whats the hint for incongruency?

The blank needs a word opposite of 'harmonious' so incongruity fits
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It may not be the case. The incongruity seems to describe pythagorans ideas not fitting with the irrational numbers.

absurdity and proscribe

Bump for further discussion
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What is the hint for 'proscribe'?
Shouldn't it be condone?

The question, especially at the beginning, sounds a bit odd in its meaning.

The (i) _________ of “surds"—irrational roots—with the Pythagoreans’ faith that all phenomena in the universe could be expressed through harmonious ra­tios of whole numbers led the cult to (ii)_________ any mention of their exis­tence to the uninitiated.

if we take a look to the first words - irrational - that is the hint to have B in the first blank.

As a contrast, the second part of the sentence tells us that the universe could be explained by something is harmonious - numbers. However, this numbers are fully understood by a restrict number of people or scientists which turns out is like a cult. This cult proibits to the people external to it to know even the existence of them

That is the meaning and unfolding of the sentence itself.

Regards
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Got it now, thank you -- I was actually thinking of 'Condone' meaning prohibit (but it actually means the opposite )

where is the contrast in the sentence

The incongruity of the irrational roots can be expressed, oddly, through the harmonious ratios

Regards
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