TauState isn't a worksheet with a timer. It's a complete training system: a mode for every mood, a lab for every configuration, and statistics that prove the work pays off.
Heads-up: the app's interface is available in 20 languages, but the learning content (math tricks, lexicon) is currently in German.
TauState is an intelligent mental-math training app for iPhone and iPad, built for anyone who wants sharper mental arithmetic. It offers 8 game modes and more than 40 operators, spanning the four basic operations, percentages, powers and roots, number theory, and number systems like binary, hexadecimal, and Roman numerals. Difficulty adapts automatically to the player's level, and a fully configurable Lab lets you build custom training sessions around exactly what you want to practise. TauState runs completely offline, with no accounts, no ads, and no tracking, and even its on-device speech recognition never leaves the phone. You can currently try it for free on TestFlight; it requires an iPhone or iPad running iOS 18 or later. This website is available in German, English, Spanish, and French, and the app's interface is available in 20 languages, with the learning content currently in German.
Play without end, until you stop. Ideal for warming up or for long, unhurried sessions with zero pressure.
A fixed number of problems, start to finish. You know exactly how long the round will take, so you can plan it on purpose.
The countdown is running. Do as much as you can before time runs out, every correct answer counts toward your high score.
A time limit per problem, no catching your breath in between. A hard, fast-paced workout for your head.
The time window per problem shrinks by 0.1 s with every correct answer, down to 1.2 s. How far can you get?
Memorise several problems and answer them with a delay, calculating while you keep them in your head.
The game ends after a set number of mistakes, and you decide how many are allowed. Here, staying calm beats rushing.
Build your own mode in the mode builder, from your own rules, time limits and operator combinations.
The Lab lets you shape every detail, operators, number ranges, modifiers. Or just press play and let adaptive difficulty meet you where you are. Every combination can be saved as its own preset and pulled back up any time, for the next run or for one specific weak spot.
Boss problems at the end for extra XP, Ghost Mode makes the task vanish, Mixed Keypad shuffles the keys, Upside-down flips everything 180°, or let chance pull 1–3 modifiers every round. Each modifier trains a different skill, from focus under pressure to spatial thinking when everything suddenly flips.
Accuracy, speed, stars and streaks, rendered in calm, readable charts. A weekly recap and an activity heatmap show the work paying off. No chart overload, just the numbers that actually show where you stand and how far you've come since day one.
A daily challenge, streaks worth protecting, and a heatmap that fills in as you practise, gentle structure that turns calculation into a habit you keep. Like training, consistency here beats the odd perfect run, ten quiet days add up to more than one flawless one.
Forty-plus operators across four worlds: basic arithmetic, advanced math, number theory and number systems. Start gentle, there's always another step up.
Basic arithmetic. Addition, subtraction, multiplication, division, the core where speed is built. This is where you train the automatic reflexes every other operator builds on, from single-digit sums to multi-digit multiplication in your head.
Advanced math. Powers, roots, logarithms, sine & friends, modulo, percentages, fractions, factorials, absolute values. A full toolkit for everything beyond grade school, built the way you'd know it from school or university.
Number theory. Primes, divisibility, digit sums, gcd & lcm, Fibonacci, square numbers. The discipline that shows numbers have their own patterns and rules, far beyond plain calculation.
Number systems. Binary, octal, hexadecimal, Roman, base-4, base-12, including conversion and arithmetic inside the system. Useful from computing fundamentals to a playful look at other ways of counting.
Just speak your answers, recognition runs entirely on the device, offline. Handy for hands-free training, or whenever typing just isn't practical.
The app senses where you are and keeps you right at the edge of growth. Not too easy, not frustrating, just the zone where real learning happens.
Operators, ranges, modifiers, build and save any training configuration. That's how you build your own presets for exactly the weak spot you're working on.
A fresh challenge every day, and a streak you won't want to break. A small, reliable anchor for daily practice.
Twelve ranks from Novice to Singularity. Every correct answer pays in, progress becomes visible without ever feeling forced.
66 trophy tiers across milestones, combos, streaks and mastery, five of them secret. Small side goals that spice up training without ever getting in the way.
Four sound themes, Standard, Retro, Subtle and Epic, plus finely tuned haptics. Or switch everything off and calculate in silence.
Your complete history as CSV or JSON, your data belongs to you. No vendor lock-in, you can take everything with you, any time.
Free on TestFlight. iPhone and iPad. Private by design.
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