Velazquez's origin, like so much relating to the Houston Spies, is ultimately a mystery. The prevailing hypotheses hold that Velazquez is a metaphysical construct created by a secret, forbidden sect of mathematicians for some unknown purpose, a normal human forced into this present form after a disastrous attempt to divide by zero, or the universe attempting to experience itself.
Some Spies fans have postulated that Velazquez began playing Blaseball since Velazquez's previous outreach effort to convince the general public to appreciate the mathematical discipline, coolmathgames.com, was removed from the Internet—or possibly since Blaseball's geometric fields, many statistics, and parabolic curves appeal to Velazquez's sensibilities. Velazquez has also been observed trying to convince everyone's son, Son Scotch, to enter a stable and profitable career in mathematics.
Conjecture as to the original Velazquez's true motives is necessary since, according to intel from an indeterminate inside source, no one on the Houston Spies was good enough at math to decipher what Velazquez wants to say. Unfortunately, this meant that in order to communicate, Velazquez usually had to individually graph each word that they want to say on a TI-84 calculator, a process that was laborious at best.
This linguistic  barrier is likely the reason why the Spies have always had a problem with optimizing their team lineup; after asking Velazquez about the subject in hopes of finding a mathematically perfect optimization, the output was so confusing that players were rumored to resort to measures such as charades and the 'hot and cold' game to find a lineup they could actually use. The Spies eventually decided to put Velazquez's talents at obfuscation to use, assigning Velazquez to run the Hungarian numbers station that serves as the team's official form of communication.
After spending several seasons learning Blojban, reading computer assembly code, and acquiring a custom keyboard with a button layout identical to that of the TI-84, Velazquez began to use the increased memory and automation capabilities of computers to communicate more efficiently. Velazquez's missives remained brief and cryptic, but became significantly more readable, and some of them were even in a language the Spies could comprehend.
During early seasons of Blaseball, Math Velazquez consulted with several eminent mathematicians in the hopes of developing an experimental algorithm which would allow Velazquez to become the first Blaseball player with a negative star rating. It was unknown how Velazquez intended to achieve this, why Velazquez considered this outcome desirable, and what impact it would have on Blaseball as a whole.
Velazquez published academic papers theorising that achieving negative values could be a first step towards opening Blaseball up to ever more esoteric mathematics—vectors, infinite series, and perhaps even beyond that into complex numbers, tensors, higher dimensions, and more. It remains unknown why Velazquez considered this outcome desirable, and opposing scholars warned that success in this project could critically destabilise Blaseball. This was because Velazquez appears as patterns in everything, and is therefore, for all practical purposes, omnipresent. Though "Math is Math," as both mathematicians and Houston Spies fans are wont to chant, swapping one variant for another could potentially have had far-reaching, undetectable consequences we cannot begin to fathom.
Velazquez was often credited with being the reason for the Spies' often unpredictable performance, as Velazquez was a wild and experimental pitcher. Velazquez's pitches often involved complex algorithms unfathomable to other players, resulting in as many thrown balls as strikes and hits. One theory proposes that Velazquez's attempts to reach a negative star value was also an attempt to research new and bizarre pitching forms, though this rumor has been staunchly denied by the Houston Spies.
Prior to Season 4, Velazquez was spotted spending a lot of time with Spies colleague Fitzgerald Blackburn. When pressed, Velazquez said that Blackburn is a doctor in all the ways that count, xe was helping Math achieve a negative star rating and any relationship between the two is nobody's business.
According to heavily redacted documents left by Velazquez before the departure, both Fitzgerald Blackburn and then-Spy Collins Melon aided in an experiment intended to help Velazquez become the first player in ILB history to boast a negative star rating. How Velazquez achieved the swap is a mystery, but the experiment swapped both Velazquez and Melon for beings who were, to all appearances, the exact same as their previous selves but with new skills.
After the decree finalizing the Alternation was ratified at the end of Season 4, Spies fans were shocked and dismayed to discover that Velazquez had been replaced. Neither Velazquez nor the Houston Spies organization have ever made an official statement regarding what precisely happened when making the dimension swap with Old Math, but an anonymous investigative journalist for The Blaseball Chimes released a short—albeit dramatised—article, the first of its kind that the Spies had ever allowed to be published:
Math had stated that they had been feeling strange throughout the fourth season. Most of The Spies chalked this up to their overall wins declining; an imbalance in the numbers, some had said. But something wasn't adding up. Math had pitched against the odds in the past, but this season, it was like the percentages had been flipped on their heads. Math pushed Mathself in every game despite Math's clear discomfort. Math was spending more time with Son playing catch, and even gifted Son Math's gold-plated protractor; the same one Math had used the past 3+ seasons to predict opposing hits and calculate Math's own precise, baffling pitches. Blackburn was given Math's TI-84, the most expensive piece of computing technology Math could think of. Melon was pulled aside and spoken to, but as of yet has not commented on what Math told them. Donia Bailey was given a hug, the first she claims she's ever received.
After the Spies were put into party time, Math was nowhere to be found except during games. While festivities were held, Math was alone. Surprisingly, new Spies member Morrow was the first to comment that "something wasn't adding up" with Math, but was generally shot down with phrases from the team such as, "Math is Math," and "The numbers don't lie."
Then the postseason came, and the Tigers won the fourth season, and Math had reportedly been heard saying "I just wish the Talkers had accounted for the wind in the 11th." Math's vibes were stable, but the numbers on Math's face were looking more and more imaginary. Until finally, as all the ILB teams gathered to view the blessing and decree results, Math refused to join them. Instead, Math simply said the words, "I'll see you all again. You can count on it." The Spies all knew what was coming, and instead of viewing the results, stayed and sat with Math for Math's final hour. It all happened very quickly, according to eyewitness reports. There was a loud crunching sound, followed by a low hum and pop—and where Math stood, no two reports are the same on what took place.
Outside of one detail.
When New Math appeared, in Math's pitching hand, everyone claims to have seen a faint glimmer.
The glimmer of a star—a star that nobody even knew was there.
"Math was always a variable—but Math's love for the Spies was, and always will be, a constant."
Rumors that Velazquez was specifically targeted for a performance-enhancement Alternation by the ILB to prevent Velazquez from reaching a negative star rating have no supporting evidence and can be safely dismissed.