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

And astronomers say that, given irreducible gaps in our knowledge of ’Oumuamua, this new proposal may never be fully accepted either.

From Scientific American • Mar. 22, 2023

This is a moment of clarity, in which all of the women in the room witness together both the necessity of forgiveness and its irreducible complications, its transformative power alongside its dangerous amenability to injustice.

From Salon • Feb. 4, 2023

At what point we reach the irreducible bottom is not easy to say.

From "A Short History of Nearly Everything" by Bill Bryson