Rabbi Nachum Zev Ziv was born around 1857, the son of Rabbi Simcha Zissel Ziv, the Alter of Kelm. As a youth he studied at the Kelm Talmud Torah, followed his father to Grobin and back to Kelm, and spent a period at the Perushim yeshiva of Eishishok.

After his marriage he settled near his father-in-law and went into business, later trading timber in Königsberg. Even in business he lived by the discipline of Kelm: rising every day at three in the morning to learn until the morning prayer, he gave his trade only a few fixed hours and left it at a set time for the beit midrash. Already in Grobin, when his father was ill, he had helped him run the Talmud Torah.

At the end of 1911 he returned to Kelm and joined the leadership of the institution alongside his brother-in-law, Rabbi Tzvi Hirsch Broida. When the latter died in 1913, he bore its whole burden while still following the schedule himself as one of the avreichim. Kelm was one of the most demanding institutions of the Mussar movement, cultivating order, self-mastery and precision in every act; he gave talks there and trained many disciples. During the First World War, under German occupation, he made sure every set time was kept.

He fell ill and passed away on Friday, 2 Shevat 5676 (January 1916).