The hottest Theoretical Substack posts right now

And their main takeaways
Category
Top Technology Topics

Don't Shut Up And Calculate; Read Fields & Energy and Understand

Contemplations on the Tree of Woe • 2194 implied HN points • 08 Aug 25
🔬 Science Theoretical
  1. Electromagnetism has traditional theories that might be based on incorrect ideas. Revisiting older theories from scientists like Faraday and Maxwell can help clear up confusion.
  2. The current approach to electromagnetism often ignores practical applications and leads to contradictions. A new understanding suggests that fields guide energy, changing how we think about radiation and charge behavior.
  3. There's a push against conformity in science, with traditional peer review sometimes hindering innovation. Exploring new ideas, even outside typical channels, can revitalize scientific thought.

Turing's Work on the Riemann Hypothesis

Cantor's Paradise • 379 implied HN points • 24 Jan 25
🔬 Science Theoretical
  1. Alan Turing is famous for his work in computer science and cryptography, but he also made important contributions to number theory, specifically the Riemann hypothesis.
  2. The Riemann hypothesis centers on a mathematical function which helps in understanding the distribution of prime numbers, and it remains unproven after over 160 years.
  3. Turing created special computers to help calculate values related to the Riemann hypothesis, showing his deep interest in the question of prime numbers and mathematical truth.

Games in projective space

A Piece of the Pi: mathematics explained • 48 implied HN points • 16 Jun 25
🔬 Science Theoretical
  1. Projective geometry removes the concepts of distance and parallel lines, which changes how we think about shapes and space. It's a unique way to understand geometry differently.
  2. In projective space, there are still points, lines, and planes, but the rules are different from traditional geometry. This can lead to interesting and complex interactions.
  3. Games can be explored in the context of projective space, allowing for creative new strategies and outcomes based on its unique properties.

Shape, Symmetries, and Structure: The Changing Role of Mathematics in Machine Learning Research

The Gradient • 87 implied HN points • 16 Nov 24
🕹 Technology Theoretical
  1. Mathematics is playing a bigger role in machine learning by connecting with fields like topology and geometry. This helps researchers create better tools and methods.
  2. It's not just about scaling up current methods; there's a need for new approaches based on mathematical theories. This can lead to more innovative solutions in machine learning.
  3. Mathematicians should view advancements in machine learning as chances to explore and deepen their theoretical work, not as threats to their field. Embracing these changes can lead to new discoveries.

Boomerang tilings

Infinitely More • 15 implied HN points • 25 Jun 25
🔬 Science Theoretical
  1. Boomerangs are special shapes called nonconvex quadrilaterals. They can be used to explore interesting questions about tiling.
  2. The main question is whether a convex polygon can be tiled completely using just a few boomerangs. This is a challenging mathematical problem.
  3. Finding a solution to this problem requires careful thought and may not be easy. Just because one attempt fails, it doesn’t mean that it can’t be done at all.
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