If you have an apple and I have an apple and we exchange apples, we each still have one apple. But if you have an idea and I have an idea and we exchange ideas, we each now have two ideas, perhaps even more.

According to basic economic principles, the following 2 conditions constitute the sufficient conditions for non-depreciating assets:

• Supply is non-strictly monotonically decreasing
• Demand is non-strictly monotonically increasing

"Non-strictly" means that conservation cases are allowed. For example, when both supply and demand are conserved, value is also conserved, thus not depreciated, and therefore still qualifies as a non-depreciating asset.

Although this is an idealized financial product, there have been some approximate non-depreciating assets throughout history. For example, gold's supply is scarce and approximately conserved, while demand increases with population growth and economic prosperity, thus approximately satisfying the above sufficient conditions. However, gold's demand may still be threatened by substitutes, such as the emergence of digital gold driven by black swan blockchain technology, which will inevitably split gold's demand.

This article proposes an alternative non-depreciating asset: mathematics (including axioms, theorems, conjectures, algorithms, code, papers, or any abstract ideas).

Unlike traditional non-depreciating assets, mathematics' demand is not limited or scarce, but rather ∞, because it can be infinitely replicated, but ∞ is also a form of conservation, thus satisfying the definition of non-strictly monotonically decreasing. Meanwhile, as civilization develops, human demand for mathematics will inevitably be non-strictly monotonically increasing. Unlike physical assets such as gold, the emergence of substitutes $x'$ in most cases not only doesn't weaken the value of the original $x$, but rather increases it. Because now $x$ has gained another value: it gave birth to $x'$. Because in the history of mathematical development, in most cases, it would be difficult to have $x'$ without first having $x$. For example, fractions $\frac{1}{b}$ can replace division, but how could we have fractions without first having division?

So what is the value of a mathematical product? It's the cumulative historical number of times it has benefited others. And mathematics' characteristic is that it can always generate altruistic value in unexpected scenarios.

Therefore, mathematics can even better satisfy the sufficient conditions of non-depreciating assets than gold.

About the Replacement of Open Source Code Projects

There are 2 possibilities for the replacement of open source code projects:

• The first is the continuous evolution of the same project, which follows the above plan.
• The second is new projects replacing old projects, which can be divided into 2 cases,
  • Standing on the shoulders of giants to replace the giants (still following the above plan)
  • Completely innovative from 0 to 1 (these are mathematicians and thinkers who can go down in history. The probability is almost 0).

For example, GPT5 will eventually replace GPT3, but how could there be GPT5 without GPT3? Although GPT3's commercial value may end, from an academic perspective, GPT3's milestone significance is even greater. Consensus will solve this problem. Newton's theory was overthrown by Einstein long ago, but Newton will forever remain the father of science.

Present Value (PV) Floor Valuation Formula

Under the strict assumption of non-depreciation, assuming that during a short current time period $\delta t$, this non-depreciating asset generates cash flow $\delta v$, and the risk-free rate is $r$, then the present value valuation inequality for this non-depreciating asset is

$$ PV \geq \int_0^\infty \frac{\delta v }{\delta t} (1+r)^{-t} dt = \frac{\frac{\delta v }{\delta t}}{\ln (1+r)} \approx \frac{\delta v }{r \delta t} $$