# How much does Mathematics change in a generation?

I had an interesting thought where I wondered that if I had a grandparent who had been a mathematician (or at least studied mathematics), how much of modern undergraduate mathematics would they understand?

I think in other sciences this gap would be much greater than in mathematics. So I guess my question is, how much does mathematics, that is taught to students, change in a generation? In particular, how much has it changed in the last generation?

• I think it is important here to define which generation, I mean mathematics in a generation now evolves much more than in a generation say 2000 years ago (I suppose!) Are you referring to recent times? Maybe to the gap between last generation and this generation? – Euler_Salter Dec 26 '16 at 20:35
• @Euler_Salter Yes I suppose I am, I'll update my question! – user5140 Dec 26 '16 at 20:41
• now it is clearer! :) – Euler_Salter Dec 26 '16 at 20:44
• I got my math degree 30 years ago, and I can never remember what's a surjection, bijection, etc. As an example of bigger changes over longer periods, ca. 1900 you had to decide whether you wanted to learn quaternions or vectors. – Ben Crowell Dec 28 '16 at 1:29
• According to Max Planck, one funeral at a time. Someone even did a study! – Spencer Mar 11 '17 at 15:06

## 1 Answer

Mathematics advances rapidly. A generation ago, ultrafiltres and category theory were pretty new and niche, now they are pretty close to foundational as concepts in algebra and topology. Theoretical Computer Science has changed massively in the past 30 years. Some of the greatest results in the field are recent discoveries. PCP Theorem, the Regularity Lemma, and the Triangle Removal Lemma are all pretty new. The classification of finite simple groups is another thing that has massively changed mathematics. Almost all of these things caused massive changes at the undergraduate level, and a few are first year graduate topics.

By comparison, I think quantum computing and M-theory are the main changed in physics that would percolate to the undergraduate level (physicists please double check me though!).