Beyond Black Box ML: Why Scientific Domains Demand Mathematical Foundations
Machine learning is fundamentally about distributions—how data is spread, how uncertainty propagates, and how patterns emerge from noise.
A common beginner’s mistake is thinking you need deep mathematics and statistics to get into machine learning. This isn’t necessarily true. You can treat machine learning as a black box and use it to solve problems without understanding the underlying mathematics.
In some cases, this works fantastically well. You use tools that are carefully designed by others. If it works, it works. In this case, mathematics can be a distraction that keeps you from thinking about the problem you’re trying to solve.
But when you get closer to the limitations of your methods, knowledge of the underlying mathematics starts to pay dividends.
The limitations of machine learning on natural language
Large language models can work with text remarkably well, but they have fundamental limitations. One of the most significant is their lack of true reasoning abilities—they excel at pattern matching but struggle with logical inference and causal reasoning.
If you want to push beyond these limitations, understanding how LLMs work becomes crucial. Insights from statistics, physics, engineering, and information theory all contribute to building better language models and working around their current constraints.
The limitations in chemistry and biology
In chemistry and biology, the mathematical foundations of machine learning aren’t just helpful—they’re essential. Unlike computer vision or natural language processing, where massive datasets and pre-trained models provide a safety net, scientific domains force you to confront the fundamental limitations of machine learning from day one.
Consider these challenges:
Small sample sizes: A typical drug discovery dataset might have hundreds of compounds, not millions of images. Every data point is precious and expensive to obtain.
High-dimensional, sparse data: Molecular properties exist in vast chemical spaces with complex interactions. Traditional “big data” approaches often fail.
Domain-specific priors: Understanding protein folding, chemical reactivity, or biological pathways requires incorporating scientific knowledge that pure data-driven methods miss.
Interpretability requirements: You can’t just predict that a molecule will be toxic—you need to understand why, for regulatory approval and scientific insight.
In these domains, treating machine learning as a black box is a recipe for failure. You need to understand distributions, uncertainty quantification, and how to incorporate prior knowledge. The mathematics isn’t a distraction—it’s the foundation that makes the difference between a model that works in the lab and one that advances human knowledge.
This is where the real power of machine learning in science lies: not in replacing human expertise, but in augmenting it with principled mathematical frameworks that can handle uncertainty, incorporate domain knowledge, and provide interpretable insights.
Practical implications: Nanoparticle synthesis research
These insights have directly shaped my approach to nanoparticle synthesis research, illustrating why mathematical foundations matter in practice:
1. Building a spectroscopy data platform
Understanding that data is the foundation of scientific ML led me to create a comprehensive spectroscopy data platform. In domains with limited data, every spectrum matters. The platform addresses this by:
- Making data discoverable: Advanced search interfaces help researchers find relevant spectral data across different experimental conditions
- Enabling data reuse: Standardized formats and metadata ensure spectra can be compared and combined across studies
- Providing analytical tools: Built-in visualization and analysis tools help researchers extract maximum value from each dataset
- Facilitating collaboration: Shared access to curated datasets accelerates research across the community
This isn’t just about convenience—it’s about recognizing that in scientific domains, data scarcity demands sophisticated data management and discovery tools.
2. Investigating distributions in chemistry and biology
The mathematical foundations discussed here motivated a dedicated project on understanding distributions in chemical and biological systems. This work recognizes that:
- Traditional assumptions break down: Standard ML assumes large, representative datasets, but chemical synthesis often involves small, biased samples
- Uncertainty quantification is critical: Understanding confidence intervals and prediction uncertainty is essential for experimental design
- Domain-specific priors matter: Chemical knowledge about reaction mechanisms and molecular properties must be incorporated into models
These projects exemplify the principle that successful scientific ML requires both computational tools and mathematical understanding—you can’t treat the models as black boxes when every data point is precious and every prediction guides expensive experiments.