1. How can we speak Math? Richard Fateman Computer Science
Univ. Calif, Berkeley
The Evolution of Mathematical Communication in the Age of Digital Libraries
December, 2006

2. Humans speaking math into computers
A primary input method
Correction of errors (secondary)
Simultaneous with handwriting, supportive of ambiguity resolution, error correction

3. The reverse: computers speaking math aloud
AsTeR (T.V. Raman) – for blind readers
Display-free communication (e.g. telephone)
Simultaneous with handwriting, supportive of ambiguity resolution, error correction

4. Ambiguity and Expectation
minus b plus or minus square root of b squared minus 4 a c divided by 2 a .
Without prior knowledge of this formula how could you know if the 4ac or even the 2a belongs within the square-root?
Could it be -b± b ^2 -4ac/2a ?
In Lisp, ambiguity is removed with one mechanism, parentheses/prefix
(/ (+ (- b) (sqrt (- (^ b 2) (* 4 a c))) (* 2 a))
(/ (+ (- b) (-(sqrt (- (^ b 2) (* 4 a c)))) (* 2 a))

5. Digression on math input/output
Written Math Output
TeX, other typesetting systems
Interactive systems with selection
MathML, other “notations”
Not entirely solved but good enough for most work
Written Math Input
Traditional keyboard
Menu selection
Handwriting
Mixture of above

6. Speaking math into computers
Why bother?
Speed. Compare
“bold italic gamma” γ
Convenience: Write with hand or mouse, modify with voice. Correction. Markup.
Keyboard-impaired users
Note: there is a trivial non-solution. Spell out G-A-M-M-A

7. Pick a subset of the problem. Numbers are easy, right?
1/10, 9/10/ 10/11
14/100, 14/10000
3/100, 300
34/100, 30/400
1-3,
7-4-6,
Pick a number from 1, 2, 10 .

8. OK, we can delimit the speaker’s flexibility on numbers. Then what?
Still problems
Homophones (sine, sin, sign)
Near Homophones (p,b,t)
Learning discrimination of ambiguous math
a(b+c)
f(b+c)
Bracketing []{}(), “The quantity … end quantity”

9. Looks tough
We believe it is not as tough as handwriting. Grammar-based tools are part of advanced speech recognition.
No special hardware (maybe cheap microphone, already used for Skype etc)
Combined with selection, menu, keyboarding, looks promising.

10. What next Continued development of tools and interfaces (Lisp, .net)
Relying on technology from other domains (fun, frustration)
Integration with Computer Algebra Systems, Math Browsers, Education projects, Disabled-access