This 24-Year-Old Founder Raised $64M to Build World’s First AI Mathematician | Axiom, Carina Hong

Key Concepts

• AI Mathematician: A core focus – developing an AI capable of performing mathematical research, theorem proving, and problem-solving at a high level, eventually evolving into a self-improving super-intelligent reasoner.
• Axiom: The company founded by Karina, aiming to build the aforementioned AI Mathematician.
• Deductive Reasoning: A fundamental principle underpinning the AI’s approach, inspired by axiomatic systems and rigorous proof construction.
• Jevons Paradox: The principle that technological progress increasing the efficiency of resource use can lead to increased consumption of that resource due to lowered costs and expanded applications.
• Combinatorics & Number Theory: Karina’s mathematical background, emphasizing patterns and relationships within numbers and sets.
• Taste & Intuition in Mathematics: The subjective, yet crucial, element of mathematical judgment that Axiom aims to understand and potentially replicate in AI.
• Lean: A programming language for proofs used by Axiom to build its knowledge graph and facilitate deductive reasoning.

The Pursuit of an AI Mathematician: A Deep Dive into Axiom’s Vision

Karina, founder and CEO of Axiom, details the company’s ambitious goal: to create an AI mathematician capable of independent research and ultimately, super-intelligent reasoning. Her journey, spanning mathematics, physics, neuroscience, and law at institutions like MIT, Oxford, and Stanford, culminated in founding Axiom after recognizing the potential of AI to revolutionize mathematical discovery. Axiom has secured $64 million in seed funding, valuing the company at $300 million.

The Three Pillars of AI Mathematical Development

Karina emphasizes that building an AI mathematician requires a convergence of three core disciplines:

1. Artificial Intelligence: Specifically, leveraging deep learning and transformer models for code generation and symbolic manipulation. Hugh Leather’s team has been applying deep learning to code generation since 2017, and Chart’s work in 2019 demonstrated that AI could outperform computer algebra systems in symbolic integration.
2. Programming Languages: Utilizing languages designed for formal verification and proof construction, notably Lean. Lean allows Axiom to build a knowledge graph and operate through deductive logic.
3. Mathematics: A deep understanding of mathematical principles, particularly in areas like combinatorics and number theory, is essential for guiding the AI’s development and evaluating its results.

The Nature of Mathematical Research & the Role of AI

Karina contrasts the immediate gratification of solving competitive math problems (like those encountered in math Olympiads, where she participated at age 15) with the prolonged, often frustrating, nature of research mathematics. She describes research as a process of “delay gratification,” where months can pass without significant progress.

She highlights the potential for AI to alleviate this hardship, envisioning a collaborative future where AI mathematicians assist human mathematicians by tackling difficult proofs, allowing researchers to focus on guiding the process and formulating new conjectures. This collaboration, she believes, will dramatically accelerate the pace of mathematical discovery. She notes that human mathematicians rarely collaborate directly with applied scientists, but AI mathematicians can bridge this gap, solving complex systems previously beyond theoretical understanding.

Historical Precedents & Jevons Paradox

Karina draws parallels between the development of mathematical tools and subsequent technological breakthroughs. She cites the abacus enabling trade, calculus leading to the industrial revolution, and Babbage’s difference engine as a precursor to the computer. This illustrates a recurring pattern: mathematical innovation sparks real-world applications, driving demand for further computational tools.

She introduces Jevons Paradox – the counterintuitive idea that increased efficiency in resource use can lead to increased overall consumption. Applying this to AI, she argues that making mathematical tools more accessible and powerful will unlock unforeseen use cases and markets, further increasing the demand for these tools. AI will compress the centuries-long timeline typically observed between mathematical invention and widespread application.

The Importance of "Taste" and Intuition

Karina acknowledges that while AI can excel at computation, the subjective element of “taste” and intuition remains crucial in mathematics. Defining what constitutes an “elegant” proof or an “interesting” conjecture is a uniquely human skill. Axiom aims to understand and potentially replicate this aspect of mathematical reasoning using machine learning techniques, recognizing it as a key differentiator between good and mediocre scientists. Her experience at the Ross Mathematics Program, where she was challenged to prove seemingly obvious statements from first principles, instilled in her the value of axiomatic and deductive reasoning.

Building a World-Class Team & a Fast-Paced Environment

Axiom’s approach is highly interdisciplinary, assembling experts in AI, programming languages, and mathematics. The team includes individuals with backgrounds from FAIR (Facebook AI Research), known for large reinforcement learning models like OpenGo. Karina emphasizes the importance of tackling the hardest problems to attract top talent and foster a fast-paced, execution-focused startup environment. She finds the instant reward signals of startup life reminiscent of the dopamine hits experienced while solving math problems as a child.

Mathematics as a "Sandbox of Reality"

Karina articulates a compelling view of mathematics as a fundamental science and a “sandbox of reality.” She explains that mathematics allows us to abstract real-world problems into theoretical variables, enabling analysis and solution. Furthermore, mathematics provides a “digital version” of reality, allowing for reasoning and experimentation without relying on real-world data. This makes it an ideal environment for testing and refining our understanding of the universe.

The Hardships and Rewards of Mathematical Pursuit

Karina candidly discusses the struggles inherent in mathematical research, describing it as akin to “a monk praying in the temple,” requiring relentless dedication and perseverance. She acknowledges the potential for mathematicians to become overly identified with their work, blurring the lines between their identity and their research. However, she believes that AI can alleviate these hardships, making the process more enjoyable and collaborative.

Conclusion

Axiom’s vision is to fundamentally transform the landscape of mathematical research through the development of a powerful AI mathematician. By combining cutting-edge AI techniques with rigorous mathematical principles and a collaborative approach, they aim to accelerate discovery, unlock new applications, and ultimately, deepen our understanding of the universe. Karina’s personal journey and the company’s ambitious goals position Axiom as a key player in the emerging era of mass intelligence.