As someone on the mathematics side, I had no idea this misperception existed. Why would the Fields Medal be capped to recipients under age 40, otherwise? It is idiotic to think that an award for "greatest mathematical genius" (which is a clumsy way of describing any prize) would just ignore accomplishments over a certain age, it is almost offensive. It has always been an award recognizing emerging talent, and it has always been entirely clear to anyone who paid attention to it.
A perfect example is Sir Andrew Wiles, who proved the Taniyama–Shimura and thus resolved Fermat's last theorem, who received Abel and Wolf prize. But he was 40 when he began presenting his proof and was too old to qualify by the time he fixed his initial issues with Iwasawa theory. He was recognized by the Fields committee with a special "IMU silver plaque", instead.
The Abel prize (https://abelprize.no/) and Wolf prize (https://wolffund.org.il/the-wolf-prize/) exist to recognize general accomplishments in mathematics.
A perfect example is Sir Andrew Wiles, who proved the Taniyama–Shimura and thus resolved Fermat's last theorem, who received Abel and Wolf prize. But he was 40 when he began presenting his proof and was too old to qualify by the time he fixed his initial issues with Iwasawa theory. He was recognized by the Fields committee with a special "IMU silver plaque", instead.