Recent research reveals a phenomenon of convergent evolution in artificial intelligence, where diverse language models independently develop similar mathematical representations despite being trained with different architectures and methods. A new study shows that models such as Transformers, Linear RNNs, LSTMs, and classical word embeddings all learn to represent numbers using periodic features with dominant frequencies corresponding to T values of 2, 5, and 10. These features manifest as distinct spikes in the Fourier domain, indicating a shared underlying structure in how neural networks process numerical data. However, the study identifies a critical two-tiered hierarchy within these learned features. While all the aforementioned models exhibit Fourier domain sparsity, meaning they detect these periodic patterns, only a subset achieves geometric separability. Geometric separability is essential for the model to linearly classify a number based on its modulus T. The researchers prove that while Fourier sparsity is a necessary condition, it is not sufficient to guarantee that a model can mathematically distinguish numbers in this way. To explain why some models succeed in this task while others fail, the authors conducted empirical investigations into the specific factors influencing feature learning. The findings indicate that data composition, model architecture, optimization algorithms, and tokenization strategies all play pivotal roles. The study identifies two distinct pathways through which models acquire the necessary geometrically separable features. The first route involves learning from complementary co-occurrence signals found in general language data. This includes interactions where numbers appear alongside text and relationships between different numbers within the same context. The second route involves exposure to multi-token addition problems. Notably, the research clarifies that single-token addition tasks are insufficient for developing these advanced representations; the model requires the complexity of multi-token arithmetic to learn the required geometric properties. This discovery highlights the robust nature of convergent evolution in feature learning. Regardless of whether a model is a Transformer or a recurrent neural network, or whether it is trained on general text or specific arithmetic tasks, the pressure to represent numbers effectively drives them toward similar internal structures. The ability to form geometrically separable features appears to be a fundamental outcome of learning from sufficient statistical signals, whether those signals come from natural language patterns or explicit mathematical operations. The implications of this work extend beyond theoretical understanding. By identifying that geometric separability is not automatic but depends on specific training conditions, the study offers insights for improving AI models' mathematical reasoning capabilities. It suggests that merely exposing a model to numbers is not enough; the training data must contain specific structural cues, such as cross-number interactions or multi-token arithmetic, to foster the development of robust numerical representations. This research provides a clearer map for how different model families converge on similar solutions to the complex problem of number representation, bridging the gap between diverse architectural approaches.