Use 'insuperable' to stress extreme difficulty, implying it's not just hard but impossible to tackle the problem. The insuperable challenges of deep space travel fascinate scientists.
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Not Physical
'Insuperable' often describes figurative barriers or problems, not physical ones. Her fear of public speaking was an insuperable obstacle in her career.
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Serious Tone
The word 'insuperable' is formal and serious, suitable for academic or professional contexts. The committee was faced with an insuperable task, demanding profound contemplation.