When did Hilbert Space First Enter the Undergrad Math Curriculum?

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The discussion centers on the timeline for integrating newly discovered mathematical and physics concepts into undergraduate curricula, particularly focusing on Hilbert space. It is suggested that standardization can take 30-40 years, influenced by the significance of the concept and the course level. While fundamental theories may take longer to be included in early undergraduate courses, significant discoveries can be introduced more rapidly, as seen with the WMAP experiment results being discussed in classes shortly after their announcement. The integration process is often gradual, starting with introductory courses that may not delve deeply into new material. Advances in communication technology have accelerated this process, allowing for quicker dissemination and refinement of ideas within the academic community.
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How long does it take for newly discovered math material or physics material to be standardized into the math undergrad curriculum? Just wondering about hilbert space as well. When did hilbert space first go into the undergrad curriculum?
 
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kramer733 said:
When did hilbert space first go into the undergrad curriculum?

Before 1970, in the UK. (I have no idea how many years it was there before 1970.)
 
I would hazard a guess of 30-40 years depending on the importance of the idea.
 
Pyrrhus said:
I would hazard a guess of 30-40 years depending on the importance of the idea.

And depending on the level of the undergrad course. The fundamentals have been so well established that even a unified theory is unlikely to make it into a sophomore course, but a senior level mechanics course is a different story.
 
Sometimes it happens immediately, like the results of the WMAP experiment measuring the age of the universe. I remember discussing it in my cosmology class the week it was announced, and it comes up in almost all astronomy classes now.
 
kramer733 said:
How long does it take for newly discovered math material or physics material to be standardized into the math undergrad curriculum? Just wondering about hilbert space as well. When did hilbert space first go into the undergrad curriculum?

It depends.

Sometimes courses can be offered at the undergraduate level that present an introductory level course on a particular topic without going into great detail.

Also with research, it usually takes a little while before things become polished. You typically start out with unorganized ideas and lots of pieces of paper (or nowadays, electronic documents), and then it takes a little while for that to be processed, refined, and presented in an optimal way.

Also nowadays, this process can happen a lot quicker since there is a much higher rate of involvement of people in this process, and the major bottleneck which was communication has largely been reduced with technologies like the internet.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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