Colombo's determinant problem asks when the matrix 
with entries 
has nonzero determinant
for distinct real numbers 
, 
, ..., 
and a positive integer 
.
The proposed characterization, attributed to Colombo's work by Ma (2026), is the
following for 
.
The determinant is nonzero iff 
and either 
or 
is even.
Two obstructions explain the necessary conditions. Expanding the powers gives matrix rank at most 
, so 
forces singularity. If 
is odd, the matrix is skew symmetric and therefore has zero
determinant when 
is odd. For 
, its determinant is 
and never vanishes.
Ma (2026) reported a proof of the remaining case, even 
and odd 
,
together with a Lean formalization. The even-exponent case follows from earlier results
discussed in that paper. The proof was developed with AI
assistance, and Li et al. (2026) supplied an independent proof.
Journal publication of these reports had not been confirmed as of Sep. 7, 2026.
