grammar - Use of would in past tense

So I was writing a biography and my teacher (Who is not an English teacher, he is a math teacher) made several marks on my paper for my use of would. For example, I wrote,

"He would publish his first mathematical paper at the age of eighteen."

My teacher said I should have used published instead of would publish. He also said in class that since it is a biography that takes place in the past that this wasn't the correct use of past tense. I don't think he is right and I feel that this issue is more a stylistic difference. However, I am unsure as well so any help would be appreciated. I will put some more example below too.

1) me-> "One year later he went on to earn his Ph.D..."

him-> should have been earned and I should've got rid of went on to

2) me-> "He would be associated with the project until 1955."
him-> should have been was and not would be

3) me-> "Von Neumann would go on to write, "[boring qoute]"
him-> should have been went and not would go

4)
me-> "Between 1927-1930 Von Neumann would teach Mathematics at University of Berlin."

him-> should have been taught and not would teach