Since the last answer was posted, Destiny 2 as received many updates, seasons, and expansions. As a result, this effectively increased the maximum triumph score. While I was unable to locate a break down of the scores for each category as shown in the previous answer, the highest triumph score I was able to locate was 103k (Reddit thread was posted roughly 1 month prior to Beyond Light release).
With the release of Beyond Light, the maximum triumph score has drastically changed. Since the expansion archived a good chunk of older content, the maximum triumph score dropped as a result.
While viewing the the triumph screen, you will now see two different numbers:
Legacy Score: This is the set of numbers on the right. Your legacy score shows the highest triumph score you achieved prior to Beyond Light.
Active Score: This is the set numbers on the left, formatted as current / maximum1. The active score is your score that is based on triumphs that are available in Beyond Light.
1 Since Beyond Light has only been recently released, the current known maximum triumph score is 16,770 as shown on Bungie's website. When viewing my triumph score, it only displays 16,610. The maximum score that is shown probably increases has you find and complete hidden triumphs.