New Einsteins need positive environment, independent spirit

The article “Why No ‘New Einstein’?” and the ensuing letters perhaps raise a similar question in fields other than physics. In the mathematical arena, one could ask “Why no new Euler?” Of course, Leonhard Euler’s name could be replaced by the names of several other great mathematicians, but an argument could be made that Euler shared with Einstein an amazing intuition that, it seems, is a trait of a select few. I believe William Dunham’s wonderful book gives insight to Euler’s intuition. ¹

It may be the common opinion among modern mathematicians that many of Euler’s methods would not stand up to current mathematical rigor. And, as an engineer, I dare not take issue with that. But it seems one reason why no new Euler has arisen is that for scientists and engineers, at least, the flame of intuition too often is extinguished in the very first university mathematics class they take. Certainly mathematical rigor has its place. But an intuitive line of thought that leads to a correct mathematical result ought not to be discouraged, beyond a possible admonition about where such thinking could lead one astray. In fact, intuitive thinking ought to be celebrated, as long as we non-mathematicians do not make any claims to rigor or demand that mathematicians strictly agree with us.

A new Euler would not necessarily emerge from the non-mathematician class, although that possibility cannot be ruled out either. Paul Dirac, Richard Feynman’s hero, comes to mind immediately as one who resembled Euler in the way he did some of his mathematics. His book on quantum mechanics shows how he masterfully created a new mathematical formulation in order to do his physics. ² The mathematicians were left the task of showing that his results could also be proven rigorously. After all, who will argue with one whose non-rigorous mathematics leads to the discovery of a new particle?