Someone is 36 years old and is a committed, practicing Muslim. However, he did not start fasting until he was 20. Is he required to make up for the days that he missed in the past?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and messenger.

You have to fast all the months (of Ramadan) that you failed to fast after having reached the age of puberty. In addition, you have to provide food to thirty poor people for every month that you make up for. That you are under the obligation of making up the missed months is explained by the fact that you have not fasted these months, so fasting them is still due upon you. Also, feeding is required because you need to expiate for the delay of making up for the missed fasts beyond the time specified by the religion; meaning, for every month you missed, you had to fast it during the eleven-month-interval that falls between two months of Ramadan. 

It is worth noting that if you made the intention to fast one day in Ramadan and, after you started the fast, you nullified your fasting by having sexual intercourse during daytime, then this is a violation that you need to expiate for by observing one of three actions: freeing a slave, but if you cannot then move to fasting two consecutive months, and if you still cannot then move to providing food to sixty poor people. This is proven by the Hadeeth narrated by Al-Bukhari and Muslim on the authority of Abu Hurayrah . If, however, you nullified the fasting by something other than sexual intercourse, then scholars held different opinions regarding this issue: some held that it is obligatory to offer expiation,  while others held it is not.

Anyway, you need to turn to Allah in repentance very often and  perform as many good deeds as you can. This is because your negligence of the obligatory fasting is a huge sin whereby you have abandoned an integral pillar of Islam for a very long time. The Prophet said: “Islam is built upon five pillars: the worship of Allaah alone and abandoning the worship of whatever else, establishing Prayer, paying Zakah, performing Hajj to the House, and fasting the month of Ramadan.” [Al-Bukhari and Muslim and this is the wording of Muslim] You definitely know what a pillar means to a construction.

Allah Knows best.