Why math suddenly clicks years later: the geometric intuition hiding under symbols
techNmak · x · 2026-09-28
The author observes that we can manipulate equations for years without a mental picture — learning notation, following derivations, getting answers — until someone shows the idea visually and reveals the geometric intuition underneath:
- A Fourier sum becomes rotating vectors added head-to-tail
- Attention becomes a weighted combination you can watch being formed
- SVD becomes a sequence of transformations to follow step by step
- The diffusion equation becomes a point moving through a changing vector field
None of this replaces the math — precision lives in the equations — but once you have a picture, notation has something to attach to. That's why some ideas suddenly click years later: we stop seeing equations as symbol manipulation and start seeing the process they describe. He wishes more math were taught this way.
More from AGI Musings
- Critic slams 'relevance-chasing' influencers reinventing themselves as AI prophets — PierceLilholt · 2026-09-28
- Beff Jezos slams AI safety establishment: create risks, then sell tokens as insurance — beffjezos · 2026-09-28
- Claude Code creator Boris Cherny: bet on general models, skip fine-tuning — rohanpaul_ai · 2026-09-28
- Sarvam RL lead leaves after 2.5 years to build verification for AI-accelerated science — sumanthd17 · 2026-09-28
- Fractal AI CEO: AI bots take first contact, human intuition still drives final calls — srikanth · 2026-09-28
- App devs face two paths in the personal-agent era: integrate MCP or become the agent — sujingshen · 2026-09-28