Peter Scholze and the Future of Arithmetic Geometry (2016)
&gt; “To this day, that’s to a large extent how I learn,” he said. “I never really learned the basic things like linear algebra, actually — I only assimilated it through learning some other stuff.”<p>This was interesting to me. My math profs always admonished us to ensure foundations are completely watertight before advancing to the next thing in tiny increments. I&#x27;ve absorbed this to the point where I perhaps get stuck filling in inconsequential gaps at roughly the same level, kitting out base camp as fully as possible but postponing the ascent.<p>I have no dreams of becoming a professional mathematician, but maybe I&#x27;d have quicker insights and more creative ideas if I tried this approach too, tackling something impossible and working backwards.