Wikipedia is actually helpful here), and 17 as the sum of 10 (representing the law) and 7 (representing the Holy Spirit) (Comm. Jo. 72.8). Jerome observed that a Greek zoologist had counted that there were 153 different types of fish (Comm. Ez. 47.6-12). The great Raymond Brown considered a number of interpretations and threw up the white flag: "One cannot deny that some of these interpretations (they are not mutually exclusive) are possible, but they all encounter the same objection: we have no evidence that any such complicated understating of 153 would have been intelligible to John's readers" (Gospel according to John XIII-XXI, 1075). Interestingly, he proposes that, like the details in 19:35 and 20:7, the exact number is intended to give the impression that the Beloved Disciple is reporting the exact number of fish caught. (He hastens to add: "By way of caution we should note in conclusion that the explanation we have offered of the number's origin is not a solution to the problem of historicity" ). In a 2002 Neotestamentica article later republished in The Testimony of the Beloved Disciple (2007, Baker Academic), Bauckham takes us back to a numerical solution to the numerical problem. Following M. J. J. Menken's 1985 dissertation published by Brill in NovTSup, concerning which Bauckham says, "I have seen no reference to it in any work of Johannine scholarship" (Testimony, 275n.15), Bauckham notes a number of supposed instances of numerical composition in GJohn. For example, he argues that the Johannine prologue contains 496 syllables and the Johannine epilogue contains 496 words (Testimony, 277). 496 is not only a triangular number, but also the numerical value of "only begotten" in Greek (John 1:18; cf. also 3:16). On this basis, Bauckham then proposes that the presence of 153 is another instance of gematria, as 153 is the numerical value of the Hebrew for "sons of God," a phrase that appears in Greek in 1:12 and 11:52 (NB: inarthrous in the former, arthrous in the latter). Thus, gematria in the prologue parallels gematria in the epilogue, and Bauckham makes this one plank in an argument for the originality of John 21 to GJohn.
What to make of this solution for the 153 fish? Honestly, I have no idea. And I should be upfront about the fact that I don't have a better solution. Further, it's abundantly clear that gematria was important for early Christians as well as the Fathers in their interpretations of Scripture. For the life of me, though, I can't get my skeptical eyebrow to come back down when I'm reading this type of thing.
**UPDATE: Thanks to Mikeal Parsons for pointing out his article on early Christian numerological exegesis ("Exegesis 'By the Numbers': Numerology and the New Testament," PRSt 35 : 25-43), wherein he addresses this and other issues. Building upon Augustine's observation of 153 as a triangular number reducing to 17, he suggests that 17, being one "under" 18, indicates that the created order is "under" Jesus since 18 is the value of iota-eta, the first two letters of "Jesus." (That 18 had special value for Christians for specifically this reason is clear in Barn. 9.7-9.) That is, Parsons suggests the numerology expresses the theology present elsewhere in, e.g., Col. 1.16-17.