Learn Polish: Ten stary pies był mądrzejszy, niż myślisz. - This old dog was smarter than you think.

The basic adjective is mądry. To make it comparative ('smarter'), we drop the final -y. Because the remaining part (mądr-) ends in a group of consonants, Polish adds the suffix -ejszy instead of just -szy. (For comparison, notice how the word stary in this sentence only needs -szy to become starszy). The -ejszy suffix causes the final consonant to soften, so the r changes to rz, giving us mądrzejszy.

Why does mądrzejszy end in -y?

Even though it is in the comparative degree, it still acts like a normal adjective and must match the gender and case of the noun it describes. Since pies (dog) is a masculine noun acting as the subject of the sentence (Nominative case), the adjective takes the standard masculine ending -y. If we were describing a feminine noun, it would change to mądrzejsza.

Why do we use niż for 'than' here instead of od?

In Polish, you can often use either niż or od to compare things. However, because we are comparing the dog's intelligence to a whole action or verb phrase (myślisz - 'you think'), we must use niż. You can only use od when comparing directly to a noun or pronoun, such as mądrzejszy od ciebie (smarter than you).