Welcome to Tensors & Quarks
Exploring the cosmos of Physics & the depths of Machine Learning.
Latest Posts
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From Prompts to Proofs: Can ChatGPT Pass the Gödel Test?
ChatGPT has become a part of our daily lives in ways we could not have imagined just a few years ago. From writing emails and polishing presentations to generating working code for side projects, it has become a universal assistant. But beyond these everyday tasks, what are the true capabilities of models like ChatGPT and its successors? Can they go beyond imitating human output and actually contribute to fields that demand creativity and rigor—like mathematics? This question is at the heart of a recent research paper, Gödel Test: Can Large Language Models Solve Easy Conjectures? published just a week ago. The paper does not ask whether large language models can memorize or recall results, but whether they can engage in something far more ambitious: creating new mathematics. In this blog, I want to walk through what the paper does, why it matters, and what it means for the future of artificial intelligence and mathematical discovery.
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Why the Higgs Discovery Was Physics’ Greatest Detective Story
Precursor: Why the Higgs Story Matters
For more than half a century, physicists chased one gap in an otherwise triumphant theory. The Standard Model (SM) precisely describes quarks and leptons and the forces among them, yet it left a conceptual hole: why are the W and Z bosons heavy while the photon is massless? The Higgs mechanism answered this by positing a scalar field that permeates all of space. Particles interacting with this field acquire mass; particles that do not remain massless. Fluctuations of the field appear as a new particle—the Higgs boson.
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Life: A Cosmic Fluke or a Common Spark?
One of the most fundamental questions in astrobiology is whether life is common in the universe. The Earth provides an encouraging clue: fossil evidence suggests that life began relatively quickly after our planet became habitable. A naïve interpretation of this fact is that abiogenesis, the origin of life from non-living chemistry, is easy and should occur rapidly wherever conditions are right. Yet this reasoning runs into a major complication: the emergence of intelligent observers like us took almost the entire span of Earth’s habitable history. If intelligence is slow, then life had to begin early on Earth, otherwise we would not exist at all. This selection effect makes early life a weak indicator of rapid abiogenesis unless intelligence is modeled explicitly alongside it.
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The Equation That Birthed String Theory
In the late 1960s, theoretical physics was at a turning point. The Standard Model was still under construction, and quantum chromodynamics—the theory of the strong force—had not yet emerged in its modern form. Physicists struggled to make sense of how hadrons—particles like protons, neutrons, and pions—scattered at high energies. These interactions exhibited puzzling patterns: an endless tower of resonances and strange scaling behaviors, all seemingly unrelated to point-like particles. Amid this confusion, a single equation appeared that not only modeled these scattering processes with uncanny precision, but also laid the groundwork for what would become string theory.
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The Rumors Are Wrong: Private Equity Still Outperforms
In the investment world, few debates have grown as intense—or as consequential—as the one surrounding the long-term performance of private equity (PE). A growing number of analysts, including a high-profile paper by Ilmanen, Chandra, and McQuinn from AQR, have argued that the golden age of private equity may be over. According to them, net-of-fee returns from private equity no longer provide the edge they once did over public equities. Instead, they suggest that investors are increasingly drawn to private equity for its return-smoothing features, rather than for genuine alpha.
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