mathematically
adv.using numbers or math rules to solve a problem or explain something. You use this when you want to show that something is proven by calculation.
adv.in a manner relating to or using the principles of mathematics. Often describes the logical or numerical basis of a conclusion.
“The problem is mathematically impossible to solve.”
“The scientist proved her theory mathematically before she ever started the physical experiment.”
“While the strategy seemed sound in theory, the economist demonstrated that it was mathematically flawed once the long-term inflation variables were properly accounted for.”
Typically modifies adjectives or verbs to indicate that a statement is based on calculation rather than opinion.
“Janovitch and his colleagues have now demonstrated mathematically that this is possible with their approach.”
“This is precisely what Janovitch and his colleagues have now been able to show mathematically.”
From mathematical + -ly.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.