irreducible

American  

[ir-i-doo-suh-buhl, -dyoo-] / ˌɪr ɪˈdu sə bəl, -ˈdyu- /

adjective

1. not reducible; incapable of being reduced or of being diminished or simplified further.

   the irreducible minimum.

2. incapable of being brought into a different condition or form.

3. Mathematics.

   1. of or relating to a polynomial that cannot be factored.

   2. of or relating to a group that cannot be written as the direct product of two of its subgroups.

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irreducible British  

/ ˌɪrɪˈdjuːsɪbəl /

adjective

1. not able to be reduced or lessened

2. not able to be brought to a simpler or reduced form

3. maths

   1. (of a polynomial) unable to be factorized into polynomials of lower degree, as ( x ² + 1)

   2. (of a radical) incapable of being reduced to a rational expression, as √( x + 1)

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Other Word Forms

• irreducibility noun
• irreducibleness noun
• irreducibly adverb

Etymology

Origin of irreducible

First recorded in 1625–35; ir- ² + reducible

Explanation

Something irreducible is as simple, basic, or straightforward as it possibly can be. How a certain person grows up to be a genius is irreducible to the sum of her experiences and genetic material — it's not that simple. And you might say that you can't generalize about your favorite poet, that her brilliant work is irreducible to such simplification. Irreducible is a big word, but it basically just means "you can't make it any simpler than this."

Example Sentences

Taken in isolation, these three irreducible realities are opaque; for Rosenzweig they become intelligible only in relation to one another.

From The Wall Street Journal • Mar. 6, 2026

For so many Labour MPs, that safety net, and a passionate commitment to it, form their irreducible core.

From BBC • Jun. 26, 2025

I realize this is heresy, but I think it’s important to acknowledge the irreducible strangeness of the drama.

From Los Angeles Times • Nov. 4, 2024

The larger the integrated information, the more the circuit is irreducible, the less it can be considered just the superposition of independent subcircuits.

From Scientific American • Sep. 8, 2023

No doubt I am guilty of some injustice here, but it is irreducible, since I cannot risk assuming that the humanity of these people is more real to them than their uniforms.

From "The Fire Next Time" by James Baldwin