Topic

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A diagram of all knowledge topics.

Topics (also Tech or Innovations) are part of knowledge.

There are around 300 innovations that can be discovered. Many of them have requirements, and many do not, so it's kind of a tech forest/grassland rather than a tree. Notably missing are innovations related to practical labors in the game (which will be added later in development). Only the discovery of literary form topics has any effect on gameplay, as it allows scholars to write new types of books.

Several innovations require innovations from other branches, and since all knowledge is individually tracked, that implies some investigators will need to be at least well-read if not skilled in various topics (there aren't currently joint research projects). There are some old and new mechanisms in place to ensure this happens.

There are 9 "branches" of the knowledge system. Each branch is further divided into categories of topics, such as methodologies, theories, etc.

Discovering Topics

According to a Future of the Fortress reply:

Fortress scholars do activity cycles, the length of which is 1-2 days (whether they are pondering or discussing etc.) Once they get through 50 cycles, it rolls 0-50 vs. the number of completed cycles minus 50 to see if they get "breakthrough credit." So at 51, they have a 2% chance, and at 100, they have a 100% chance. Then, it resets the cycle number to zero and gives them breakthrough credit, based on a skill roll plus 100 (for discuss, the other researchers contribute half of their summed skill rolls.) Based on the difficulty (1-4) of the topic, total lifetime breakthrough credit is then assigned a number of 50-sided dice. An easy topic is dice=credit/2500, then /5000, then /10000, then /20000 for level 4 topics. The number of dice cannot exceed 10. Then roll these dice -- if you get a 50 on any of them, discovery! This is a bit archaic, and I'm not suggesting it works particularly well. But that is how it works. Also: if they fail to get the breakthrough after the 50-sided rolls, they have a 2% chance of switching topics, or if their credit exceeds 100000, they always switch topics (though they keep the credit, so returning to the topic later gives them a decent chance at breakthrough.)

For unskilled roles, some initial back-of-the-envelope calculations and some rough estimates observed through dfHack gives a basic idea of just how long research can take. Note that player testing had found that the skill roll contributes a lot to the breakthrough credit. Even dabbling dwarves can gain over 2000 breakthrough credit at once and may average around 1000 breakthrough credit. Additionally the formula for the skill roll seems to have a very large spread, players have reported as low as 3000 breakthrough credit and as high as 25000 breakthrough credit awarded to a dwarf with legendary skill. Analytically calculating from the algorithm Toady gave, it takes an average of 58.54 cycles to get a breakthrough credit. Player testing has confirmed breakthrough credits typically take 55-65 cycles, so this calculation seems plausible. Likewise, player testing has not shown any correlation between skill level and number of cycles to get breakthrough credit. An unskilled dwarf might average around 120+ cycles to get their first breakthrough die for a level 1 topic. With only a single research die, it would take an average of 2528 cycles to get a breakthrough. Pondering takes slightly over 2 days per cycle, so this would be around 14 years. In a real fortress, the research dice and skill level will be increasing during the process. However, in a real fortress, the scholars will also need to take breaks to eat, drink, and meet other needs. A more reasonable estimate is around 5-10 years for a breakthrough starting with no skills. In short, research takes an unreasonably long time with an unskilled dwarf.

To optimize for research, there are several ideas worth considering. Discussion is faster, taking only a single day, but requires at least 2 dwarves. Player testing has found discussion also awards more XP, (0-5 for pondering vs. 15-30 for discussion). So to optimize research, dwarves should be separated by topic/skill, with unskilled dwarves paired with skilled dwarves. This way, discussions will be equally divided between increasing the skilled dwarf's cycle count and the unskilled dwarf's cycle count. Only half the cycles will go to the skilled dwarf's cycle count, but discussion only takes a single day, so this is at net the same speed for the skilled dwarf with the additional bonus of the unskilled dwarf's cycle count also being increased. Both dwarves benefit from the increased XP gain.

Note that several topics benefit from skills that can be trained through faster means. Diagnostician and Wound Dresser can be trained through intentionally causing injuries or simply engaging in dangerous activities that require regular dwarf healthcare. Organizer can be trained through assigning make work to the manager, or Mechanic can be trained by spamming the creation of mechanisms. Skill level will increase much faster through these activities than through pondering or discussion. Thus, to optimize for producing breakthroughs in engineering topics, mechanics could first be quickly trained to a legendary within a year or two at only the cost of the stones for the mechanisms, and then assigned as a scholar.

Player testing has also found that visitors can come with research credits already done, thus, for forts aiming to maximize research, it makes sense to prioritize attracting wandering scholars.

Astronomy

These topics are relevant to astronomers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Empirical observation	Methods of empirical observation in astronomy	Empirical evidence	Method	Astronomer
Path models	The method of forming precise models for the paths of astronomical objects	Orbit modeling	Method	Astronomer
Astrography	The creation of star charts	Star chart	n/a	Astronomer, Record keeper
Dates of lunar and solar eclipses	The dates of lunar and solar eclipses	Saros (astronomy)	n/a	Astronomer, Record keeper
Daylight variation with solar year	The variation of daylight with the seasons	Daytime § Daytime variations with latitude and seasons	n/a	Astronomer
Geocentrism	The theory that the sun moves around the world	Geocentric model	n/a	Astronomer
Height of tides vs moon and sun	The height of the tides, the moon and the sun	Pytheas § Pytheas on the tides and Tide	n/a	Astronomer
Heliocentrism	The theory that the world moves around the sun	Heliocentric model	n/a	Astronomer
Path of the moon	The path of the moon	Orbit of the Moon	n/a	Astronomer
Phases of the moon	The phases of the moon	Lunar phase	n/a	Astronomer
Precession of equinoxes	The precession of equinoxes over great periods of time	Axial precession	n/a	Astronomer, Record keeper
Relationship between lunar/solar year	The relationship between the lunar and solar year	Lunisolar calendar	n/a	Astronomer, Record keeper
Shape of the world	The shape of the world	Spherical Earth	n/a	Astronomer
Star catalogues 100	The compilation of information about stars	Star catalogue	n/a	Astronomer, Record keeper
Star catalogues 1000	The precise compilation of information about stars	Star catalogue	n/a	Astronomer, Record keeper
Star magnitude classification	The classification of stars according to brightness	Magnitude (astronomy)	n/a	Astronomer, Record keeper
Stellar Spectroscopy	The classification of stars according to color	Astronomical spectroscopy	n/a	Astronomer, Record keeper
Summer/winter moon	The rise of the moon according to the season	Lunar calendar	n/a	Astronomer
Summer/winter sun	The rise of the sun according to the season	Solar calendar	n/a	Astronomer
Tides and the moon	The relationship between the moon and the tides	Seleucus of Seleucia § Tides and Tide	n/a	Astronomer

Chemistry

These topics are relevant to chemists.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Adhesives	The preparation and use of adhesive materials	Adhesive	Chemicals	Chemist
Aqua regia	The preparation of aqua regia	Aqua regia	Chemicals	Chemist
Oil of vitriol	The preparation of oil of vitriol	Sulfuric acid	Chemicals	Chemist
Spirit of niter	The preparation of spirit of niter	Nitric acid	Chemicals	Chemist
Alkali and acids	The classification of alkali and acids	pH	Classification	Chemist, Record keeper
Combustibles	The classification of combustible materials	Combustibility	Classification	Chemist, Record keeper
Elemental theory	The classification of materials based on which elemental materials might form them	Classical element or Atomic theory	Classification	Chemist
Ores	The classification of ores	Ore	Classification	Chemist
Scratch test	A method of classifying the hardness of materials by scratching them against each other	Scratch hardness	Classification	Chemist, Record keeper
Alembic	The construction and use of the alembic	Alembic	Laboratory	Chemist
Blast furnace	The construction and use of the blast furnace	Blast furnace	Laboratory	Chemist
Crucible	The construction and use of the crucible	Crucible	Laboratory	Chemist
Lab ovens	The construction and use of laboratory ovens	Laboratory oven	Laboratory	Chemist
Systematic experiments	Methods for performing experiments systematically in the laboratory	Scientific method	Laboratory	Chemist, Record keeper
Theory of distillation	The theory and methods involved in distillation	Distillation	Laboratory	Chemist
Theory of evaporation	The theory and methods involved in evaporation	Evaporation	Laboratory	Chemist
Theory of liquid-liquid extraction	The theory and methods involved in the extraction of a constituent liquid from one solution to another	Liquid–liq