Math: Discovered or invented? And Why It Matters to Dev Guys❗

There's a fundamental question that has puzzled thinkers
for centuries: Is mathematics discovered, or is it invented? This long-standing debate within the philosophy of mathematics isn't just an academic exercise.

For us in software development, as designers, modelers, architects, and developers, understanding this dichotomy, and its nuances, directly impacts how we approach complex problems and build robust systems.

--------------------
✅ The "Discovered" View:
From the perspective that mathematical truths exist independently of human thought, software professionals often find themselves acting as explorers. When I delved into domains like accounting or payroll, I encountered deeply embedded principles and seemingly immutable rules.

The precise logic of financial transactions, the established principles of double-entry bookkeeping, the complex yet consistent calculations for tax liabilities or social contributions, these feel-like inherent truths governing how money and compensation work.

A big confession:
I simply discover that I'm not(and must not!) invent the principle that a debit equals a credit, or that gross pay minus deductions equals net pay.

We are accurately modeling fundamental relationships that exist independently, uncovering the mathematical structure of the real world within that domain.

--------------------
✅ The "Invented" View:
Aligned with the view that mathematics is a human-constructed system of symbols and rules we create, much of what we do in software involves invention. While the core accounting principles might be discovered, the way we implement them within a digital system is a creative act of invention. We invent abstract data structures to represent ledgers, design custom algorithms to handle intricate tax rules across different jurisdictions, or devise new abstract models for payroll processing that ensure scalability, auditability, and performance.

Example:
Consider the solution we invent for managing a large-scale accounting ledger. While debits and credits are discovered principles, the invented part is how we represent, store, and process millions of transactions efficiently in software. This involves devising custom data structures for journal entries, creating indexing strategies for rapid querying, and designing algorithms for real-time balance calculations. These aren't just paper-to-digital translations; they're new mathematical constructs and rules invented to harness computational power, ensuring consistency and performance in complex digital environments.

--------------------
✅ The Nuance of the Dichotomy:
Some philosophers, like George Lakoff, argue that this dichotomy is too simplistic, suggesting mathematics emerges from our embodied human experience. From a software professional's perspective, this nuanced view resonates strongly. We are constantly observing and discovering the underlying mathematical nature of the problem space, recognizing the inherent patterns and constraints. Simultaneously, we are inventing abstract tools, languages, and systems, from low-level algorithms to high-level architectural patterns, to articulate, solve, and extend those problems.

🧐For Example:
The recognition of recurring problems in software led to the discovery of design patterns as effective solutions. However, the formalization and naming of these patterns, along with the rules for their application, were distinct acts of invention that codified and communicated this discovered knowledge in a reusable, mathematical way.

Our work is a continuous cycle of recognizing existing mathematical structures and then creatively constructing the digital scaffolding around them.

--------------------
Understanding this dynamic, knowing when we are accurately reflecting a discovered truth versus when we are inventing a new paradigm, is crucial for making sound design decisions, ensuring system integrity, fostering innovation, and ultimately, building effective software solutions.

- Masoud Bahrami