Let’s Make a Game: Tabletop Part 4

Here’s the third homebrew player class that I’ve got working for the spire setting. It was a bit of a struggle to try and keep coming up with math-related effects that makes psuedosense in terms of how I’ve been thinking the magic/science works. My aim was to make a sort of spellcaster class with a little bit more utility than just blasting things away with fireballs. Kind of like the 4th edition D&D wizard with less forced movement effects. It’s ended up looking a little more combat oriented than I originally intended but hopefully a lot of that combat usability comes from its ability to make things super difficult for enemies to do things and then setting up for big slam dunks like the “prove impossible” proof. I also really loved the idea of a guerrilla wizard, using scrappy magic and science cobbled together to make reality shattering things happen. I also reworked the progression system a little bit by implementing a level requirement for picking the spells. It’ll work the same for the other classes with feats instead of proofs. It’s a bit more railroad-y, but I think there’s enough variation in the abilities relative to the size of the booklet I’m looking to make out of this. Getting really excited to playtest this again, along with a better encounter system and a bit more direction. Hope you enjoy!


Bend the world with logic and skill.


-A long lost art, once purely academic, that now presides as a reality-bending force of reason. Eschewing the dogma and zealous hypocrisy of the architects, the earliest mathematicians ignited a war for control of the tower. Utilizing high-casualty tactics mimicked from Primarch Augustus and their physics-shattering science, the Mathematicians shook the very foundations of the tower itself. Now, massacred and martyred, they are closely monitored by the Architects. Their existence only allowed by the grace and utility of their art in the construction of the tower and the extension of it’s influence over the ruins.

HP: 6 (plus a d4 each level after.)

At first level only: +1 to WIS or INT score.

Saves: Paralyze- 13, Poison-13, Breath-16, Device-,13 Magic-14.
Skill points: 3

Class Traits:

Booksmart: Mathematicians begin with the “Math” skill and with one trait from the quirks chart below. They also know how to speak and understand Binary or Old Numbers in addition to the common tongue. In addition to this, a mathematician is always able to…

  • Calculate the exact time by measuring the angle of the sun.
  • Figure out exact location with an accurate set of maps.
  • Count the exact quantity of something, given one full minute or less.
  • Memorize a series of digits after seeing them once. (digits only, i.e, no text or titles)
  • Recognize when Mathematics has been used to alter the world physically. (does not nullify illusory math.)

Number Cruncher: Once per short rest, the mathematician can take their knowledge of a situation and apply a simple formula to calculate the probability of a specific incident happening. You may the GM a five word question about a the likelihood of a situation playing out in a specific way (this includes asking whether someone may be lying, how much damage a character might take from an attack, etc.) They then make an intelligence check, with a DC set by the GM based on how plausible or ridiculous the chances of such a thing happening are. The GM does not notify the player if they passed this check. Requires a writing utensil and something to write on.

Civilized Slayers: A mathematician will not bat an eye at something being forcibly turned inside-out by a proof, but is likely to blanch at the sight of a blade wound or gunshot. Though there are many schools of thought, all mathematicians are uncomfortable with non-mathematics related tech and weaponry. They can bring themselves to use basic conveniences such as vehicles, elevators, and medical equipment, a mathematician will not use a weapon over math unless absolutely given no other option. As such, they take a -2 penalty to hit with non-minor melee weapons. However due to their intricate knowledge of force, vectors, and probability, they may spend up to two turns calculating their next attack will be. Each turn spend concentrating adds +2 to the subsequent hit roll, and +1 to the damage on that attack, should it succeed. (This is squibbly still. Need to rebalance or trash entirely)



Choose or roll for one.

  1. The mathematician perpetually has their nose in a book. If they do not have an academic text of some sort in their possession, they may become irritable, rash, or generally insufferable to be around.
  2. The mathematician is a megalomaniac. They either disguise this fact very well, or not at all.
  3. The mathematician has a debilitating fear of being wrong. If called out on a mistake they have made they may freeze up entirely or lash out in anger.
  4. The mathematician is blissfully ignorant of anything that goes on outside their own mind while they are concentrating on a problem. Once they begin to try and solve something, they cannot stop unless physically dragged away from it.
  5. The mathematician is a dedicated night owl. They generally volunteer for the night watch, but spend most of it reading or tinkering with formulas.
  6. The mathematician must carry with them some sort of “thinking trinket.” It can be as intricate or simplistic as the player wishes, but it must be small enough to fit in the palm of their hand. They fiddle with it while concentrating. If lost, they will despair until it is found or replaced.
  7. The mathematician occasionally speaks entirely in strings of cryptic nonsense letters and numbers to a transistor they carry with them.
  8. The mathematician has a terrible memory, and as such records literally everything they need to know in one way or another, i.e, proofs might be tattooed on their body, all documents filed neatly, or they may have a jumble of papers and scribblings only they can decipher. The method of this archival is up to the player.  



Instead of feats, mathematicians gain the use of proofs. Powerful theorems that affect the world around them in subtle or bombastic ways. Proofs can be used as often as the mathematician pleases, but are complex to cast, take total concentration and time, and can backfire if incorrectly cast. The necessary components for a proof can be bought at any outpost or town large enough to have a shop of oddities, unless specified by the proof. Mathematicians begin with one proof, and the components for them. Components are always consumed upon casting a proof. After this choose one new proof every level as you would a feat.

On level up, you may choose to take a +1 in the math skill instead of a proof up to two times.

Proof List

Level 0

Add – You may use your turn to increase the physical properties of a nonliving object smaller than you within 100 feet. This includes size, weight, or density. Increasing an object’s size also increases its weight respectively. This process cannot be undone by any means except subtraction. The mathematician is considered helpless during this time. Components/Requirements: One full round of concentration and equivalent mass carried by the mathematician in lead ball bearings or inventory items.

Human Antennae – Allows the caster to turn themselves into a receiver for frequencies on the airwaves. The mathematician prepares an equation circle, then enters a trance state. During this time they can tune into and pick up infrasound from sources within a twenty-mile radius. After the trance ends, the Mathematician will know the direction, general size, and distance of any settlements, vehicles, massive constructs, or large machinery of any other kind within the radius. Components/Requirements: A half-hour of total concentration, tinfoil headgear, chalk, incense.

Level 1

Subtract – Allows the mathematician to remove a portion of something from existence by annihilating another, equal amount of matter. To cast the proof, the mathematician focuses on two distinct piece of matter (solid or liquid only). They must be physically touching at least one of these objects. After a full round of concentration, the mathematician makes a math check. If successful, both pieces of matter are forcibly ripped out of existence. If part of the matter belongs to a living being, it gets to make a save vs magic. If the save is failed, it takes 1d10 of damage per cubic foot of matter being removed. The mathematician may only subtract 1 cubic foot of matter per level. Choosing this proof a second time allows the caster to subtract non-corporeal substances. This proof may also be used to reverse the effects of the“add” proof by making a successful math check. Upon a failed math check, the proof backfires. Roll on chart below for effect. Components/Requirements: One full round of concentration, and an inkwell of road tar/bag of chalk to mark the object for subtraction.

Machinespeak – Allows the mathematician to provide a voice to a digital system, computer, simple robot, or other electronic machine that otherwise cannot speak. Functions as “Bookspeak” but with electronic systems. Systems without perceptive ability such as doors or service robots will only be able to tell the mathematician when they were accessed or utilized. Archives can provide information about what they contain, if they are willing. Can be cast on anything that speaks binary as a translation spell, as well. Components/Requirements: One minute of concentration, a small transistor radio, and chalk.

Level 2

Imaginary numbers – Given ten minutes of total concentration, the mathematician can roll to construct an illusory effigy of a person that they can see. They may puppeteer up to five of these effigies at once, but doing anything more than walking requires a check for each illusion currently controlled. The illusions deal no damage and can only move 140 feet away from the mathematician before dissipating. The mathematician cannot move while channeling this spell and is considered helpless. Components/Requirements: two feet of fine metal wire, a vial of mud.

Sense Trajectory – The mathematician focuses their mind on the vector of an incoming ranged attack then makes a snap judgement on where it will fly, reacting with near-prescience to it’s exact location. After casting, the next targeted, non-AOE ranged attack made against the Mathematician triggers a math check as a response from the Mathematician. On a successful check, the attack misses. If the attack uses a tangible item the mathematician  may make a dexterity check to attempt to snatch the object from flight. The mathematician cannot move or speak while concentrating on this proof and is considered helpless to melee attackers. Components/Requirements: None.

Level 3

Ability Increase – Instead of choosing a proof, you may increase your INT or WIS score by 1.

Change Face Value – The mathematician may use math and a reflective face salve of insects to bend the light reflecting off their face into a different shape. This reflected face does not have to be human. The mathematician must have seen this face clearly to correctly conjure its image. On a successful math check, the proof lasts for up to six hours. Using another proof while disguised will nullify the effect. Components/Requirements: 15 minutes of total concentration, a small bottle of live reflective beetles.

Level 4

Multiply – Creates an exact copy of an object, with one notable defect as governed by the GM. Can also be cast on a willing or restrained/paralyzed being. Sentient copies behave exactly as the original would. A mathematician may only create one copy of a unique object or creature. If the copy and original make physical contact in any way, both will cease to exist. Picking this proof a second time allows the multiplication to yield two exact copies instead of one. Components/Requirements: Two hours of unbroken concentration polished silver mirror and chalk.

Divide – The mathematician cuts the fabric of reality to sunder an enemy or obstacle with deadly precision. Split something smaller than you exactly into halves, thirds, quarters, or eighths. This includes organic and inorganic matter. Make an unarmed melee attack and math check against the target. Inanimate objects only require a math check. Upon success, the object is divided exactly lengthwise or crosswise at the mathematician’s discretion. Living creatures are entitled to a save vs magic to avoid the splitting effect. Upon a failed math check, the proof backfires. Roll on chart below for effect. Components/Requirements: One scalpel sized metal blade prepared previously during a short rest.

Level 5

Fearful Symmetry – On a successful Math check, the mathematician throws a handful of carefully prearranged ultralight mirror shards. The shards reflect and twist the light near them to conjure the image of the unknowable and eldritch triangle-god. Any enemy who fails a save against magic must spend their next turn fleeing from the image however they can with no regard for life or limb. Anyone who fails the save and somehow is forced to look at the image for a turn must save against death or be split exactly in half. Upon a failed math check, the proof backfires. Roll on chart below for effect.  Components/Requirements: One prepared pouch of polished, reflective metal. Cannot be cast in darkness.

Double down – The mathematician increases their capability for/susceptibility to everything by a degree of two. While in this state they take and deal double damage, run twice as fast but get tired twice as easy, may jump twice as high but take twice as much damage from falls, and heal twice as fast but must eat twice as much. The mathematician may stay in this state for up to two days before having to revert back to their normal state for two cooldown days. The mathematician may end this state as an action. Components/Requirements: One hour of concentration, dark ink, feather pen, and 10 chips worth of parchment strips to wrap their arms and legs in.

Level 6

Probability Jaunt – The mathematician rips a geometric hole in spacetime and leaps through, teleporting next to a creature up to 30 feet away. On a successful math check this creature is a random ally within range, on a failed check this creature is a random enemy or neutral creature. The effect is instantaneous and takes the mathematician’s entire turn. Components/Requirements: A specially made glass polyhedron.

Prove Impossible – Through a series of complex calculations, the mathematician provides irrefutable physical and logical proof that something cannot exist. The reality of the target is shattered, and it disappears forever. The mathematician may attempt this proof against anything two levels below them, and up to one size larger than them. Upon a successful math check, a conscious target is allowed a save vs death. After a successful save, the target can never be proven impossible by the caster. After a failed save, the target ceases to exist entirely. Upon a failed math check, the proof backfires. Roll on chart below for effect. Components/Requirements: One round of total concentration and a strip of paper-thin gallium formed into a mobius strip or an iron penrose triangle heated to incandescence.

Backfired Proof Effects

  1. The intended effect of the proof is carried out randomly upon the caster or an object they carry.
  2. Mathematical fission occurs. Anything within 5 feet of them must save vs breath or take 1d6+1 damage. The mathematician does not get to roll this save.
  3. The proof changes permutations rapidly as its cast and swaps the positions of the mathematician and one random, similarly sized player, NPC, or creature within 300 feet.
  4. A random item in the mathematician’s inventory turns into thousands of useless, miniscule versions of that item.
  5. The mathematician forgets to carry a two and accidentally turns the proof into a stasis field. They are paralyzed until save ends.
  6. The proof expands rapidly out of control, it scrambles the speech center of the caster’s brain, rendering them mute for 1d4 hours.
  7. The intended effect of the proof is carried out upon one random creature, player, NPC or object they carry within sight.
  8. The proof fizzles with no adverse effects.

Images from The Phantom Tollbooth (illustrations by Jules Feiffer) and Shadowrun Returns concept art.

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