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I guess one can construct rational arguments for turning down money if one doesn't believe in capitalism or economics or money, but that doesn't make the act of turning down money economically non-rational.

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For him, marginal dollars have negative utility. This may be because of morality -- he could consider the act of giving mathematics prizes antithetical to promoting good math research; it may be because of his focus -- he knows that he would have to manage the money if he got it, which would distract him from doing math; it may be because of fear -- there may be people that would kidnap his family to get access to that money.

If you consider "economics" to deal only with maximizing money, it's economically non-rational to decline this prize. If you consider "economics" to deal with maximizing utility, it could easily be rational to decline this prize.

His wealth-generating function does not take money as an input, beyond that which is required to sustain his physical body. He happily specializes in the production of theorems, and does not require financial rewards as an incentive.

If he had a family to support, it might be a different matter.

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