DeepSeek and GRPO: How Reinforcement Learning Mathematics Outperformed OpenAI

The AI Race Has Begun: DeepSeek Enters the Global Stage

A week before DeepSeek’s arrival, the United States announced Project Stargate — a plan to invest $500 billion into AI development. And then it happened:

• Almost simultaneously, DeepSeek emerged on the world stage — China’s answer to ChatGPT, built by a small team from a former hedge fund
• The results turned out to be not just comparable, but arguably better than OpenAI’s best models
• Training costs, by various estimates, were 10 to 100 times (!) lower than OpenAI’s
• DeepSeek is also open source — with publicly available code and an open license
• Investors panicked: markets lost more than $1,000,000,000,000 in capitalization in a single Monday; the DeepSeek app surpassed ChatGPT in downloads
• Meanwhile, DeepSeek quietly released a realistic image generation model — again, on par with the world’s best

Reasoning, Benchmarks, and the Real Meaning of the Results

To be fair, the true cost of training DeepSeek is hard to verify. But the result speaks for itself. Reasoning — the model’s ability to explain how it arrived at an answer — is significantly stronger than that of competitors. Benchmark scores beat the competition. Chat and image generation are already live, and video generation appears to be on the way.

So what does this mean? The leading American AI companies turned out to be not so untouchable after all. And building the world’s most powerful AI apparently doesn’t require hundreds of billions of dollars or massive computational infrastructure. How is that even possible? The answer is simple: mathematics.

DeepSeek Reinforcement Learning vs. OpenAI’s Supervised Approach

The key difference from OpenAI is a focus on reinforcement learning — a training paradigm where the model teaches itself, rather than relying on human-guided supervised fine-tuning (SFT). Remember AlphaGo back in 2017? It managed to defeat the world Go champion — and the algorithm learned entirely on its own.

Beyond RL, DeepSeek incorporated various reward and evaluation mechanisms during training. These are precisely what gave rise to its powerful reasoning capabilities. The central innovation was GRPO — Group Relative Policy Optimization — which eliminates the need for a separate reward model (required in OpenAI’s pipeline), thereby reducing costs, training complexity, and error accumulation.

In simple terms: instead of evaluating each answer individually, GRPO compares answers against each other. Imagine a classroom where, instead of the teacher grading every student’s work separately, students compare their answers with one another. The best answers get rewarded, and students learn not just from their own mistakes, but from the strongest examples in the group. Students improve fast — the teacher gets a break.

The Mathematical Foundations of DeepSeek Reinforcement Learning

What’s truly remarkable here? Mathematics is often criticized for being theoretical, impractical, and disconnected from reality. But the moment mathematics steps into the real world, millions of people are shocked, markets move, headlines explode, progress accelerates, and a distant future becomes the present.

It has always been this way — from the Pythagorean theorem and the square root of two, through calculus, group theory, probability, differentiation, and optimal control. The Black-Scholes formula, blockchain, numerical methods, cryptography, information theory — all of these built the world we live in today.

And now, once again, mathematics is reshaping everything: machine learning combined with optimal control, game theory, optimization methods, calculus, and linear algebra — all of it made DeepSeek possible.

What Comes Next: The Untapped Potential of Pure Mathematics

And this is only the beginning. What we’ve seen so far is just one branch — applied mathematics. There are entire domains that remain purely theoretical: complex, intimidating, yet breathtakingly beautiful. Algebraic geometry, homological algebra, extremal combinatorics, functional analysis, differential topology, category theory.

Just imagine what happens when all of that makes its way into real-world applications.

The world will never look the same.