This has risky interactions with certain class features.
The second benefit, tie-breaking in contests where a stalemate is possible, isn't especially problematic. It effectively acts like a +1 bonus to ability checks that only activates a fraction of the time. I don't think there's too much to say about that benefit other than that it is highly situational.
However, the first benefit, being able to round up or down at will, is quite problematic from a balance perspective, because it can benefit character advancement in ways I don't think you intended. The following are just a couple of examples of what I mean.
When a Circle of the Moon Druid is 6th level or higher, they can wildshape into a beast form whose CR is 1/3 of their Druid level rounded down. For example, at 6th, 7th, and 8th levels they can transform into a CR 2 beast, and at 9th level they attain the ability to transform into a CR 3 beast. With the proposed Mathematician feat, they would be able to transform into CR 3 beasts as soon as 7th level. Effectively, every CR attainment threshold would be shifted down 2 levels for the Moon Druid. Given that the Moon Druid is already considered a fairly powerful Druid subclass in addition to a fairly powerful character period, this is a bit overpowering.
Any full spellcaster (Bard, Cleric, Druid, Sorcerer, or Wizard) multiclassed into a half-equivalent spellcasting class (Paladin or Ranger) or a third-equivalent spellcasting subclass (Eldritch Knight or Arcane Trickster) would advance their spell slot progression faster than they are supposed to. By the book, a 5th level Wizard who switches to only gaining levels in Arcane Trickster would attain an effective spellcasting slot progression level of 5th + (1/3 of 3rd rounded down) = 6th level by the time they have 3 levels in Arcane Trickster and would not attain an effective level of 7th = 5th + (1/3 of 6th rounded down) until they gained 6th level in Arcane Trickster. With the proposed Mathematician feat, they would reach an effective 6th level in their slot progression at 4th level in Arcane Trickster since 6th = 5th + (1/3 of 4th rounded up), once again another 2 levels sooner than anticipated.
There are more examples, but the fundamental problem is that rounding up will have very minor benefits in normal gameplay but quite major balance-breaking benefits in significant cases where an aspect of character advancement is calculated based on division rather than by consulting a class feature table. For this reason, I strongly recommend against adopting this feat.
Not to mention that a Half-Elf or Half-Orc could transform at will into a full-blooded Elf or Orc, respectively. (Just kidding.)