How many calories do we burn when we try to understand mathematical proofs? While thinking we burn calories. For comparison: "And if it’s the right wood and the right chess grand masters in the middle of a tournament, they are going through 6,000 to 7,000 calories a day thinking" from here...

How many calories do we burn when we try to understand mathematical proofs?
How does it depend on the representation of the proof? For example, there are plenty of proofs for the Pythagorean theorem, even some without words...
Not many.


  Although firing neurons summon extra blood, oxygen and glucose, any local increases in energy consumption are tiny compared with the brain's gluttonous baseline intake. So, in most cases, short periods of additional mental effort require a little more brainpower than usual, but not much more. Most laboratory experiments, however, have not subjected volunteers to several hours' worth of challenging mental acrobatics.


-Scientific America Does Thinking Really Hard Burn More Calories?


  Our results conclude that the measured Ff,ATPase reflects the oxidative phosphorylation rate in resting rat brains, that this flux is tightly correlated to the change of energy demand under varied brain activity levels, and that a significant amount of ATP energy is required for “housekeeping” under the isoelectric state. These findings reveal distinguishable characteristics of ATP metabolism between the brain and heart, and they highlight the importance of in vivo 31P MT approach to potentially provide a unique and powerful neuroimaging modality for noninvasively studying the cerebral ATP metabolic network and its central role in bioenergetics associated with brain function, activation, and diseases.


-PNAS Tightly coupled brain activity and cerebral ATP metabolic rate