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Category: mathematics

String Theory in 2037 | Brian Greene & Edward Witten

Edward Witten, widely regarded as one of the greatest living theoretical physicists, sits down with Brian Greene to explore the deepest questions at the frontiers of modern science. From string theory and quantum gravity to black holes, cosmology, and the nature of consciousness, Witten reflects on what physics has revealed—and what remains profoundly mysterious.

The only physicist to receive the Fields Medal, Witten discusses why unifying quantum mechanics and general relativity has proven so difficult, how string theory forces gravity into its framework, and why decades of progress have still not revealed the fundamental principles underlying the theory. He also examines powerful ideas such as duality, extra dimensions, and the controversial anthropic principle, offering rare insight into how physicists grapple with uncertainty at the edge of human understanding.

The conversation moves beyond equations into philosophy, addressing questions about free will, the quantum measurement problem, and whether consciousness plays a role in how reality is observed. Witten reflects candidly on discovery, doubt, beauty in mathematics, and what it feels like to work at the limits of knowledge.

This discussion is essential viewing for anyone interested in theoretical physics, cosmology, quantum theory, and the future of our understanding of the universe.
This program is part of the Rethinking Reality series, supported by the John Templeton Foundation.

Participant: Edward Witten.
Moderator: Brian Greene.

0:00:00 — Introduction: Free Will, Physics, and the Quest to Unify Reality.

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Behold the Manifold, the Concept that Changed How Mathematicians View Space

The world is full of such shapes—ones that look flat to an ant living on them, even though they might have a more complicated global structure. Mathematicians call these shapes manifolds. Introduced by Bernhard Riemann in the mid-19th century, manifolds transformed how mathematicians think about space. It was no longer just a physical setting for other mathematical objects, but rather an abstract, well-defined object worth studying in its own right.

This new perspective allowed mathematicians to rigorously explore higher-dimensional spaces—leading to the birth of modern topology, a field dedicated to the study of mathematical spaces like manifolds. Manifolds have also come to occupy a central role in fields such as geometry, dynamical systems, data analysis, and physics.

“Gödel, Escher, Bach”: Minds, Machines, And Math

NOTE: Some folks have mentioned my pronunciation of Gödel is wrong, I do apologize for that.

Any author mulling artificial intelligence as a story element owes it to themselves to encounter this spellbinding, one-of-a-kind book. You also deserve to sit down with it if you’re curious about any number of other SF&F-adjacent topics: mathematics, pattern recognition, the definition of consciousness, the concepts of recursion (finite and infinite)… but most of all, the way profundity can be made to look like pure play.

“Gödel, Escher, Bach” at Amazon.com: https://www.amazon.com/dp/0465026567?tag=lifeboatfound-20

Opening music: “Crystal City” by Karl Casey @ White Bat Audio.
Opening background: “XANNN” @ https://vimeo.com/165286507 (Creative Commons)

My SF&F writing: https://www.infinimata.com/writing/
My blog: https://www.infinimata.com/b/
Buy me something interesting: https://www.amazon.com/hz/wishlist/ls/ZCWCKOKV6N9O?tag=lifeboatfound-20
Buy me coffee, keep me going: https://ko-fi.com/infinimata

Introducing TinyAleph: Revolutionizing How Computers Understand Meaning with Primes and Oscillators

Imagine if meaning — the elusive essence of language and thought — could be broken down into mathematical building blocks as fundamental as prime numbers. What if computers could “reason” by synchronizing oscillators, much like neurons firing in harmony in our brains?

That’s the bold idea behind TinyAleph, a new framework and library I’ve developed for semantic computing. Unlike today’s AI models that gobble up massive datasets to mimic understanding, TinyAleph grounds meaning in pure math: primes, hypercomplex algebra, and dynamic oscillators.

In this article, I’ll walk you through the core ideas of TinyAleph, stripping away the academic jargon to show why this could be a game-changer for AI, cryptography, and even quantum-inspired simulations. No PhD required — just an open mind.

The simulation hypothesis: Mathematical framework redefines what it means for one universe to simulate another

The simulation hypothesis—the idea that our universe might be an artificial construct running on some advanced alien computer—has long captured the public imagination. Yet most arguments about it rest on intuition rather than clear definitions, and few attempts have been made to formally spell out what “simulation” even means.

A new paper by SFI Professor David Wolpert aims to change that. In Journal of Physics: Complexity, Wolpert introduces the first mathematically precise framework for what it would mean for one universe to simulate another—and shows that several longstanding claims about simulations break down once the concept is defined rigorously.

His results point to a far stranger landscape than previous arguments suggest, including the possibility that a universe capable of simulating another could itself be perfectly reproduced inside that very simulation.

AI is solving ‘impossible’ math problems. Can it best the world’s top mathematicians?

Despite these potential limitations, Lackenby sees AI’s promise in mathematical hypothesis generation. “So many different areas of mathematics are connected to each other, but spotting new connections is really of interest and this process is a good way of seeing new connections that you couldn’t see before,” he said.

Lackenby’s work demonstrates that AI can be helpful in suggesting conjectures that mathematicians can then go on to prove. And despite Saunders’ reservations, Tao thinks AI could be useful in proving existing conjectures.

The most immediate payoff might not be in tackling the hardest problems but in picking off the lowest-hanging fruit, Tao said.

Functions in Hyperspace

Functions describe the world. Join me on a tour of hyperspace, and see the many strange creatures that live there. They are just functions with lots of inputs and outputs. They are parametric surfaces that take inputs u and v, and output spatial x, y, z coordinates, and r, g, b, a color outputs. This produces a colored 3D surface. Then you can add additional inputs and visualize a single slice of each input parameter, and slide through different parameter values to see different slices of the function over time. This causes the colored surface to evolve over time.
I take my time to build up the mathematical intuitions behind visualizing functions, starting with 1-in-1-out functions, and pushing it up to 7-in-7-out functions, and beyond.

Enter Hyperspace: https://evolvecode.io/hyperspace/inde… Code: https://github.com/MaxRobinsonTheGrea… Discord: / discord ~SUPPORT ME~ Scrimba: https://scrimba.com/?via=EmergentGarden Patreon: / emergentgarden Ko-fi: https://ko-fi.com/emergentgarden Twitter: / max_romana Bluesky: https://bsky.app/profile/emergentgard… ~SOURCES~ Functions Describe the World: • On Mathematical Maturity Thomas Garrity Hyperspace animation: • Blender Hyperspace Jump Shell Surfaces: https://www.geogebra.org/m/twfwsxb9 Music: / @acolyte-compositions Most come from this new album: • Stellar Nurseries (Full Album) AI Disclaimer: I used AI code tools for the website and animations. No AI video, images, script, voice, or music were used. ~TIMESTAMPS~ (0:00) Functions in Hyperspace (2:47) Visualizing Functions (5:37) Parametric Surfaces (10:01) Slices of Slices (14:55) More Parameters (18:28) Exploring the Zoo.
Source Code: https://github.com/MaxRobinsonTheGrea…
Discord: / discord.

~SUPPORT ME~
Scrimba: https://scrimba.com/?via=EmergentGarden.
Patreon: / emergentgarden.
Ko-fi: https://ko-fi.com/emergentgarden.
Twitter: / max_romana.
Bluesky: https://bsky.app/profile/emergentgard…

~SOURCES~
Functions Describe the World: • On Mathematical Maturity Thomas Garrity.
Hyperspace animation: • Blender Hyperspace Jump.
Shell Surfaces: https://www.geogebra.org/m/twfwsxb9

Music: / @acolyte-compositions.
Most come from this new album: • Stellar Nurseries (Full Album)

AI Disclaimer:

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Number’s up: Calculators hold out against AI

The humble pocket calculator may not be able to keep up with the mathematical capabilities of new technology, but it will never hallucinate.

The device’s enduring reliability equates to millions of sales each year for Japan’s Casio, which is even eyeing expansion in certain regions.

Despite lightning-speed advances in artificial intelligence, chatbots still sometimes stumble on basic addition.

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