How many hard problems are really waiting for better search, not just bigger models?
The question has become a serious discussion in AI research recently. The AlphaEvolve Ramsey result is a good example of the “better search” paradigm, which is quite different from scaling neural networks.
Let’s unpack it.
1. Bigger models vs better search
In modern AI there are two broad strategies:
Bigger models
Train massive neural networks with more data and compute.
Examples:
GPT‑4
Gemini
These work well for:
language
perception
coding
reasoning approximations
But they don’t directly explore large discrete spaces.
Better search
Instead of predicting answers, the system explores possibilities and verifies them.
Famous examples:
AlphaGo used Monte Carlo tree search
AlphaFold searched structure space
AlphaEvolve searches mathematical constructions
Here the AI:
Generates candidate solutions
Evaluates them with strict rules
Iteratively improves them
This is closer to scientific discovery than prediction.
2. Yes — the Ramsey improvement was a search breakthrough
The improvement to Ramsey bounds was not because of a larger neural network.
It happened because the system could:
explore enormous graph spaces
mutate structures intelligently
keep partial improvements
This falls into Combinatorics, where many problems are essentially search over huge spaces.
So the quote you saw is quite accurate.
Many hard problems are like:
“The solution exists somewhere in a gigantic space of possibilities.”
3. Fields where better search may unlock breakthroughs
These areas are widely believed to be ripe for AI-guided search.
Extremal combinatorics
Area of:
Extremal Combinatorics
Problems often ask:
What is the largest structure avoiding some pattern?
Examples likely to improve:
Ramsey numbers
Turán-type graph problems
hypergraph constructions
These are perfect for evolutionary search.
Coding theory
Field:
Coding Theory
Goal: find codes with best error-correcting properties.
Historically many codes were discovered by clever search.
AI could find:
new record-breaking codes
improved storage systems
better satellite communication schemes
Materials science
Huge design space for molecules and crystals.
AlphaFold already showed the power of AI in biology.
Next targets include:
superconductors
catalysts
battery materials
These are essentially search in chemical configuration space.
Algorithms
AI could discover new algorithms.
Some early examples already happened with:
AlphaTensor
AlphaTensor discovered faster matrix multiplication algorithms for certain sizes.
That shocked many mathematicians.
4. Why search is suddenly becoming powerful
Three changes happened recently:
Massive compute
We can evaluate billions of candidates.
Hybrid AI systems
Neural networks guide the search.
Fast verification
Computers can instantly check if a candidate is valid.
That combination is extremely powerful.
5. Problems people think AI search may solve next
Researchers often mention:
Small Ramsey numbers
Especially:
Ramsey number R(6,6) bounds
hypergraph Ramsey numbers
Sphere packing variations
Related to:
Sphere Packing Problem
New constructions might appear.
New error-correcting codes
Important for:
deep space communication
storage systems
quantum computing
Circuit optimization
Finding minimal circuits for cryptographic operations.
Huge search space.
6. About SolveAll.org
Yes — SolveAll has been discussed in the AI research community.
The idea behind it is roughly:
Build AI systems specifically designed to attack unsolved scientific and mathematical problems.
Their philosophy aligns with the search paradigm:
structured problem databases
automated conjecture generation
algorithmic exploration
verification loops
It’s similar in spirit to projects like:
Lean
Coq
but aimed at problem-solving pipelines rather than proof verification.
The general concept is gaining traction because of results like:
AlphaFold (biology)
AlphaTensor (algorithms)
AlphaEvolve (combinatorics)
7. The deeper idea: “scientific search engines”
Some researchers think future AI systems will look like:
generate hypothesis
→ test
→ refine
→ repeat
This mirrors the scientific method.
Instead of asking AI for answers, we ask it to explore possibility space.
8. A provocative prediction
Many scientists now think the first major math breakthrough by AI will not be a proof like the:
Riemann Hypothesis
Instead it will likely be something like:
discovering a new combinatorial construction
finding new algorithms
optimizing structures humans overlooked
Exactly the type of problem that better search excels at.
✅ The key insight from that quote
Some problems are hard because:
we don’t understand them
But many are hard simply because:
The search space is enormous and humans can only explore tiny parts of it.
AI is beginning to change that.
If you're interested, I can also show you 5 famous open problems that are almost purely search problems (and therefore extremely likely to fall to AI in the next 10–20 years). They’re fascinating because they look deceptively simple.
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