Sediment accumulation rates and thermal trackers suggest a substantial and global increase in erosion rates over the last few million years. That increase is commonly associated with the impact of the Northern Hemisphere glaciation, but methodological biases have led researchers to debate this hypothesis. Here, we test whether Himalayan erosion rates increased by measuring beryllium 10 (10Be) in the sediment of the Bengal Bay seabed. Sediment originated from rocks that produced 10Be under the impact of cosmic rays during erosion near surface. Thus, the 10Be concentrations tell erosion rates. The 10Be concentration of the Bengal Bay sediment depends on the contributions of the Ganga and Brahmaputra Rivers. Their sediments have distinct 10Be concentrations because of distinct elevations and erosion in their drainage basins. Variable contributions could thus complicate erosion rate calculation. We traced these contributions by a provenance study using the Sr and Nd isotopic sediment compositions. Within uncertainties of ±30%, our reconstructed past erosion rates show no long-term increase for the last six million years. This stability suggests that climatic changes during the late Cenozoic have an undetectable impact on the erosion patterns in the Himalayas, at least on the ten-thousand to million-year timescales accounted for by our dataset.