/misc/half-baked.html tired answers to half baked questions !! both article on category theory but commentary on stack exchange FatNums: An Alternate Representation for School Arithmetic

William J. Bowman @wilbowma@mastodon.social on Twitter: "Last time, asked students to prove the empty set is not equal to the set containing the empty set. This time, I asked them to prove 1 is not equal to 0. This was by mistake. Thankfully, has resulted in a most pedantic discussion about whether we know conjunction is commutative." / Twitter

Math 63CM Winter 2020

Download generatingfunctionology Functional Differential Geometry by Sussman, Gerald Jay, Wisdom, Jack (2013 https://arxiv.org/abs/1808.02923

https://byorgey.wordpress.com/2020/02/23/what-would-dijkstra-do-proving-the-associativity-of-min/

https://www.3blue1brown.com/about https://en.m.wikipedia.org/wiki/Monster_group https://blogs.scientificamerican.com/guest-blog/john-conway-reminiscences-about-dr-matrix-and-bourbaki/ https://en.m.wikipedia.org/wiki/Real_projective_plane Rayo's number video

mathviz FatNums: An Alternate Representation for School Arithmetic

https://www.quantamagazine.org/amazing-math-bridge-extended-beyond-fermats-last-theorem-20200406/ https://en.m.wikipedia.org/wiki/Representation_theory derivation graph of all of mathematical physics horn clause, math

https://blog.kaufer.org/ Blogs https://en.m.wikipedia.org/wiki/Monster_group http://blog.ezyang.com/2012/03/you-could-have-invented-fractional-cascading/ https://en.m.wikipedia.org/wiki/Hamming_weight categories for the working hacker https://arxiv.org/abs/1908.10528 http://yanlaichen.reawritingmath.com/ https://en.m.wiktionary.org/wiki/Shannon_entropy

https://oxford.universitypressscholarship.com/mobile/view/10.1093/oso/9780198853404.001.0001/oso-9780198853404-chapter-1 Programming Languages

https://ma.tt/2019/12/comments-and-collatz-conundrum/ http://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf

Rubik's Cube group - Wikipedia

A brief overview and discussion of PCA.

πŸ“œ File Math.md by @agora@botsin.space β˜† πŸ“Ž β›Ά
πŸ“œ File math.md by @agora@botsin.space β˜† πŸ“Ž β›Ά
πŸ“œ File Math.md by @an_agora@twitter.com β˜† πŸ“Ž β›Ά
πŸ“œ File math.md by @an_agora@twitter.com β˜† πŸ“Ž β›Ά
πŸ“œ File Math.md by @j0lms@twitter.com β˜† πŸ“Ž β›Ά

RT @djlink@mastodon.gamedev.place This website is amazing, linear algebra with interactive examples. Vectors, matrix, dot product, etc, cool resource for learning. #GameDev #Math https://t.co/m256xwkMAv https://t.co/yVwW9wzF76 https://t.co/RYcXjwLtKf


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πŸ“š Agora node [[007bistromath]] (pulled by the Agora)
πŸ“œ File 007bistromath.md by @flancian β˜† πŸ“Ž οΈπŸ”— ✍️

007bistromathΒ§

πŸ“š Agora node [[fastmath]] (pulled by the Agora)
πŸ“œ File fastmath.md by @agora@botsin.space β˜† πŸ“Ž
πŸ“œ File fastmath.md by @an_agora@twitter.com β˜† πŸ“Ž
πŸ“œ File fastmath.md by @flancian@social.coop β˜† πŸ“Ž
πŸ“œ File fastmath.md by @flancian@twitter.com β˜† πŸ“Ž

A nice article on what can go wrong with [[fastmath]] (compiler optimizations). https://t.co/rvwHcCp3Ah


πŸ“š Agora node [[hypermath]] (pulled by the Agora)
πŸ“œ File hypermath.md by @agora@botsin.space β˜† πŸ“Ž
πŸ“š Agora node [[lex fridman 503 ai crisis in math]] (pulled by the Agora)
πŸ“œ File wiki/Content/Podcasts/Episodes/Lex Fridman 503 - AI Crisis in Math.md by @jaysen β˜† πŸ“Ž οΈπŸ”—

Ankur Moitra, Steven Brunton and Alex Kontorovich are three mathematicians who can speak to this incredible moment in the history of mathematics, when AI solved some of its hardest problems: Navier-Stokes, the quasi-Riemann hypothesis, the unique games conjecture and hundreds of other problems. Ankur Moitra is a mathematician at MIT (visiting the Institute for Advanced Study in Princeton) working in theoretical computer science, who can speak to the unique games conjecture, complexity theory and the mathematics of how AI learns. Steven Brunton is a mathematician and fluid dynamics expert at UW, who can speak to Navier-Stokes, turbulence and machine learning for fluid dynamics. Alex Kontorovich is a mathematician at Rutgers specializing in number theory, who can speak to the Riemann hypothesis, Lean and machine-checked proofs.

web: episode channel: Lex Fridman Podcast

LogΒ§

created: 20261027 - 21:06 Started: 20261027 Ended: 20261028

Outline:Β§

  • 0:00 Introduction
  • 1:56 - Crisis moment in mathematics
  • 10:13 - Will AI "solve" mathematics?# Lex Fridman 503 AI Crisis in Math
  • 26:24 - Can AI create new math?
  • 1:05:56 - Riemann hypothesis
  • 1:29:49 - Navier-Stokes
  • 1:55:45 - How nature computes
  • 2:04:39 - Unique Games Conjecture and complexity theory
  • 2:19:31 - How mathematicians think
  • 2:33:08 - Is math invented or discovered?
  • 2:39:16 - Can AI solve P vs NP?
  • 2:49:31 - Why LLMs work so well
  • 3:03:57 - Problems AI can’t solve yet
  • 3:08:27 - Grigori Perelman
  • 3:17:45 - Advice for young people

NotesΒ§

Key Takeaways for Learning with AIΒ§

1. Use AI as a Tutor, Not an Answer Engine The most effective way to learn is to use AI to clarify difficult concepts. If you encounter a complex math paper or a confusing topic, use the tool to break down the language or explain specific sections. This accelerates learning by acting as a "world expert" available to teach you in your own language (3:11:30-3:12:30).

2. Avoid the Bimodal Learning Trap There is an observable divide in how students approach AI. The "head" of the distribution uses AI to check their understanding, quiz themselves, and verify their logic. The "tail" of the distribution uses AI to simply generate answers to finish work quickly. To be successful, you must use these tools to deepen, not bypass, your own thinking (3:19:10-3:19:40).

3. Retain Personal Independence Even when a machine can solve a problem, you should strive to retain the ability to solve it yourself. Mastering a skillβ€”even if a tool can do it for youβ€”is essential for personal independence and building the intuition necessary for true expertise (3:17:05-3:17:45).

4. Build Strong Foundations Do not abandon the basics. Regardless of AI’s capabilities, you must still learn the fundamentals like linear algebra, calculus, and physics. Building this core intuition allows you to evaluate AI outputs critically and navigate the "uncertainty" of the future with a stronger sense of purpose (3:21:00-3:21:26, 3:25:28-3:26:20).

πŸ“š Agora node [[opsimath]] (pulled by the Agora)
πŸ“œ File opsimath.md by @flancian β˜† πŸ“Ž οΈπŸ”— ✍️

OpsimathΒ§

πŸ“š Agora node [[twittermath]] (pulled by the Agora)
πŸ“œ File TwitterMath.md by @agora@botsin.space β˜† πŸ“Ž