I have a conjecture: people don't particularly like the number 4. Archimedes, Newton, Gauss: that's 3. Euler makes 4. Who makes 5?

There's the rub: there's no clear #5 (Poincaré? Riemann? Fourier? Hilbert?). The rub-within-a-rub: why should it matter? What's wrong with capping the "greatest mathematician" list at 4?

It seems that people like 3 (possibly hard-wired); they like 5 (fingers); they don't like 4. Alas, Euler's reputation suffers for it.