Java Integers Min_Value negative then compare

Because of silent integer overflow: Integer.MIN_VALUE is -2^31 and Integer.MAX_VALUE is 2^31-1, so -Integer.MIN_VALUE is 2^31, which is Integer.MAX_VALUE + 1, which by definition is too large for an integer. So it overflows and becomes Integer.MIN_VALUE...

You can also check that:

System.out.println(Integer.MAX_VALUE + 1);

prints the same thing.

More technically, the result is defined by the Java Language Specification #15.18.2:

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

Basically, because Integer.MAX_VALUE is actually only 2147483647, so -Integer.MIN_VALUE, which would be +2147483648, actually overflows the capacity of the internal binary representation of integers. Thus, the result "loops around" back to Integer.MIN_VALUE, or -2147483648.

If you did long b = -((long)a); instead, you would get the expected result.