1. Emil Fischer’s proof of the structure of glucose.
1891 (Nobel Prize 1902)
(+)-Glucose is an aldohexose
* * * *
CH2-CH-CH-CH-CH-CH=O
OH OH OH OH OH
Four chiral centers  24 = 16 stereoisomers

3. Therefore, (+)-Glucose must be one of the following:

4. Fisher also discovered that (-)-arabinose is an aldopentose from which (+)-glucose can be made.
* * *
CH2-CH-CH-CH-CH=O
OH OH OH OH
three chiral centers  23 = 8 stereoisomers
If we arbitrarily assign C-4 to be D (as Fisher did for Glucose), then there are 4 stereoisomers:

5. Fact: Fisher oxidized (-)-arabinose and observed that an optically active dicarboxylic acid was formed.

6. Only two of the stereoisomers can possibly be arabinose:

7. In (-)-arabinose, the configuration about C-2 must be:

8. Fact: Using the Kiliani-Fischer synthesis to add a new chiral center to (-)-arabinose yields a mixture of (+)-glucose and (+)-mannose.

9. Fact: Oxidation of both (+)-glucose and (+)-mannose yield optically active dicarboxylic acids.

10. The only way that both (+)-glucose and (+)-mannose can give optically active dicarboxylic acids upon oxidation is if the configuration about C-4 is with the –OH on the right in the Fischer projection.
But, which compound is (+)-glucose and which one is (+)-mannose?
Fact: Oxidation of both (+)-glucose and (+)-gulose yield the same dicarboxylic acid.
Fact: The dicarboxylic acid produced from (+)-mannose is not made by the oxidation of any other aldohexose.

12. HO

13. Therefore, (+)-glucose has the following configuration:
C-5 was assigned arbitrarily by Fischer.
C-3 is known from the observation that the oxidation product of (-) arabinose is optically active; and (+)-glucose and (+)-mannose can be made from (-)-arabinose by the Kiliani-Fischer synthesis.
C-4 is known from the fact that both (+)-glucose and (+)-mannose yield optically active dicarboxylic acids.
C-2 is known from the fact that both (+)-glucose and (+)-gulose yield the same dicarboxylic acid.