Thomas Garrity discusses mathematical maturity, a concept mathematicians use for professional development, and how it can inform teaching, mentoring and careers. It was given at the IAS/PCMI Park City Mathematics Institute.
Why Hacker News points people here: HN mostly cites it as a source or related clip in math and neural network discussions, not as a strong recommendation.
Cited as a source in a video about neural networks.
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A video about neural networks, function approximation, machine learning, and mathematical building blocks. This is a submission for #SoME3 (0:00) Functions Describe the World (3:15) Neural Architecture (5:35) Higher Dimensions (11:55) Taylor Series (15:20) Fourier Series (21:25) The Real World (24:32) An Open Challenge Links and Content: • On Mathematical Maturity, Thomas Garrity: this video • Earth Rotation Loop: link • Earth Rotation Loop Modeling Shell Surfaces: link • Fourier Features Paper: link • Code for mandelbrot/image approximations: link • Code for line/surface approximations: link
Cites itpeter_d_shermanNov 2023
“The above short clip is from the following series”
Full series the short clip comes from.
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The above short clip is from the following series: "On Mathematical Maturity (1) Thomas Garrity": this video "On Mathematical Maturity (2) Thomas Garrity": link
Cites itbob1029Feb 2025
“Remember, everything is a function [0] and LLMs support calling them.”
Functions as a framing idea.
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I think the more realistic long term victims will be implementation specialists and business analysts. The middlemen who sit between product (developer) and customer. Giving your product the ability to talk & work directly with the customer seems to me a much more valuable activity than covering all the edge cases that would arise during the development of such a solution with an LLM. Remember, everything is a function [0] and LLMs support calling them. The trick is having the skill and domain expertise to establish bounded contexts and prompts that align with realistic product use cases and transition between them cleanly. I know there is a lot of doubt that users would enjoy using a chat interface, but I strongly believe it would be popular as long as it actually works. If it's not well designed and the GUI tools are faster even for a novice, you will have wasted a lot of time/money for nothing. [0] this video
