@diff_eq when I was a student, I thought this was a great influential paper, but now I think this is a bit overrated (the catchy title certainly played a role). In my opinion, Meyers and Serrin definitely have produced much better Mathematics
@torgeirlysen "I still view writing papers primarily as a way of sharing something that I have learned with the world" that's a good point, it's the same for me
I am so tired of seeing these posts.
I am so tired of seeing my beloved field of study be the testing lab for a technology that is disrupting everyday life at such a high pace.
Mathematics were always about the beauty of seeing the ideas of a person unfolded in an extremely precise language so we can all look into a mathematician's mind and see their purest form of ideas, their understanding of a problem, their style, their way of communicating to other fellow researchers through mathematical results... this often transcends the common language humans use to communicate with each other and it is incredibly exciting to bump into shared ideas another person had thousands of kilometers away several years ago without even knowing them.
I am extremely unexcited about AI-breakthroughs in Mathematics in the same way I am extremely unexcited about a picture created by AI or an AI-generated video, not to speak about AI-generated text. Mathematics requires soul and intention. Mathematics need not be useful by definition, Mathematics are pure art that need hard work and effort to understand. The high you get when a year of work gets condensed in a one-page result is incomparable to anything else and, certainly, a machine is not apt to relate to humans in such a humane way.
I am not interested in the truth of the results. I am interested in how was the mind behind a result able to connect those dots. I am interested in the diversity human thoughts bring to Mathematics. I am not interested in a bunch of servers running probabilities to return a Theorem, even if true: that lacks the objective of Mathematics as I see them.
@DSP_fact are you sure? the Fourier transform is the Laplace transform evaluated on the imaginary axis. I think the z-transform on the unit circle is related to Fourier series