ɪɾ ɛksplˈeɪnz hˌaʊ ðɪ ˈɔːθɚz pɹˈuːvd mˌæθɪmˈæɾɪkli ðæt ðɛɹˌɑːɹ ɐ tˈoʊɾəl ʌv ˈeɪɾi fˈaɪv dɪstˈɪŋkt tˈaɪ nˈɑːts, mˈoʊst əv wˌɪtʃ hæd nˌɑːt bˌɪn pɹˈiːviəsli nˈoʊn.
It explains how the authors proved mathematically that there are a total of 85 distinct tie knots, most of which had not been previously known.