ALRIGHT, time for some integers in a grid!

Question

What's the answer to this puzzle?

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Answer 1

I think you are looking for

PYTHAGORAS

Reasoning:

ALRIGHT clues that we are looking for integers all related to right triangles (all right). These would be sets of Pythagorean triples, the sets of 3 integers forming sides to a right triangle.
We can fill in the grid according to the clues, following some general guidelines:
- Instead of listing in traditional order, list from long to short, per line segments above the grid (20,16,12 instead of 12,16.20)
- Generally favor lower values over higher values, to ensure that the "BLUE" squares will fall in the range 1-26 for conversion to A-Z later to generate an answer. (although with the descending restriction that I noticed after the fact, this may not apply)
- Where multiple options exist, we can choose the option that leads to a logical final answer: (although with the descending restriction that I noticed after the fact, this may not apply)

All entries are filled in, and converting the blue squares to letters, we get PYTH?GOR?S. If we treat the ?'s as A's, we get PYTHAGORAS.
Noting that no triple would ever include a "1" to generate the A's, that explains why the "A" rows are filled in red.

At first, I assumed the op was looking for a three word phrase (per the blanks at top), so I thought the best option was the full name of Pythagoras: PYTHAGORAS OF SAMOS. But that doesn't match the lengths of the blanks. Nice misdirection!
Instead, the blanks (long, medium, short) clue that the side lengths are listed in descending order, with 'c', the long side, in column 1. That would mean the answer is simply PYTHAGORAS.